Al-Khwarizmi was born in the epicentre of an Islamic empire which then stretched from the Mediterranean to India. This was a very fortuitous time for Arabic learning. The rulers of the Abbasid dynasty who were leading this huge empire, founded an academy in Baghdad called the House of Wisdom where the learned men collected and translated all the scientific works that they could get hold of. House of Wisdom had a large library – first famous library established after the library of Alexandria was destroyed.

Al-Khwarizmi was one of the learned men who worked in the House of Wisdom. His interests lied in the fields of algebra, geometry, astronomy and geography. His now most famous work is that from which we got the name for algebra itself – Hisab al-jabr w’al-muqabala.

Abu Ja’far Muḥammad ibn Musa al-Khwarizmi (c. 780, Khwarizm – c. 850) was a Persian mathematician, astronomer, and geographer, who worked most of his life as a scholar in the House of Wisdom in Baghdad.

His Algebra was the first book on the systematic solution of linear and quadratic equations. Consequently he is considered to be the father of algebra, a title he shares with Diophantus. Latin translations of his Arithmetic, on the Indian numerals, introduced the decimal positional number system to the Western world in the twelfth century. He revised and updated Ptolemy’s Geography as well as writing several works on astronomy and astrology.

His contributions not only made a great impact on mathematics, but on language as well. The word algebra is derived from al-jabr, one of the two operations used to solve quadratic equations, as described in his book. The words algorism and algorithm stem from Algoritmi, the Latinization of his name. His name is also the origin of the Spanish word guarismo and of the Portuguese word algarismo, both meaning digit.

Life

Few details about al-Khwarizmi’s life are known; it is not even certain where he was born. His name indicates he might have come from Khwarezm (Khiva), then part of Greater Khorasan, which at that time was part of the Persian Empire (the eastern part of the territory of Persia), now Xorazm Province of Uzbekistan. Abu Rayhan Biruni (a native Chorasmian) explicitly states: “The people of Khwarizm are a branch of the Persian tree”.

The historian Tabari gave his name as Muhammad ibn Musa al-Khwarizmi al-Majousi al-Katarbali (Arabic: محمد بن موسى الخوارزميّ المجوسـيّ القطربّـليّ). The epithet al-Qutrubbulli indicates he might instead have come from Qutrubbull, a small town near Baghdad. However, Rashed points out that:

There is no need to be an expert on the period or a philologist to see that al-Tabari’s second citation should read “Muhammad ibn Musa al-Khwarizmi and al-Majusi al-Qutrubbulli,” and that there are two people (al-Khwarizmi and al-Majusi al-Qutrubbulli) between whom the letter wa [Arabic ‘و' for the article ‘and'] has been omitted in an early copy. This would not be worth mentioning if a series of errors concerning the personality of al-Khwarizmi, occasionally even the origins of his knowledge, had not been made. Recently, G. J. Toomer with naive confidence constructed an entire fantasy on the error which cannot be denied the merit of amusing the reader.

Regarding al-Khwarizmi’s religion, Toomer writes:

Another epithet given to him by al-Ṭabari, “al-Majusi,” would seem to indicate that he was an adherent of the old Zoroastrian religion. This would still have been possible at that time for a man of Iranian origin, but the pious preface to al-Khwarizmi’s Algebra shows that he was an orthodox Muslim, so al-Ṭabari’s epithet could mean no more than that his forebears, and perhaps he in his youth, had been Zoroastrians.

In Ibn al-Nadim’s Kitab al-Fihrist we find a short biography on al-Khwarizmi, together with a list of the books he wrote. Al-Khwarizmi accomplished most of his work in the period between 813 and 833. After the Islamic conquest of Persia, Baghdad became the centre of scientific studies and trade, and many merchants and scientists from as far as China and India traveled to this city-as such apparently so did Al-Khwarizmi. He worked in Baghdad as a scholar at the House of Wisdom established by Caliph al-Maʾmun, where he studied the sciences and mathematics, which included the translation of Greek and Sanskrit scientific manuscripts.

Contributions

His major contributions to mathematics, astronomy, astrology, geography and cartography provided foundations for later and even more widespread innovation in algebra, trigonometry, and his other areas of interest. His systematic and logical approach to solving linear and quadratic equations gave shape to the discipline of algebra, a word that is derived from the name of his 830 book in the Arabic language on the subject, al-Kitab al-mukhtasar fi hisab al-jabr wa’l-muqabala (Arabic الكتاب المختصر في حساب الجبر والمقابلة) or: “The Compendious Book on Calculation by Completion and Balancing”. The book was first translated into Latin in the twelfth century.

His book On the Calculation with Hindu Numerals written about 825, was principally responsible for the diffusion of the Indian system of numeration in the Middle-East and then Europe. This book also translated into Latin in the twelfth century, as Algoritmi de numero Indorum. From the name of the author, rendered in Latin as algoritmi, originated the term algorithm.

Some of his contributions were based on earlier Persian and Babylonian Astronomy, Indian numbers, and Greek sources.

Al-Khwarizmi systematized and corrected Ptolemy’s data in geography as regards to Africa and the Middle east. Another major book was his Kitab surat al-ard (“The Image of the Earth”; translated as Geography), which presented the coordinates of localities in the known world based, ultimately, on those in the Geography of Ptolemy but with improved values for the length of the Mediterranean Sea and the location of cities in Asia and Africa.

He also assisted in the construction of a world map for the caliph al-Ma’mun and participated in a project to determine the circumference of the Earth, supervising the work of 70 geographers to create the map of the then “known world”.

When his work was copied and transferred to Europe through Latin translations, it had a profound impact on the advancement of basic mathematics in Europe. He also wrote on mechanical devices like the astrolabe and sundial.

Algebra

A page from al-Khwarizmi’s algebra

Al-Kitab al-mukhtaṣar fi ḥisab al-jabr wa-l-muqabala (Arabic: الكتاب المختصر في حساب الجبر والمقابلة “The Compendious Book on Calculation by Completion and Balancing”) is a mathematical book written approximately 830 CE. The term algebra is derived from the name of one of the basic operations with equations (al-jabr) described in this book. The book was translated in Latin as Liber algebrae et almucabala by Robert of Chester (Segovia, 1145) hence “algebra”, and also by Gerard of Cremona. A unique Arabic copy is kept at Oxford and was translated in 1831 by F. Rosen. A Latin translation is kept in Cambridge.

The al-jabr is considered the foundational text of modern algebra. It provided an exhaustive account of solving polynomial equations up to the second degree, and introduced the fundamental methods of “reduction” and “balancing”, referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation.

Al-Khwarizmi’s method of solving linear and quadratic equations worked by first reducing the equation to one of six standard forms (where b and c are positive integers)

• squares equal roots (ax² = bx)
• squares equal number (ax² = c)
• roots equal number (bx = c)
• squares and roots equal number (ax² + bx = c)
• squares and number equal roots (ax² + c = bx)
• roots and number equal squares (bx + c = ax²)

by dividing out the coefficient of the square and using the two operations al-ǧabr (Arabic: الجبر “restoring” or “completion”) and al-muqabala (“balancing”). Al-ǧabr is the process of removing negative units, roots and squares from the equation by adding the same quantity to each side. For example, x² = 40x − 4x² is reduced to 5x² = 40x. Al-muqabala is the process of bringing quantities of the same type to the same side of the equation. For example, x² + 14 = x + 5 is reduced to x² + 9 = x.

Several authors have also published texts under the name of Kitab al-ğabr wa-l-muqabala, including Abu Ḥanifa al-Dinawari, Abu Kamil Shuja ibn Aslam, Abu Muḥammad al-ʿAdli, Abu Yusuf al-Miṣṣiṣi, ‘Abd al-Hamid ibn Turk, Sind ibn ʿAli, Sahl ibn Bišr, and Šarafaddin al-Ṭusi.

J. J. O’Conner and E. F. Robertson wrote in the MacTutor History of Mathematics archive:

“Perhaps one of the most significant advances made by Arabic mathematics began at this time with the work of al-Khwarizmi, namely the beginnings of algebra. It is important to understand just how significant this new idea was. It was a revolutionary move away from the Greek concept of mathematics which was essentially geometry. Algebra was a unifying theory which allowed rational numbers, irrational numbers, geometrical magnitudes, etc., to all be treated as “algebraic objects”. It gave mathematics a whole new development path so much broader in concept to that which had existed before, and provided a vehicle for future development of the subject. Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before.”

R. Rashed and Angela Armstrong write:

“Al-Khwarizmi’s text can be seen to be distinct not only from the Babylonian tablets, but also from Diophantus’ Arithmetica. It no longer concerns a series of problems to be resolved, but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study. On the other hand, the idea of an equation for its own sake appears from the beginning and, one could say, in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems.”

Page from a Latin translation, beginning with “Dixit algorizmi”

Arithmetic

Al-Khwarizmi’s second major work was on the subject of arithmetic, which survived in a Latin translation but was lost in the original Arabic. The translation was most likely done in the twelfth century by Adelard of Bath, who had also translated the astronomical tables in 1126.

The Latin manuscripts are untitled, but are commonly referred to by the first two words with which they start: Dixit algorizmi (“So said al-Khwarizmi”), or Algoritmi de numero Indorum (“al-Khwarizmi on the Hindu Art of Reckoning”), a name given to the work by Baldassarre Boncompagni in 1857. The original Arabic title was possibly Kitab al-Jamʿ wa-l-tafriq bi-ḥisab al-Hind(“The Book of Addition and Subtraction According to the Hindu Calculation”)

Al-Khwarizmi’s work on arithmetic was responsible for introducing the Arabic numerals, based on the Hindu-Arabic numeral system developed in Indian mathematics, to the Western world. The term “algorithm” is derived from the algorism, the technique of performing arithmetic with Hindu-Arabic numerals developed by al-Khwarizmi. Both “algorithm” and “algorism” are derived from the Latinized forms of al-Khwarizmi’s name, Algoritmi and Algorismi, respectively.

Astronomy

Corpus Christi College MS 283

Al-Khwarizmi’s Zij al-Sindhind (Arabic: زيج “astronomical tables of Sind and Hind”) is a work consisting of approximately 37 chapters on calendrical and astronomical calculations and 116 tables with calendrical, astronomical and astrological data, as well as a table of sine values. This is the first of many Arabic Zijes based on the Indian astronomical methods known as the sindhind. The work contains tables for the movements of the sun, the moon and the five planets known at the time. This work marked the turning point in Islamic astronomy. Hitherto, Muslim astronomers had adopted a primarily research approach to the field, translating works of others and learning already discovered knowledge. Al-Khwarizmi’s work marked the beginning of non-traditional methods of study and calculations.

The original Arabic version (written c. 820) is lost, but a version by the Spanish astronomer Maslamah Ibn Ahmad al-Majriti (c. 1000) has survived in a Latin translation, presumably by Adelard of Bath (January 26, 1126). The four surviving manuscripts of the Latin translation are kept at the Bibliothèque publique (Chartres), the Bibliothèque Mazarine (Paris), the Bibliotheca Nacional (Madrid) and the Bodleian Library (Oxford).

Al-Khwarizmi made several important improvements to the theory and construction of sundials, which he inherited from his Indian and Hellenistic predecessors. He made tables for these instruments which considerably shortened the time needed to make specific calculations. His sundial was universal and could be observed from anywhere on the Earth. From then on, sundials were frequently placed on mosques to determine the time of prayer. The shadow square, an instrument used to determine the linear height of an object, in conjunction with the alidade for angular observations, was also invented by al-Khwarizmi in ninth-century Baghdad.

The first quadrants and mural instruments were invented by al-Khwarizmi in ninth century Baghdad. The sine quadrant, invented by al-Khwarizmi, was used for astronomical calculations. The first horary quadrant for specific latitudes, was also invented by al-Khwarizmi in Baghdad, then center of the development of quadrants. It was used to determine time (especially the times of prayer) by observations of the Sun or stars. The Quadrans Vetus was a universal horary quadrant, an ingenious mathematical device invented by al-Khwarizmi in the ninth century and later known as the Quadrans Vetus (Old Quadrant) in medieval Europe from the thirteenth century. It could be used for any latitude on Earth and at any time of the year to determine the time in hours from the altitude of the Sun. This was the second most widely used astronomical instrument during the Middle Ages after the astrolabe. One of its main purposes in the Islamic world was to determine the times of Salah.

Geography

Hubert Daunicht’s reconstruction of al-Khwarizmi’s planisphere.

Al-Khwarizmi’s third major work is his Kitab ṣurat al-Arḍ (Arabic: كتاب صورة الأرض “Book on the appearance of the Earth” or “The image of the Earth” translated as Geography), which was finished in 833. It is a revised and completed version of Ptolemy’s Geography, consisting of a list of 2402 coordinates of cities and other geographical features following a general introduction.

There is only one surviving copy of Kitab ṣurat al-Arḍ, which is kept at the Strasbourg University Library. A Latin translation is kept at the Biblioteca Nacional de España in Madrid. The complete title translates as Book of the appearance of the Earth, with its cities, mountains, seas, all the islands and rivers, written by Abu Ja’far Muhammad ibn Musa al-Khwarizmi, according to the geographical treatise written by Ptolemy the Claudian.

The book opens with the list of latitudes and longitudes, in order of “weather zones”, that is to say in blocks of latitudes and, in each weather zone, by order of longitude. As Paul Gallez points out, this excellent system allows us to deduce many latitudes and longitudes where the only document in our possession is in such a bad condition as to make it practically illegible.

Neither the Arabic copy nor the Latin translation include the map of the world itself, however Hubert Daunicht was able to reconstruct the missing map from the list of coordinates. Daunicht read the latitudes and longitudes of the coastal points in the manuscript, or deduces them from the context where they were not legible. He transferred the points onto graph paper and connected them with straight lines, obtaining an approximation of the coastline as it was on the original map. He then does the same for the rivers and towns.

Al-Khwarizmi corrected Ptolemy’s gross overestimate for the length of the Mediterranean Sea^[30] (from the Canary Islands to the eastern shores of the Mediterranean); Ptolemy overestimated it at 63 degrees of longitude, while al-Khwarizmi almost correctly estimated it at nearly 50 degrees of longitude. He “also depicted the Atlantic and Indian Oceans as open bodies of water, not land-locked seas as Ptolemy had done.” Al-Khwarizmi thus set the Prime Meridian of the Old World at the eastern shore of the Mediterranean, 10-13 degrees to the east of Alexandria (the prime meridian previously set by Ptolemy) and 70 degrees to the west of Baghdad. Most medieval Muslim geographers continued to use al-Khwarizmi’s prime meridian.

Jewish calendar

Al-Khwarizmi wrote several other works including a treatise on the Hebrew calendar (Risala fi istikhraj taʾrikh al-yahud “Extraction of the Jewish Era”). It describes the 19-year intercalation cycle, the rules for determining on what day of the week the first day of the month Tishri shall fall; calculates the interval between the Jewish era (creation of Adam) and the Seleucid era; and gives rules for determining the mean longitude of the sun and the moon using the Jewish calendar. Similar material is found in the works of al-Biruni and Maimonides.

Other works

Several Arabic manuscripts in Berlin, Istanbul, Tashkent, Cairo and Paris contain further material that surely or with some probability comes from al-Khwarizmi. The Istanbul manuscript contains a paper on sundials, which is mentioned in the Fihirst. Other papers, such as one on the determination of the direction of Mecca, are on the spherical astronomy.

Two texts deserve special interest on the morning width (Maʿrifat saʿat al-mashriq fi kull balad) and the determination of the azimuth from a height (Maʿrifat al-samt min qibal al-irtifaʿ).

He also wrote two books on using and constructing astrolabes. Ibn al-Nadim in his Kitab al-Fihrist (an index of Arabic books) also mentions Kitab ar-Ruḵama(t) (the book on sundials) and Kitab al-Tarikh (the book of history) but the two have been lost.The shaping of our mathematics can be attributed to Al-Khwarizmi (c.780-c.850), the chief librarian of the observatory, research center and library called the House of Wisdom in Baghdad. His treatise, “Hisab al-jabr w’al-muqabala” (Calculation by Restoration and Reduction), which covers linear and quadratic equations, solved trade imbalances, inheritance questions and problems arising from land surveyance and allocation. In passing, he also introduced into common usage our present numerical system, which replaced the old, cumbersome Roman one.

Italian mathematician and philosopher, considered to be the first woman in the Western world to have achieved a reputation in mathematics.

Maria Gaetana Agnesi (May 16, 1718 – January 9, 1799) was an Italian linguist, mathematician, and philosopher. Agnesi is credited with writing the first book discussing both differential and integral calculus. She was an honorary member of the faculty at the University of Bologna. According to Dirk Jan Struik, Agnesi is “the first important woman mathematician since Hypatia (fifth century A.D.)”.

Early life

Her father, Pietro, was a wealthy man of business and a professor of mathematics at the University of Bologna who desired to elevate his family into the Milanese nobility.

Having been born in Milan, Maria was recognized as a child prodigy very early; she could speak both French and Italian at five years of age. By her eleventh birthday she had acquired Greek, Hebrew, Spanish, German, Latin, and was referred to as the “Walking Polyglot”. She even educated her younger brothers. When she was 9 years old, she composed and delivered an hour-long speech in Latin to an academic gathering. The subject was women’s right to be educated. When she was fifteen, her father began to regularly gather in his house a circle of the most learned men in Bologna, before whom she read and maintained a series of theses on the most abstruse philosophical questions. Records of these meetings are given in Charles de Brosses’ Lettres sur l’Italie and in the Propositiones Philosophicae, which her father had published in 1738. These displays, being probably not altogether congenial to Maria (who wanted to retire) ceased by her twentieth year because she strongly desired to enter a convent at that time. Although her father refused to grant this wish, he agreed to let her live from that time on in an almost conventual semi-retirement, avoiding all interactions with society and devoting herself entirely to the study of mathematics. During that time, Maria studied both differential and integral calculus. Pietro Agnesi also married twice more after Maria’s mother died, so that Maria Agnesi ended up the eldest of 21 children. In addition to her performances and lessons, her responsibility was to teach her siblings. This task kept her from her own goal of entering a convent. Scholars thought she was dazzingly beautiful and hers was recognized as one of the richest noble families in Milan.

Contributions to mathematics

Instituzioni analitiche

First page of Instituzioni analitiche (1748)

The most valuable result of her labours was the Instituzioni analitiche ad uso della gioventu italiana, a work of great merit, which was published at Milan in 1748 and “was regarded as the best introduction extant to the works of Euler.” The first volume treats of the analysis of finite quantities and the second of the analysis of infinitesimals. A French translation of the second volume by P. T. d’Antelmy, with additions by Charles Bossut (1730-1814), appeared at Paris in 1775; and an English translation of the whole work by John Colson (1680-1760), the Lucasian Professor of Mathematics at Cambridge, “inspected” by John Hellins, was published in 1801 at the expense of Baron Maseres.

Witch of Agnesi

Madame Agnesi also wrote a commentary on the Traite analytique des sections coniques du marquis de l’Hôpital, which, though highly praised by those who saw it in manuscript, was never published. She discussed the curve known as the “witch of Agnesi” or “versiera” as she named it in 1748. The name derives from the Italian for the rope that turns a sail, taken from the Latin vertere, versus meaning “to turn,” which was the term used by Luigi Grandi before her. Colson, who translated Agnesi’s text to English, perhaps confused “la versiera” with “l’avversiera”, and so mistranslated it as “she-devil” or “the witch”, with the result that English-speakers and, for some reason, Spanish speakers from Mexico, Cuba, and Spain, know the curve as the “Witch of Agnesi” (La Bruja de Agnesi).). Struik mentions that:

The word [versiera] is derived from Latin vertere, to turn, but is also an abbreviation of Italian avversiera, female devil. Some wit in England once translated it ‘witch’, and the silly pun is still lovingly preserved in most of our textbooks in English language. The curve had already appeared in the writings of Fermat (Oeuvres, I, 279-280; III, 233-234) and of others; the name versiera is from Guido Grandi (Quadratura circuli et hyperbolae, Pisa, 1703). The curve is type 63 in Newton’s classification. The first to use the term ‘witch’ in this sense may have been B. Williamson, Integral calculus, 7 (1875), 173; see Oxford English Dictionary.

Agnesi’s diploma from Università di Bologna

Examples of the curve are those given by the equations:

where a is any non-zero constant. The equation:

is the simplest among these.

English physicist and mathematician who was born into a poor farming family. Luckily for humanity, Newton was not a good farmer, and was sent to Cambridge to study to become a preacher. At Cambridge, Newton studied mathematics, being especially strongly influenced by Euclid, although he was also influenced by Baconian and Cartesian philosophies. Newton was forced to leave Cambridge when it was closed because of the plague, and it was during this period that he made some of his most significant discoveries. With the reticence he was to show later in life, Newton did not, however, publish his results.

Sir Isaac Newton, FRS (4 January 1643 - 31 March 1727 was an English physicist, mathematician, astronomer, natural philosopher, alchemist, theologian and one of the most influential men in human history. His Philosophiae Naturalis Principia Mathematica, published in 1687, is considered to be the most influential book in the history of science. In this work, Newton described universal gravitation and the three laws of motion, laying the groundwork for classical mechanics, which dominated the scientific view of the physical universe for the next three centuries and is the basis for modern engineering. Newton showed that the motions of objects on Earth and of celestial bodies are governed by the same set of natural laws by demonstrating the consistency between Kepler’s laws of planetary motion and his theory of gravitation, thus removing the last doubts about heliocentrism and advancing the scientific revolution.
In mechanics, Newton enunciated the principles of conservation of momentum and angular momentum. In optics, he built the first “practical” reflecting telescope^[6] and developed a theory of colour based on the observation that a prism decomposes white light into a visible spectrum. He also formulated an empirical law of cooling and studied the speed of sound.

In mathematics, Newton shares the credit with Gottfried Leibniz for the development of the differential and integral calculus. He also demonstrated the generalised binomial theorem, developed the so-called “Newton’s method” for approximating the zeroes of a function, and contributed to the study of power series.

Newton was also highly religious (though unorthodox), producing more work on Biblical hermeneutics than the natural science he is remembered for today.

Newton’s stature among scientists remains at the very top rank, as demonstrated by a 2005 survey of scientists in Britain’s Royal Society asking who had the greater effect on the history of science, Newton was deemed much more influential than Albert Einstein.

Biography

Early years

Isaac Newton was born on 4 January 1643  at Woolsthorpe Manor in Woolsthorpe-by-Colsterworth, a hamlet in the county of Lincolnshire. At the time of Newton’s birth, England had not adopted the latest papal calendar and therefore his date of birth was recorded as Christmas Day, 25 December 1642. Newton was born three months after the death of his father. Born prematurely, he was a small child; his mother Hannah Ayscough reportedly said that he could have fit inside a quart mug. When Newton was three, his mother remarried and went to live with her new husband, the Reverend Barnabus Smith, leaving her son in the care of his maternal grandmother, Margery Ayscough. The young Isaac disliked his stepfather and held some enmity towards his mother for marrying him, as revealed by this entry in a list of sins committed up to the age of 19: Threatening my father and mother Smith to burn them and the house over them.

According to E.T. Bell and H. Eves:

Newton began his schooling in the village schools and was later sent to The King’s School, Grantham, where he became the top student in the school. At King’s, he lodged with the local apothecary, William Clarke and eventually became engaged to the apothecary’s stepdaughter, Anne Storer, before he went off to the University of Cambridge at the age of 19. As Newton became engrossed in his studies, the romance cooled and Miss Storer married someone else. It is said he kept a warm memory of this love, but Newton had no other recorded “sweet-hearts” and never married.

There are rumours that he remained a confirmed celibate. However, Bell and Eves’ sources for this claim, William Stukeley and Mrs. Vincent (the former Miss Storer - actually named Katherine, not Anne), merely say that Newton entertained “a passion” for Storer while he lodged at the Clarke house.

From the age of about twelve until he was seventeen, Newton was educated at The King’s School, Grantham (where his signature can still be seen upon a library window sill). He was removed from school, and by October 1659, he was to be found at Woolsthorpe-by-Colsterworth, where his mother, widowed by now for a second time, attempted to make a farmer of him. He hated farming. Henry Stokes, master at the King’s School, persuaded his mother to send him back to school so that he might complete his education. This he did at the age of eighteen, achieving an admirable final report.

In June 1661, he was admitted to Trinity College, Cambridge. According to John Stillwell, he entered Trinity as a sizar.^[11] At that time, the college’s teachings were based on those of Aristotle, but Newton preferred to read the more advanced ideas of modern philosophers such as Descartes and astronomers such as Copernicus, Galileo, and Kepler. In 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that would later become infinitesimal calculus. Soon after Newton had obtained his degree in August of 1665, the University closed down as a precaution against the Great Plague. Although he had been undistinguished as a Cambridge student, Newton’s private studies at his home in Woolsthorpe over the subsequent two years saw the development of his theories on calculus, optics and the law of gravitation.

Middle years

Mathematics

Most modern historians believe that Newton and Leibniz developed infinitesimal calculus independently, using their own unique notations. According to Newton’s inner circle, Newton had worked out his method years before Leibniz, yet he published almost nothing about it until 1693, and did not give a full account until 1704. Meanwhile, Leibniz began publishing a full account of his methods in 1684. Moreover, Leibniz’s notation and “differential Method” were universally adopted on the Continent, and after 1820 or so, in the British Empire. Whereas Leibniz’s notebooks show the advancement of the ideas from early stages until maturity, there is only the end product in Newton’s known notes. Newton claimed that he had been reluctant to publish his calculus because he feared being mocked for it. Newton had a very close relationship with Swiss mathematician Nicolas Fatio de Duillier, who from the beginning was impressed by Newton’s gravitational theory. In 1691 Duillier planned to prepare a new version of Newton’s Philosophiae Naturalis Principia Mathematica, but never finished it. However, in 1694 the relationship between the two men changed. At the time, Duillier had also exchanged several letters with Leibniz^{[citation needed]}.

Starting in 1699, other members of the Royal Society (of which Newton was a member) accused Leibniz of plagiarism, and the dispute broke out in full force in 1711. Newton’s Royal Society proclaimed in a study that it was Newton who was the true discoverer and labeled Leibniz a fraud. This study was cast into doubt when it was later found that Newton himself wrote the study’s concluding remarks on Leibniz. Thus began the bitter Newton v. Leibniz calculus controversy, which marred the lives of both Newton and Leibniz until the latter’s death in 1716.

Newton is generally credited with the generalised binomial theorem, valid for any exponent. He discovered Newton’s identities, Newton’s method, classified cubic plane curves (polynomials of degree three in two variables), made substantial contributions to the theory of finite differences, and was the first to use fractional indices and to employ coordinate geometry to derive solutions to Diophantine equations. He approximated partial sums of the harmonic series by logarithms (a precursor to Euler’s summation formula), and was the first to use power series with confidence and to revert power series. He also discovered a new formula for calculating pi.

He was elected Lucasian Professor of Mathematics in 1669. In that day, any fellow of Cambridge or Oxford had to be an ordained Anglican priest. However, the terms of the Lucasian professorship required that the holder not be active in the church (presumably so as to have more time for science). Newton argued that this should exempt him from the ordination requirement, and Charles II, whose permission was needed, accepted this argument. Thus a conflict between Newton’s religious views and Anglican orthodoxy was averted.

Optics

From 1670 to 1672, Newton lectured on optics. During this period he investigated the refraction of light, demonstrating that a prism could decompose white light into a spectrum of colours, and that a lens and a second prism could recompose the multicoloured spectrum into white light.

He also showed that the coloured light does not change its properties by separating out a coloured beam and shining it on various objects. Newton noted that regardless of whether it was reflected or scattered or transmitted, it stayed the same colour. Thus, he observed that colour is the result of objects interacting with already-coloured light rather than objects generating the colour themselves. This is known as Newton’s theory of colour.

A replica of Newton’s 6-inch (150 mm) reflecting telescope of 1672 for the Royal Society

From this work he concluded that any refracting telescope would suffer from the dispersion of light into colours (chromatic aberration), and invented a type reflecting telescope (today known as a Newtonian telescope) to bypass that problem. By grinding his own mirrors, using Newton’s rings to judge the quality of the optics for his telescopes, he was able to produce a superior instrument to the refracting telescope, due primarily to the wider diameter of the mirror. In 1671 the Royal Society asked for a demonstration of his reflecting telescope. Their interest encouraged him to publish his notes On Colour, which he later expanded into his Opticks. When Robert Hooke criticised some of Newton’s ideas, Newton was so offended that he withdrew from public debate. The two men remained enemies until Hooke’s death.

Newton argued that light is composed of particles or corpuscles, which were refracted by accelerating toward the denser medium, but he had to associate them with waves to explain the diffraction of light (Opticks Bk. II, Props. XII-L). Later physicists instead favoured a purely wavelike explanation of light to account for diffraction. Today’s quantum mechanics, photons and the idea of wave-particle duality bear only a minor resemblance to Newton’s understanding of light.

In his Hypothesis of Light of 1675, Newton posited the existence of the ether to transmit forces between particles. The contact with the theosophist Henry More, revived his interest in alchemy. He replaced the ether with occult forces based on Hermetic ideas of attraction and repulsion between particles. John Maynard Keynes, who acquired many of Newton’s writings on alchemy, stated that “Newton was not the first of the age of reason: he was the last of the magicians.” Newton’s interest in alchemy cannot be isolated from his contributions to science. (This was at a time when there was no clear distinction between alchemy and science.) Had he not relied on the occult idea of action at a distance, across a vacuum, he might not have developed his theory of gravity. (See also Isaac Newton’s occult studies.)

In 1704 Newton published Opticks, in which he expounded his corpuscular theory of light. He considered light to be made up of extremely subtle corpuscles, that ordinary matter was made of grosser corpuscles and speculated that through a kind of alchemical transmutation “Are not gross Bodies and Light convertible into one another, …and may not Bodies receive much of their Activity from the Particles of Light which enter their Composition?” Newton also constructed a primitive form of a frictional electrostatic generator, using a glass globe (Optics, 8th Query).

Mechanics and gravitation

Newton’s own copy of his Principia, with hand-written corrections for the second edition

In 1677, Newton returned to his work on mechanics, i.e., gravitation and its effect on the orbits of planets, with reference to Kepler’s laws of planetary motion, and consulting with Hooke and Flamsteed on the subject. He published his results in De motu corporum in gyrum (1684). This contained the beginnings of the laws of motion that would inform the Principia.

The Philosophiae Naturalis Principia Mathematica (now known as the Principia) was published on 5 July 1687 with encouragement and financial help from Edmond Halley. In this work Newton stated the three universal laws of motion that were not to be improved upon for more than two hundred years. He used the Latin word gravitas (weight) for the effect that would become known as gravity, and defined the law of universal gravitation. In the same work he presented the first analytical determination, based on Boyle’s law, of the speed of sound in air. Newton’s postulate of an invisible force able to act over vast distances led to him being criticised for introducing “occult agencies” into science^.

With the Principia, Newton became internationally recognised. He acquired a circle of admirers, including the Swiss-born mathematician Nicolas Fatio de Duillier, with whom he formed an intense relationship that lasted until 1693. The end of this friendship led Newton to a nervous breakdown.^{[clarification needed][citation needed]}

Later life

In the 1690s, Newton wrote a number of religious tracts dealing with the literal interpretation of the Bible. Henry More’s belief in the universe and rejection of Cartesian dualism may have influenced Newton’s religious ideas. A manuscript he sent to John Locke in which he disputed the existence of the Trinity was never published. Later works - The Chronology of Ancient Kingdoms Amended (1728) and Observations Upon the Prophecies of Daniel and the Apocalypse of St. John (1733) - were published after his death. He also devoted a great deal of time to alchemy (see above).

Newton was also a member of the Parliament of England from 1689 to 1690 and in 1701, but his only recorded comments were to complain about a cold draught in the chamber and request that the window be closed.

Newton moved to London to take up the post of warden of the Royal Mint in 1696, a position that he had obtained through the patronage of Charles Montagu, 1st Earl of Halifax, then Chancellor of the Exchequer. He took charge of England’s great recoining, somewhat treading on the toes of Master Lucas (and securing the job of deputy comptroller of the temporary Chester branch for Edmond Halley). Newton became perhaps the best-known Master of the Mint upon Lucas’ death in 1699, a position Newton held until his death. These appointments were intended as sinecures, but Newton took them seriously, retiring from his Cambridge duties in 1701, and exercising his power to reform the currency and punish clippers and counterfeiters. As Master of the Mint in 1717 Newton unofficially moved the Pound Sterling from the silver standard to the gold standard by creating a relationship between gold coins and the silver penny in the “Law of Queen Anne”; these were all great reforms at the time, adding considerably to the wealth and stability of England. It was his work at the Mint, rather than his earlier contributions to science, that earned him a knighthood from Queen Anne in 1705.

Newton was made President of the Royal Society in 1703 and an associate of the French Academie des Sciences. In his position at the Royal Society, Newton made an enemy of John Flamsteed, the Astronomer Royal, by prematurely publishing Flamsteed’s star catalogue, which Newton had used in his studies.

Newton died in London on 31 March 1727 and was buried in Westminster Abbey. His half-niece, Catherine Barton Conduitt, served as his hostess in social affairs at his house on Jermyn Street in London; he was her “very loving Uncle,” according to his letter to her when she was recovering from smallpox. Although Newton, who had no children, had divested much of his estate onto relatives in his last years, he actually died intestate.

After his death, Newton’s body was discovered to have had massive amounts of mercury in it, probably resulting from his alchemical pursuits. Mercury poisoning could explain Newton’s eccentricity in late life.

Religious views

Historian Stephen D. Snobelen says of Newton, “Isaac Newton was a heretic. But like Nicodemus, the secret disciple of Jesus, he never made a public declaration of his private faith – which the orthodox would have deemed extremely radical. He hid his faith so well that scholars are still unravelling his personal beliefs.”Snobelen concludes that Newton was at least a Socinian sympathiser (he owned and had thoroughly read at least eight Socinian books), possibly an Arian and almost certainly an antitrinitarian. In an age notable for its religious intolerance there are few public expressions of Newton’s radical views, most notably his refusal to take holy orders and his refusal, on his death bed, to take the sacrament when it was offered to him.

In a view disputed by Snobelen, T.C. Pfizenmaier argues that Newton held the Eastern Orthodox view of the Trinity rather than the Western one held by Roman Catholics, Anglicans, and most Protestants.^[21] In his own day, he was also accused of being a Rosicrucian (as were many in the Royal Society and in the court of Charles II).

Although the laws of motion and universal gravitation became Newton’s best-known discoveries, he warned against using them to view the universe as a mere machine, as if akin to a great clock. He said, “Gravity explains the motions of the planets, but it cannot explain who set the planets in motion. God governs all things and knows all that is or can be done.”

His scientific fame notwithstanding, Newton’s studies of the Bible and of the early Church Fathers were also noteworthy. Newton wrote works on textual criticism, most notably An Historical Account of Two Notable Corruptions of Scripture. He also placed the crucifixion of Jesus Christ at 3 April, AD 33, which agrees with one traditionally accepted date. He also attempted, unsuccessfully, to find hidden messages within the Bible.

In his own lifetime, Newton wrote more on religion than he did on natural science. He believed in a rationally immanent world, but he rejected the hylozoism implicit in Leibniz and Baruch Spinoza. Thus, the ordered and dynamically informed universe could be understood, and must be understood, by an active reason, but this universe, to be perfect and ordained, had to be regular.

Newton’s effect on religious thought

Newton and Robert Boyle’s mechanical philosophy was promoted by rationalist pamphleteers as a viable alternative to the pantheists and enthusiasts, and was accepted hesitantly by orthodox preachers as well as dissident preachers like the latitudinarians.^[25] Thus, the clarity and simplicity of science was seen as a way to combat the emotional and metaphysical superlatives of both superstitious enthusiasm and the threat of atheism, and, at the same time, the second wave of English deists used Newton’s discoveries to demonstrate the possibility of a “Natural Religion.”

The attacks made against pre-Enlightenment “magical thinking,” and the mystical elements of Christianity, were given their foundation with Boyle’s mechanical conception of the universe. Newton gave Boyle’s ideas their completion through mathematical proofs and, perhaps more importantly, was very successful in popularising them. Newton refashioned the world governed by an interventionist God into a world crafted by a God that designs along rational and universal principles. These principles were available for all people to discover, allowed people to pursue their own aims fruitfully in this life, not the next, and to perfect themselves with their own rational powers.

Newton saw God as the master creator whose existence could not be denied in the face of the grandeur of all creation. But the unforeseen theological consequence of his conception of God, as Leibniz pointed out, was that God was now entirely removed from the world’s affairs, since the need for intervention would only evidence some imperfection in God’s creation, something impossible for a perfect and omnipotent creator. Leibniz’s theodicy cleared God from the responsibility for “l’origine du mal” by making God removed from participation in his creation. The understanding of the world was now brought down to the level of simple human reason, and humans, as Odo Marquard argued, became responsible for the correction and elimination of evil.

On the other hand, latitudinarian and Newtonian ideas taken too far resulted in the millenarians, a religious faction dedicated to the concept of a mechanical universe, but finding in it the same enthusiasm and mysticism that the Enlightenment had fought so hard to extinguish.

Views of the end of the world

In a manuscript he wrote in 1704 in which he describes his attempts to extract scientific information from the Bible, he estimated that the world would end no earlier than 2060. In predicting this he said, “This I mention not to assert when the time of the end shall be, but to put a stop to the rash conjectures of fanciful men who are frequently predicting the time of the end, and by doing so bring the sacred prophesies into discredit as often as their predictions fail.”

Newton and the counterfeiters

As warden of the Royal Mint, Newton estimated that 20% of the coins taken in during The Great Recoinage were counterfeit. Counterfeiting was high treason, punishable by being hanged, drawn and quartered. Despite this, convictions of the most flagrant criminals could be extremely difficult to achieve; however, Newton proved to be equal to the task.

Disguised as an habitue of bars and taverns, he gathered much of that evidence himself. For all the barriers placed to prosecution, and separating the branches of government, English law still had ancient and formidable customs of authority. Newton was made a justice of the peace and between June 1698 and Christmas 1699 conducted some 200 cross-examinations of witnesses, informers and suspects. Newton won his convictions and in February 1699, he had ten prisoners waiting to be executed.

Possibly Newton’s greatest triumph as the king’s attorney was against William Chaloner. One of Chaloner’s schemes was to set up phony conspiracies of Catholics and then turn in the hapless conspirators whom he entrapped. Chaloner made himself rich enough to posture as a gentleman. Petitioning Parliament, Chaloner accused the Mint of providing tools to counterfeiters (a charge also made by others). He proposed that he be allowed to inspect the Mint’s processes in order to improve them. He petitioned Parliament to adopt his plans for a coinage that could not be counterfeited, while at the same time striking false coins. Newton was outraged, and went about the work to uncover anything about Chaloner. During his studies, he found that Chaloner was engaged in counterfeiting. He immediately put Chaloner on trial, but Chaloner had friends in high places and, to Newton’s horror, Chaloner walked free. Newton put him on trial a second time with conclusive evidence. Chaloner was convicted of high treason and hanged, drawn and quartered on 23 March 1699 at Tyburn gallows.

Enlightenment philosophers

Enlightenment philosophers chose a short history of scientific predecessors-Galileo, Boyle, and Newton principally-as the guides and guarantors of their applications of the singular concept of Nature and Natural Law to every physical and social field of the day. In this respect, the lessons of history and the social structures built upon it could be discarded.

It was Newton’s conception of the universe based upon Natural and rationally understandable laws that became the seed for Enlightenment ideology. Locke and Voltaire applied concepts of Natural Law to political systems advocating intrinsic rights; the physiocrats and Adam Smith applied Natural conceptions of psychology and self-interest to economic systems and the sociologists criticised the current social order for trying to fit history into Natural models of progress. Monboddo and Samuel Clarke resisted elements of Newton’s work, but eventually rationalised it to conform with their strong religious views of nature.

Newton’s laws of motion

Classical mechanics

Newton’s Second Law

The famous three laws of motion:

Newton’s First Law (also known as the Law of Inertia) states that an object at rest tends to stay at rest and that an object in uniform motion tends to stay in uniform motion unless acted upon by a net external force.

Newton’s Second Law states that an applied force, , on an object equals the rate of change of its momentum, , with time. Mathematically, this is expressed as

Because this relation only holds when the mass is constant, that is, when , the first term vanishes, and the equation can be written in the iconic form

where

This equation states that a force applied to an object of mass m causes it to accelerate at a rate .

This equality requires a consistent set of units for measuring mass, length, and time. One such set is the SI system, where mass is in kilograms, length in metres, and time in seconds. This leads to force being in newtons, named in his honour, and acceleration in metres per second per second. The English analogous system is slugs, feet, and seconds.

Newton’s Third Law states that for every action there is an equal and opposite reaction. This means that any force exerted onto an object has a counterpart force that is exerted in the opposite direction back onto the first object. The most common example is of two ice skaters pushing against each other and sliding apart in opposite directions. Another example is the recoil of a firearm, in which the force propelling the bullet is exerted equally back onto the gun and is felt by the shooter. Since the objects in question do not necessarily have the same mass, the resulting acceleration of the two objects can be different (as in the case of firearm recoil).

Newton’s apple

Reputed descendants of Newton’s apple tree, at the Botanic Gardens in Cambridge and the Instituto Balseiro library garden

Newton himself often told that story that he was inspired to formulate his theory of gravitation by watching the fall of an apple from a tree. It fell straight down–why was that, he asked?

Cartoons have gone further to suggest the apple actually hit Newton’s head, and that its impact somehow made him aware of the force of gravity. We know from his notebooks that Newton was grappling in the late 1660s with the idea that terrestrial gravity extends, in an inverse-square proportion, to the Moon; however it took him two decades to develop the full-fledged theory. John Conduitt, Newton’s assistant at the Royal Mint and husband of Newton’s niece, described the event when he wrote about Newton’s life:

The question was not whether gravity existed, but whether it extended so far from Earth that it could also be the force holding the moon to its orbit. Newton showed that if the force decreased as the inverse square of the distance, one could indeed calculate the Moon’s orbital period, and get good agreement. He guessed the same force was responsible for other orbital motions, and hence named it “universal gravitation”.

A contemporary writer, William Stukeley, recorded in his Memoirs of Sir Isaac Newton’s Life a conversation with Newton in Kensington on 15 April 1726, in which Newton recalled “when formerly, the notion of gravitation came into his mind. It was occasioned by the fall of an apple, as he sat in contemplative mood. Why should that apple always descend perpendicularly to the ground, thought he to himself. Why should it not go sideways or upwards, but constantly to the earth’s centre.” In similar terms, Voltaire wrote in his Essay on Epic Poetry (1727), “Sir Isaac Newton walking in his gardens, had the first thought of his system of gravitation, upon seeing an apple falling from a tree.” These accounts are probably exaggerations of Newton’s own tale about sitting by a window in his home (Woolsthorpe Manor) and watching an apple fall from a tree.

Various trees are claimed to be “the” apple tree which Newton describes. The King’s School, Grantham, claims that the tree was purchased by the school, uprooted and transported to the headmaster’s garden some years later, the staff of the [now] National Trust-owned Woolsthorpe Manor dispute this, and claim that a tree present in their gardens is the one described by Newton. A descendant of the original tree can be seen growing outside the main gate of Trinity College, Cambridge, below the room Newton lived in when he studied there. The National Fruit Collection at Brogdale can supply grafts from their tree (ref 1948-729), which appears identical to Flower of Kent, a coarse-fleshed cooking variety^{[clarification needed]}.

Writings by Newton

• Method of Fluxions (1671)
• Of Natures Obvious Laws & Processes in Vegetation (unpublished, c. 1671-75)
• De Motu Corporum in Gyrum (1684)
• Philosophiae Naturalis Principia Mathematica (1687)
• Opticks (1704)
• Reports as Master of the Mint (1701-25)
• Arithmetica Universalis (1707)
• The System of the World, Optical Lectures, The Chronology of Ancient Kingdoms, (Amended) and De mundi systemate (published posthumously in 1728)
• Observations on Daniel and The Apocalypse of St. John (1733)
• An Historical Account of Two Notable Corruptions of Scripture (1754)

Fame

French mathematician Joseph-Louis Lagrange often said that Newton was the greatest genius who ever lived, and once added that he was also “the most fortunate, for we cannot find more than once a system of the world to establish.” English poet Alexander Pope was moved by Newton’s accomplishments to write the famous epitaph:

Newton himself was rather more modest of his own achievements, famously writing in a letter to Robert Hooke in February 1676

Historians generally think the above quote was an attack on Hooke (who was short and hunchbacked), rather than - or in addition to - a statement of modesty. The two were in a dispute over optical discoveries at the time. The latter interpretation also fits with many of his other disputes over his discoveries - such as the question of who discovered calculus as discussed above.

And then in a memoir later

Newton in popular culture

Newton is an important character in The Baroque Cycle by Neal Stephenson. A major theme of these novels is the emergence of modern science, with Newton’s work in the Principia being prominent. Newton’s interest in alchemy and the dispute over the discovery of calculus are prominent plot points, and there is a (fictional) debate on metaphysics between Newton and Gottfried Leibniz moderated by Caroline of Ansbach. The development of an economy based on money and credit is also a major theme, with Newton’s time with the Royal Mint and intrigues against counterfeit leading to a Trial of the Pyx.

In 2007, David Warner portrayed Newton in the Doctor Who audio drama Circular Time.

Monuments and commemoration

Newton’s monument (1731) can be seen in Westminster Abbey, at the north of the entrance to the choir against the choir screen. It was executed by the sculptor Michael Rysbrack (1694-1770) in white and grey marble with design by the architect William Kent (1685-1748). The monument features a figure of Newton reclining on top of a sarcophagus, his right elbow resting on several of his great books and his left hand pointing to a scroll with a mathematical design. Above him is a pyramid and a celestial globe showing the signs of the Zodiac and the path of the comet of 1680. A relief panel depicts putti using instruments such as a telescope and prism. The Latin inscription on the base translates as:

A statue of Isaac Newton, standing over an apple, can be seen at the Oxford University Museum of Natural History.

From 1978 until 1988, an image of Newton designed by Harry Ecclestone appeared on Series D £1 banknotes issued by the Bank of England (the last £1 notes to be issued by the Bank of England). Newton was shown on the reverse of the notes holding a book and accompanied by a telescope, a prism and a map of the Solar System.

Biographical knowledge

Little is known about Euclid other than his writings. What biographical information we do have comes largely from commentaries by Proclus and Pappus of Alexandria. Euclid was active at the great Library of Alexandria and may have studied at Plato’s Academy in Greece. The date and place of Euclid’s birth and the date and circumstances of his death are unknown.

Some writers in the Middle Ages confused him with Euclid of Megara, a Greek Socratic philosopher who lived approximately one century earlier.

The Elements

Although many of the results in Elements originated with earlier mathematicians, one of Euclid’s accomplishments was to present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis of mathematics 23 centuries later.

Although best-known for its geometric results, the Elements also includes number theory. It considers the connection between perfect numbers and Mersenne primes, the infinitude of prime numbers, Euclid’s lemma on factorization (which leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations), and the Euclidean algorithm for finding the greatest common divisor of two numbers.

The geometrical system described in the Elements was long known simply as geometry, and was considered to be the only geometry possible. Today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called Non-Euclidean geometries that mathematicians discovered in the 19th century.

Other works

In addition to the Elements, at least five works of Euclid have survived to the present day.

• Data deals with the nature and implications of “given” information in geometrical problems; the subject matter is closely related to the first four books of the Elements.
• On Divisions of Figures, which survives only partially in Arabic translation, concerns the division of geometrical figures into two or more equal parts or into parts in given ratios. It is similar to a third century AD work by Heron of Alexandria.
• Catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. The attribution to Euclid is doubtful. Its author may have been Theon of Alexandria.
• Phaenomena is a treatise on spherical Astronomy, it survives in Greek and is quite similar to “On the Moving Sphere”, by Autolycus of Pitane, who flourished around 310 BC.
• Optics is the earliest surviving Greek treatise on perspective. In its definitions Euclid follows the Platonic tradition that vision is caused by discrete rays which emanate from the eye. One important definition is the fourth: “Things seen under a greater angle appear greater, and those under a lesser angle less, while those under equal angles appear equal.” In the 36 propositions that follow, Euclid relates the apparent size of an object to its distance from the eye and investigates the apparent shapes of cylinders and cones when viewed from different angles. Proposition 45 is interesting, proving that for any two unequal magnitudes, there is a point from which the two appear equal. Pappus believed these results to be important in astronomy and included Euclid’s Optics, along with his Phaenomena, in the Little Astronomy, a compendium of smaller works to be studied before the Syntaxis (Almagest) of Claudius Ptolemy.

All of these works follow the basic logical structure of the Elements, containing definitions and proved propositions.

There are also works credibly attributed to Euclid which have been lost.

• Conics was a work on conic sections that was later extended by Apollonius of Perga into his famous work on the subject. It is likely that the first four books of Apollonius’s work come directly from Euclid. According to Pappus, “Apollonius, having completed Euclid’s four books of conics and added four others, handed down eight volumes of conics.” The Conics of Apollonius quickly supplanted the former work, and by the time of Pappus, Euclid’s work was already lost.
• Porisms might have been an outgrowth of Euclid’s work with conic sections, but the exact meaning of the title is controversial.
• Pseudaria, or Book of Fallacies, was an elementary text about errors in reasoning.
• Surface Loci concerned either loci (sets of points) on surfaces or loci which were themselves surfaces; under the latter interpretation, it has been hypothesized that the work might have dealt with quadric surfaces.
• Several works on mechanics are attributed to Euclid by Arabic sources. On the Heavy and the Light contains, in nine definitions and five propositions, Aristotelian notions of moving bodies and the concept of specific gravity. On the Balance treats the theory of the lever in a similarly Euclidean manner, containing one definition, two axioms, and four propositions. A third fragment, on the circles described by the ends of a moving lever, contains four propositions. These three works complement each other in such a way that it has been suggested that they are remnants of a single treatise on mechanics written by Euclid.

Galileo Galilei (15 February 1564 – 8 January 1642) was a Tuscan (Italian) physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations, and support for Copernicanism. Galileo has been called the “father of modern observational astronomy”, the “father of modern physics“, the “father of science“, and “the Father of Modern Science.” The motion of uniformly accelerated objects, taught in nearly all high school and introductory college physics courses, was studied by Galileo as the subject of kinematics. His contributions to observational astronomy include the telescopic confirmation of the phases of Venus, the discovery of the four largest satellites of Jupiter, named the Galilean moons in his honour, and the observation and analysis of sunspots. Galileo also worked in applied science and technology, improving compass design.

Galileo’s championing of Copernicanism was controversial within his lifetime. The geocentric view had been dominant since the time of Aristotle, and the controversy engendered by Galileo’s presentation of heliocentrism as proven fact resulted in the Catholic Church’s prohibiting its advocacy as empirically proven fact, because it was not empirically proven at the time and was contrary to the literal meaning of Scripture. Galileo was eventually forced to recant his heliocentrism and spent the last years of his life under house arrest on orders of the Roman Inquisition.

Life

Galileo was born in Pisa (then part of the Grand Duchy of Tuscany), the first of six children of Vincenzo Galilei, a famous lutenist and music theorist, and Giulia Ammannati. Of the six children four survived infancy, and the youngest Michelangelo (or Michelagnolo) became a noted lutenist and composer. Galileo’s full name was Galileo Bonaiuti de’ Galilei. At the age of 8, his family moved to Florence, but he was left with Jacopo Borghini for two years. He then was educated in the Camaldolese Monastery at Vallombrosa, 21 mi (34 km) southeast of Florence. Although he seriously considered the priesthood as a young man, he enrolled for a medical degree at the University of Pisa at his father’s urging. He did not complete this degree, but instead studied mathematics. In 1589, he was appointed to the chair of mathematics in Pisa. In 1591 his father died and he was entrusted with the care of his younger brother Michelagnolo. In 1592, he moved to the University of Padua, teaching geometry, mechanics, and astronomy until 1610. During this period Galileo made significant discoveries in both pure science (for example, kinematics of motion, and astronomy) and applied science (for example, strength of materials, improvement of the telescope). His multiple interests included the study of astrology, which in pre-modern disciplinary practice was seen as correlated to the studies of mathematics and astronomy.

Although a devout Roman Catholic, Galileo fathered three children out of wedlock with Marina Gamba. They had two daughters, Virginia in 1600 and Livia in 1601, and one son, Vincenzio, in 1606. Because of their illegitimate birth, their father considered the girls unmarriageable. Their only worthy alternative was the religious life. Both girls were sent to the convent of San Matteo in Arcetri and remained there for the rest of their lives. Virginia took the name Maria Celeste upon entering the convent. She died on 2 April 1634, and is buried with Galileo at the Basilica di Santa Croce di Firenze. Livia took the name Sister Arcangela and was ill for most of her life. Vincenzio was later legitimized and married Sestilia Bocchineri.

In 1610 Galileo published an account of his telescopic observations of the moons of Jupiter, using this observation to argue in favor of the sun-centered, Copernican theory of the universe against the dominant earth-centered Ptolemaic and Aristotelian theories. The next year Galileo visited Rome in order to demonstrate his telescope to the influential philosophers and mathematicians of the Jesuit Collegio Romano, and to let them see with their own eyes the reality of the four moons of Jupiter. While in Rome he was also made a member of the Accademia dei Lincei.

In 1612, opposition arose to the Sun-centered theory of the universe which Galileo supported. In 1614, from the pulpit of Santa Maria Novella, Father Tommaso Caccini (1574-1648) denounced Galileo’s opinions on the motion of the Earth, judging them dangerous and close to heresy. Galileo went to Rome to defend himself against these accusations, but, in 1616, Cardinal Roberto Bellarmino personally handed Galileo an admonition enjoining him neither to advocate nor teach Copernican astronomy. During 1621 and 1622 Galileo wrote his first book, The Assayer (Il Saggiatore), which was approved and published in 1623. In 1630, he returned to Rome to apply for a license to print the Dialogue Concerning the Two Chief World Systems, published in Florence in 1632. In October of that year, however, he was ordered to appear before the Holy Office in Rome.

Following a papal trial in which he was found vehemently suspect of heresy, Galileo was placed under house arrest and his movements restricted by the Pope. From 1634 onward he stayed at his country house at Arcetri, outside of Florence. He went completely blind in 1638 and was suffering from a painful hernia and insomnia, so he was permitted to travel to Florence for medical advice. He continued to receive visitors until 1642, when, after suffering fever and heart palpitations, he died^.

Scientific methods

Galileo made original contributions to the science of motion through an innovative combination of experiment and mathematics^. More typical of science at the time were the qualitative studies of William Gilbert, on magnetism and electricity. Galileo’s father, Vincenzo Galilei, a lutenist and music theorist, had performed experiments establishing perhaps the oldest known non-linear relation in physics: for a stretched string, the pitch varies as the square root of the tension. These observations lay within the framework of the Pythagorean tradition of music, well-known to instrument makers, which included the fact that subdividing a string by a whole number produces a harmonious scale. Thus, a limited amount of mathematics had long related music and physical science, and young Galileo could see his own father’s observations expand on that tradition.

Galileo is perhaps the first to clearly state that the laws of nature are mathematical. In The Assayer he wrote “Philosophy is written in this grand book, the universe … It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures; …”^. His mathematical analyses are a further development of a tradition employed by late scholastic natural philosophers, which Galileo learned when he studied philosophy. Although he tried to remain loyal to the Catholic Church, his adherence to experimental results, and their most honest interpretation, led to a rejection of blind allegiance to authority, both philosophical and religious, in matters of science. In broader terms, this aided to separate science from both philosophy and religion; a major development in human thought.

By the standards of his time, Galileo was often willing to change his views in accordance with observation. Philosopher of science Paul Feyerabend also noted the supposedly improper aspects of Galileo’s methodology, but he argued that Galileo’s methods could be justified retroactively by their results. The bulk of Feyerabend’s major work, Against Method (1975), was devoted to an analysis of Galileo, using his astronomical research as a case study to support Feyerabend’s own anarchistic theory of scientific method. As he put it: ‘Aristotelians demanded strong empirical support while the Galileans were content with far-reaching, unsupported and partially refuted theories. I do not criticize them for that; on the contrary, I favour Niels Bohr’s “this is not crazy enough.”‘ In order to perform his experiments, Galileo had to set up standards of length and time, so that measurements made on different days and in different laboratories could be compared in a reproducible fashion.

Galileo showed a remarkably modern appreciation for the proper relationship between mathematics, theoretical physics, and experimental physics. He understood the parabola, both in terms of conic sections and in terms of the ordinate (y) varying as the square of the abscissa (x). Galilei further asserted that the parabola was the theoretically ideal trajectory of a uniformly accelerated projectile in the absence of friction and other disturbances. He conceded that there are limits to the validity of this theory, noting on theoretical grounds that a projectile trajectory of a size comparable to that of the Earth could not possibly be a parabola,^[24] but he nevertheless maintained that for distances up to the range of the artillery of his day, the deviation of a projectile’s trajectory from a parabola would only be very slight^. Thirdly, he recognized that his experimental data would never agree exactly with any theoretical or mathematical form, because of the imprecision of measurement, irreducible friction, and other factors.

According to Stephen Hawking, Galileo probably bears more of the responsibility for the birth of modern science than anybody else, and Albert Einstein called him the father of modern science.

Astronomy

Contributions

The phases of Venus, observed by Galileo in 1610

Based only on uncertain descriptions of the telescope, invented in the Netherlands in 1608, Galileo, in the following year, made a telescope with about 3x magnification, and later made others with up to about 30x magnification. With this improved device he could see magnified, upright images on the earth - it was what is now known as a terrestrial telescope, or spyglass. He could also use it to observe the sky; for a time he was one of those who could construct telescopes good enough for that purpose. On 25 August 1609, he demonstrated his first telescope to Venetian lawmakers. His work on the device made for a profitable sideline with merchants who found it useful for their shipping businesses and trading issues. He published his initial telescopic astronomical observations in March 1610 in a short treatise entitled Sidereus Nuncius (Starry Messenger).

On 7 January 1610 Galileo observed with his telescope what he described at the time as “three fixed stars, totally invisible by their smallness”, all within a short distance of Jupiter, and lying on a straight line through it. Observations on subsequent nights showed that the positions of these “stars” relative to Jupiter were changing in a way that would have been inexplicable if they had really been fixed stars. On 10 January Galileo noted that one of them had disappeared, an observation which he attributed to its being hidden behind Jupiter. Within a few days he concluded that they were orbiting Jupiter: He had discovered three of Jupiter’s four largest satellites (moons): Io, Europa, and Callisto. He discovered the fourth, Ganymede, on 13 January. Galileo named the four satellites he had discovered Medicean stars, in honour of his future patron, Cosimo II de’ Medici, Grand Duke of Tuscany, and Cosimo’s three brothers. Later astronomers, however, renamed them Galilean satellites in honour of Galileo himself.

A planet with smaller planets orbiting it did not conform to the principles of Aristotelian Cosmology, which held that all heavenly bodies should circle the Earth, and many astronomers and philosophers initially refused to believe that Galileo could have discovered such a thing.

Galileo continued to observe the satellites over the next eighteen months, and by mid 1611 he had obtained remarkably accurate estimates for their periods-a feat which Kepler had believed impossible.

From September 1610, Galileo observed that Venus exhibited a full set of phases similar to that of the Moon. The heliocentric model of the solar system developed by Nicolaus Copernicus predicted that all phases would be visible since the orbit of Venus around the Sun would cause its illuminated hemisphere to face the Earth when it was on the opposite side of the Sun and to face away from the Earth when it was on the Earth-side of the Sun. In contrast, the geocentric model of Ptolemy predicted that only crescent and new phases would be seen, since Venus was thought to remain between the Sun and Earth during its orbit around the Earth. Galileo’s observations of the phases of Venus proved that it orbited the Sun and lent support to (but did not prove) the heliocentric model. However, since it refuted the Ptolemaic pure geocentric planetary model, it seems it was the crucial observation that caused the 17th century majority conversion of the scientific community to geoheliocentric geocentric models such as the Tychonic and Capellan models, and was thereby arguably Galileo’s historically most important astronomical observation.

Galileo also observed the planet Saturn, and at first mistook its rings for planets, thinking it was a three-bodied system. When he observed the planet later, Saturn’s rings were directly oriented at Earth, causing him to think that two of the bodies had disappeared. The rings reappeared when he observed the planet in 1616, further confusing him.

Galileo was one of the first Europeans to observe sunspots, although Kepler had unwittingly observed one in 1607, but mistook it for a transit of Mercury.. He also reinterpreted a sunspot observation from the time of Charlemagne, which formerly had been attributed (impossibly) to a transit of Mercury. The very existence of sunspots showed another difficulty with the unchanging perfection of the heavens posited by orthodox Aristotelian celestial physics, but their regular periodic transits also confirmed the dramatic novel prediction of Kepler’s Aristotelian celestial dynamics in his 1609 Astronomia Nova that the sun rotates, which was the first successful novel prediction of post-spherist celestial physics. And the annual variations in sunspots’ motions, discovered by Francesco Sizzi and others in 1612-1613, provided a powerful argument against both the Ptolemaic system and the geoheliocentric system of Tycho Brahe. For the seasonal variation refuted all non-geo-rotational geostatic planetary models such as the Ptolemaic pure geocentric model and the Tychonic geoheliocentric model in which the Sun orbits the Earth daily, whereby the variation should appear daily but does not. But it was explicable by all geo-rotational systems such as Longomontanus’s semi-Tychonic geo-heliocentric model, Capellan and extended Capellan geo-heliocentric models with a daily rotating Earth, and the pure heliocentric model. A dispute over priority in the discovery of sunspots, and in their interpretation, led Galileo to a long and bitter feud with the Jesuit Christoph Scheiner; in fact, there is little doubt that both of them were beaten by David Fabricius and his son Johannes, looking for confirmation of Kepler’s prediction of the sun’s rotation. Scheiner quickly adopted Kepler’s 1615 proposal of the modern telescope design, which gave larger magnification at the cost of inverted images; Galileo apparently never changed to Kepler’s design.

Galileo was the first to report lunar mountains and craters, whose existence he deduced from the patterns of light and shadow on the Moon’s surface. He even estimated the mountains’ heights from these observations. This led him to the conclusion that the Moon was “rough and uneven, and just like the surface of the Earth itself,” rather than a perfect sphere as Aristotle had claimed. Galileo observed the Milky Way, previously believed to be nebulous, and found it to be a multitude of stars packed so densely that they appeared to be clouds from Earth. He located many other stars too distant to be visible with the naked eye. Galileo also observed the planet Neptune in 1612, but did not realize that it was a planet and took no particular notice of it. It appears in his notebooks as one of many unremarkable dim stars.

Controversy over comets and The Assayer

In 1619, Galileo became embroiled in a controversy with Father Orazio Grassi, professor of mathematics at the Jesuit Collegio Romano. It began as a dispute over the nature of comets, but by the time Galileo had published The Assayer (Il Saggiatore) in 1623, his last salvo in the dispute, it had become a much wider argument over the very nature of Science itself. Because The Assayer contains such a wealth of Galileo’s ideas on how Science should be practised, it has been referred to as his scientific manifesto.

Early in 1619, Father Grassi had anonymously published a pamphlet, An Astronomical Disputation on the Three Comets of the Year 1618,^[41] which discussed the nature of a comet that had appeared late in November of the previous year. Grassi concluded that the comet was a fiery body which had moved along a segment of a great circle at a constant distance from the earth, and that it had been located well beyond the moon.

Grassi’s arguments and conclusions were criticized in a subsequent article, Discourse on the Comets,^[43] published under the name of one of Galileo’s disciples, a Florentine lawyer named Mario Guiducci, although it had been largely written by Galileo himself. Galileo and Guiducci offered no definitive theory of their own on the nature of comets, although they did present some tentative conjectures which we now know to be mistaken.

In its opening passage, Galileo and Guiducci’s Discourse gratuitously insulted the Jesuit Christopher Scheiner, and various uncomplimentary remarks about the professors of the Collegio Romano were scattered throughout the work. The Jesuits were offended, and Grassi soon replied with a polemical tract of his own, The Astronomical and Philosophical Balance,^[49] under the pseudonym Lothario Sarsio Sigensano, purporting to be one of his own pupils.

The Assayer was Galileo’s devastating reply to the Astronomical Balance. It has been widely regarded as a masterpiece of polemical literature, in which “Sarsi’s” arguments are subjected to withering scorn. It was greeted with wide acclaim, and particularly pleased the new pope, Urban VIII, to whom it had been dedicated.

Galileo’s dispute with Grassi permanently alienated many of the Jesuits who had previously been sympathetic to his ideas, and Galileo and his friends were convinced that these Jesuits were responsible for bringing about his later condemnation. The evidence for this is at best equivocal, however.

Galileo, Kepler and theories of tides

Cardinal Bellarmine had written in 1615 that the Copernican system could not be defended without “a true physical demonstration that the sun does not circle the earth but the earth circles the sun”. Galileo considered his theory of the tides to provide the required physical proof of the motion of the earth. This theory was so important to Galileo that he originally intended to entitle his Dialogue on the Two Chief World Systems the Dialogue on the Ebb and Flow of the Sea. For Galileo, the tides were caused by the sloshing back and forth of water in the seas as a point on the Earth’s surface speeded up and slowed down because of the Earth’s rotation on its axis and revolution around the Sun. Galileo circulated his first account of the tides in 1616, addressed to Cardinal Orsini.

If this theory were correct, there would be only one high tide per day. Galileo and his contemporaries were aware of this inadequacy because there are two daily high tides at Venice instead of one, about twelve hours apart. Galileo dismissed this anomaly as the result of several secondary causes, including the shape of the sea, its depth, and other factors. Against the assertion that Galileo was deceptive in making these arguments, Albert Einstein expressed the opinion that Galileo developed his “fascinating arguments” and accepted them uncritically out of a desire for physical proof of the motion of the Earth.

Galileo dismissed as a “useless fiction” the idea, held by his contemporary Johannes Kepler, that the moon caused the tides. Galileo also refused to accept Kepler’s elliptical orbits of the planets, considering the circle the “perfect” shape for planetary orbits.

Technology

A replica of the earliest surviving telescope attributed to Galileo Galilei, on display at the Griffith Observatory

Galileo made a number of contributions to what is now known as technology, as distinct from pure physics, and suggested others. This is not the same distinction as made by Aristotle, who would have considered all Galileo’s physics as techne or useful knowledge, as opposed to episteme, or philosophical investigation into the causes of things. Between 1595-1598, Galileo devised and improved a Geometric and Military Compass suitable for use by gunners and surveyors. This expanded on earlier instruments designed by Niccolò Tartaglia and Guidobaldo del Monte. For gunners, it offered, in addition to a new and safer way of elevating cannons accurately, a way of quickly computing the charge of gunpowder for cannonballs of different sizes and materials. As a geometric instrument, it enabled the construction of any regular polygon, computation of the area of any polygon or circular sector, and a variety of other calculations. About 1593, Galileo constructed a thermometer, using the expansion and contraction of air in a bulb to move water in an attached tube.

In 1609, Galileo was among the first to use a refracting telescope as an instrument to observe stars, planets or moons. The name “telescope” was coined for Galileo’s instrument by a Greek mathematician, Giovanni Demisiani, at a banquet held in 1611 by Prince Federico Cesi to make Galileo a member of his Accademia dei Lincei. The name was derived from the Greek tele = ‘far’ and skopein = ‘to look or see’. In 1610, he used a telescope at close range to magnify the parts of insects. By 1624 he had perfected a compound microscope. He gave one of these instruments to Cardinal Zollern in May of that year for presentation to the Duke of Bavaria, and in September he sent another to Prince Cesi.. The Linceans played a role again in naming the “microscope” a year later when fellow academy member Giovanni Faber coined the word for Galileo’s invention from the Greek words μικρόν (micron) meaning “small”, and σκοπεῖν (skopein) meaning “to look at”. The word was meant to be analogous with “telescope”. Illustrations of insects made using one of Galileo’s microscopes, and published in 1625, appear to have been the first clear documentation of the use of a compound microscope.

In 1612, having determined the orbital periods of Jupiter’s satellites, Galileo proposed that with sufficiently accurate knowledge of their orbits one could use their positions as a universal clock, and this would make possible the determination of longitude. He worked on this problem from time to time during the remainder of his life; but the practical problems were severe. The method was first successfully applied by Giovanni Domenico Cassini in 1681 and was later used extensively for large land surveys; this method, for example, was used by Lewis and Clark. For sea navigation, where delicate telescopic observations were more difficult, the longitude problem eventually required development of a practical portable marine chronometer, such as that of John Harrison.

In his last year, when totally blind, he designed an escapement mechanism for a pendulum clock, a vectorial model of which may be seen here. The first fully operational pendulum clock was made by Christiaan Huygens in the 1650s. Galilei created sketches of various inventions, such as a candle and mirror combination to reflect light throughout a building, an automatic tomato picker, a pocket comb that doubled as an eating utensil, and what appears to be a ballpoint pen.

Physics

Galileo’s theoretical and experimental work on the motions of bodies, along with the largely independent work of Kepler and Rene Descartes, was a precursor of the classical mechanics developed by Sir Isaac Newton.

A biography by Galileo’s pupil Vincenzo Viviani stated that Galileo had dropped balls of the same material, but different masses, from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass. This was contrary to what Aristotle had taught: that heavy objects fall faster than lighter ones, in direct proportion to weight. While this story has been retold in popular accounts, there is no account by Galileo himself of such an experiment, and it is generally accepted by historians that it was at most a thought experiment which did not actually take place.

In his 1638 Discorsi Galileo’s character Salviati, widely regarded as largely Galileo’s spokesman, held that all unequal weights would fall with the same finite speed in a vacuum. But this had previously been proposed by Lucretius and Simon Stevin. Salviati also held it could be experimentally demonstrated by the comparison of pendulum motions in air with otherwise similar but different weight bobs of lead and of cork.

Galileo proposed that a falling body would fall with a uniform acceleration, as long as the resistance of the medium through which it was falling remained negligible, or in the limiting case of its falling through a vacuum. He also derived the correct kinematical law for the distance travelled during a uniform acceleration starting from rest-namely, that it is proportional to the square of the elapsed time ( d ∝ t ² ). However, in neither case were these discoveries entirely original. The time-squared law for uniformly accelerated change was already known to Nicole Oresme in the 14th century, and Domingo de Soto, in the 16th, had suggested that bodies falling through a homogeneous medium would be uniformly accelerated Galileo expressed the time-squared law using geometrical constructions and mathematically-precise words, adhering to the standards of the day. (It remained for others to re-express the law in algebraic terms). He also concluded that objects retain their velocity unless a force-often friction-acts upon them, refuting the generally accepted Aristotelian hypothesis that objects “naturally” slow down and stop unless a force acts upon them (philosophical ideas relating to inertia had been proposed by Ibn al-Haytham centuries earlier, as had Jean Buridan, and according to Joseph Needham, Mo Tzu had proposed it centuries before either of them, but this was the first time that it had been mathematically expressed, verified experimentally, and introduced the idea of frictional force, the key breakthrough in validating inertia). Galileo’s Principle of Inertia stated: “A body moving on a level surface will continue in the same direction at constant speed unless disturbed.” This principle was incorporated into Newton’s laws of motion (first law).

Dome of the cathedral of Pisa with the “lamp of Galileo”

Galileo also claimed (incorrectly) that a pendulum’s swings always take the same amount of time, independently of the amplitude. That is, that a simple pendulum is isochronous. It is popularly believed that he came to this conclusion by watching the swings of the bronze chandelier in the cathedral of Pisa, using his pulse to time it. It appears however, that he conducted no experiments because the claim is true only of infinitesimally small swings as discovered by Christian Huygens. Galileo’s son, Vincenzo, sketched a clock based on his father’s theories in 1642. The clock was never built and, because of the large swings required by its verge escapement, would have been a poor timekeeper. (See Technology above.)

In 1638 Galileo described an experimental method to measure the speed of light by arranging that two observers, each having lanterns equipped with shutters, observe each other’s lanterns at some distance. The first observer opens the shutter of his lamp, and, the second, upon seeing the light, immediately opens the shutter of his own lantern. The time between the first observer’s opening his shutter and seeing the light from the second observer’s lamp indicates the time it takes light to travel back and forth between the two observers. Galileo reported that when he tried this at a distance of less than a mile, he was unable to determine whether or not the light appeared instantaneously.Sometime between Galileo’s death and 1667, the members of the Florentine Accademia del Cimento repeated the experiment over a distance of about a mile and obtained a similarly inconclusive result.

Galileo is lesser known for, yet still credited with, being one of the first to understand sound frequency. By scraping a chisel at different speeds, he linked the pitch of the sound produced to the spacing of the chisel’s skips, a measure of frequency.

In his 1632 Dialogue Galileo presented a physical theory to account for tides, based on the motion of the Earth. If correct, this would have been a strong argument for the reality of the Earth’s motion. In fact, the original title for the book described it as a dialogue on the tides; the reference to tides was removed by order of the Inquisition. His theory gave the first insight into the importance of the shapes of ocean basins in the size and timing of tides; he correctly accounted, for instance, for the negligible tides halfway along the Adriatic Sea compared to those at the ends. As a general account of the cause of tides, however, his theory was a failure. Kepler and others correctly associated the Moon with an influence over the tides, based on empirical data; a proper physical theory of the tides, however, was not available until Newton.

Galileo also put forward the basic principle of relativity, that the laws of physics are the same in any system that is moving at a constant speed in a straight line, regardless of its particular speed or direction. Hence, there is no absolute motion or absolute rest. This principle provided the basic framework for Newton’s laws of motion and is central to Einstein’s special theory of relativity.

Mathematics

While Galileo’s application of mathematics to experimental physics was innovative, his mathematical methods were the standard ones of the day. The analysis and proofs relied heavily on the Eudoxian theory of proportion, as set forth in the fifth book of Euclid’s Elements. This theory had become available only a century before, thanks to accurate translations by Tartaglia and others; but by the end of Galileo’s life it was being superseded by the algebraic methods of Descartes.

Galileo produced one piece of original and even prophetic work in mathematics: Galileo’s paradox, which shows that there are as many perfect squares as there are whole numbers, even though most numbers are not perfect squares. Such seeming contradictions were brought under control 250 years later in the work of Georg Cantor.

Church controversy

Western Christian biblical references Psalm 93:1, Psalm 96:10, and 1 Chronicles 16:30 include (depending on translation) text stating that “the world is firmly established, it cannot be moved.” In the same tradition, Psalm 104:5 says, “the LORD set the earth on its foundations; it can never be moved.” Further, Ecclesiastes 1:5 states that “And the sun rises and sets and returns to its place, etc.”

Galileo defended heliocentrism, and claimed it was not contrary to those Scripture passages. He took Augustine’s position on Scripture: not to take every passage literally, particularly when the scripture in question is a book of poetry and songs, not a book of instructions or history. The writers of the Scripture wrote from the perspective of the terrestrial world, and from that vantage point the sun does rise and set. In fact, it is the earth’s rotation which gives the impression of the sun in motion across the sky. He did, however, openly question the veracity of the Book of Joshua (10:13) wherein the sun and moon were said to have remained unmoved for three days to allow a victory to the Israelites.

By 1616 the attacks on Galileo had reached a head, and he went to Rome to try to persuade the Church authorities not to ban his ideas. In the end, Cardinal Bellarmine, acting on directives from the Inquisition, delivered him an order not to “hold or defend” the idea that the Earth moves and the Sun stands still at the centre. The decree did not prevent Galileo from discussing heliocentrism hypothetically. For the next several years Galileo stayed well away from the controversy. He revived his project of writing a book on the subject, encouraged by the election of Cardinal Barberini as Pope Urban VIII in 1623. Barberini was a friend and admirer of Galileo, and had opposed the condemnation of Galileo in 1616. The book, Dialogue Concerning the Two Chief World Systems, was published in 1632, with formal authorization from the Inquisition and papal permission.

Pope Urban VIII personally asked Galileo to give arguments for and against heliocentrism in the book, and to be careful not to advocate heliocentrism. He made another request, that his own views on the matter be included in Galileo’s book. Only the latter of those requests was fulfilled by Galileo. Whether unknowingly or deliberately, Simplicio (“Stupid”^{[citation needed]}), the defender of the Aristotelian Geocentric view in Dialogue Concerning the Two Chief World Systems, was often caught in his own errors and sometimes came across as a fool. This fact made Dialogue Concerning the Two Chief World Systems appear as an advocacy book; an attack on Aristotelian geocentrism and defense of the Copernican theory. To add insult to injury, Galileo put the words of Pope Urban VIII into the mouth of Simplicio. Most historians agree Galileo did not act out of malice and felt blindsided by the reaction to his book. However, the Pope did not take the suspected public ridicule lightly, nor the blatant bias. Galileo had alienated one of his biggest and most powerful supporters, the Pope, and was called to Rome to defend his writings.

With the loss of many of his defenders in Rome because of Dialogue Concerning the Two Chief World Systems, Galileo was ordered to stand trial on suspicion of heresy in 1633. The sentence of the Inquisition was in three essential parts:

• Galileo was found “vehemently suspect of heresy”, namely of having held the opinions that the Sun lies motionless at the centre of the universe, that the Earth is not at its centre and moves, and that one may hold and defend an opinion as probable after it has been declared contrary to Holy Scripture. He was required to “abjure, curse and detest” those opinions.
• He was ordered imprisoned; the sentence was later commuted to house arrest.
• His offending Dialogue was banned; and in an action not announced at the trial, publication of any of his works was forbidden, including any he might write in the future.

According to popular legend, after recanting his theory that the Earth moved around the Sun, Galileo allegedly muttered the rebellious phrase And yet it moves, but there is no evidence that he actually said this or anything similarly impertinent. The first account of the legend dates to a century after his death.^[89]

After a period with the friendly Ascanio Piccolomini (the Archbishop of Siena), Galileo was allowed to return to his villa at Arcetri near Florence, where he spent the remainder of his life under house arrest, and where he later became blind. It was while Galileo was under house arrest that he dedicated his time to one of his finest works, Two New Sciences. Here he summarized work he had done some forty years earlier, on the two sciences now called kinematics and strength of materials. This book has received high praise from both Sir Isaac Newton and Albert Einstein. As a result of this work, Galileo is often called, the “father of modern physics”.

Galileo died on 8 January 1642. The Grand Duke of Tuscany, Ferdinando II, wished to bury him in the main body of the Basilica of Santa Croce, next to the tombs of his father and other ancestors, and to erect a marble mausoleum in his honour. These plans were scrapped, however, after Pope Urban VIII and his nephew, Cardinal Francesco Barberini, protested. He was instead buried in a small room next to the novices’ chapel at the end of a corridor from the southern transept of the basilica to the sacristy. He was reburied in the main body of the basilica in 1737 after a monument had been erected there in his honour.

The Inquisition’s ban on reprinting Galileo’s works was lifted in 1718 when permission was granted to publish an edition of his works (excluding the condemned Dialogue) in Florence. In 1741 Pope Benedict XIV authorized the publication of an edition of Galileo’s complete scientific works which included a mildly censored version of the Dialogue. In 1758 the general prohibition against works advocating heliocentrism was removed from the Index of prohibited books, although the specific ban on uncensored versions of the Dialogue and Copernicus’s De Revolutionibus remained. All traces of official opposition to heliocentrism by the Church disappeared in 1835 when these works were finally dropped from the Index.

In 1939 Pope Pius XII, in his first speech to the Pontifical Academy of Sciences, within a few months of his election to the papacy, described Galileo as being among the “most audacious heroes of research … not afraid of the stumbling blocks and the risks on the way, nor fearful of the funereal monuments^“ His close advisor of 40 years, Professor Robert Leiber wrote: “Pius XII was very careful not to close any doors (to science) prematurely. He was energetic on this point and regretted that in the case of Galileo.”

On 15 February 1990, in a speech delivered at the Sapienza University of Rome, Cardinal Ratzinger cited some current views on the Galileo affair as forming what he called “a symptomatic case that permits us to see how deep the self-doubt of the modern age, of science and technology goes today.” Some of the views he cited were those of the philosopher Paul Feyerabend, whom he quoted as saying “The Church at the time of Galileo kept much more closely to reason than did Galileo himself, and she took into consideration the ethical and social consequences of Galileo’s teaching too. Her verdict against Galileo was rational and just and the revision of this verdict can be justified only on the grounds of what is politically opportune.” The Cardinal did not clearly indicate whether he agreed or disagreed with Feyerabend’s assertions. He did, however, say “It would be foolish to construct an impulsive apologetic on the basis of such views”.

On 31 October 1992, Pope John Paul II expressed regret for how the Galileo affair was handled, and officially conceded that the Earth was not stationary, as the result of a study conducted by the Pontifical Council for Culture.

His writings

Galileo’s early works describing scientific instruments include the 1586 tract entitled The Little Balance (La Billancetta) describing an accurate balance to weigh objects in air or water and the 1606 printed manual Le Operazioni del Compasso Geometrico et Militare on the operation of a geometrical and military compass.^[107]

His early works in dynamics, the science of motion and mechanics were his 1590 Pisan De Motu (On Motion) and his circa 1600 Paduan Le Meccaniche (Mechanics). The former was based on Aristotelian-Archimedean fluid dynamics and held that the speed of gravitational fall in a fluid medium was proportional to the excess of a body’s specific weight over that of the medium, whereby in a vacuum bodies would fall with speeds in proportion to their specific weights. It also subscribed to the Hipparchan-Philoponan impetus dynamics in which impetus is self-dissipating and free-fall in a vacuum would have an essential terminal speed according to specific weight after an initial period of acceleration.

Galileo’s 1610 The Starry Messenger (Sidereus Nuncius) was the first scientific treatise to be published based on observations made through a telescope and include the discovery of the Galilean moons. Galileo published a description of sunspots in 1613 entitled Letters on Sunspots suggesting the Sun and heavens are corruptible. It also reported his 1610 telescopic confirmation of the full set of phases of Venus that refuted pure geocentrism and so promoted the 17th century conversion to geoheliocentrism. In 1615 Galileo prepared a manuscript known as the Letter to Grand Duchess Christina which was not published in printed form until 1636. This letter was a revised version of the Letter to Castelli, which was denounced by the Inquisition as an incursion upon theology by advocating Copernicanism both as physically true and as consistent with Scripture. In 1616, after the order by the inquisition for Galileo not to hold or defend the Copernican position, Galileo wrote the Discourse on the tides (Discorso sul flusso e il reflusso del mare) based on the Copernican earth, in the form of a private letter to Cardinal Orsini. In 1619, Mario Guiducci, a pupil of Galileo’s, published a lecture written largely by Galileo under the title Discourse on the Comets (Discorso Delle Comete), arguing against the Jesuit interpretation of comets.^[111]

In 1623, Galileo published The Assayer – Il Saggiatore, which attacked theories based on Aristotle’s authority and promoted experimentation and the mathematical formulation of scientific ideas. The book was highly successful and even found support among the higher echelons of the Christian church.^[112] Following the success of The Assayer, Galileo published the Dialogue Concerning the Two Chief World Systems (Dialogo sopra i due massimi sistemi del mondo) in 1632. Despite taking care to adhere to the Inquisition’s 1616 instructions, the claims in the book favouring Copernican theory and a non Geocentric model of the solar system led to Galileo being tried and banned on publication. Despite the publication ban, Galileo published his Discourses and Mathematical Demonstrations Relating to Two New Sciences (Discorsi e Dimostrazioni Matematiche, intorno a due nuove scienze) in 1638 in Holland, outside the jurisdiction of the Inquisition.

• The Little Balance (1586)
• On Motion (1590)
• Mechanics (c1600)
• The Starry Messenger (1610; in Latin, Sidereus Nuncius)
• Letters on Sunspots (1613)
• Letter to the Grand Duchess Christina (1615; published in 1636)
• Discourse on the Tides (1616; in Italian, Discorso del flusso e reflusso del mare)
• Discourse on the Comets (1619; in Italian, Discorso Delle Comete)
• The Assayer (1623; in Italian, Il Saggiatore)
• Dialogue Concerning the Two Chief World Systems (1632; in Italian Dialogo dei due massimi sistemi del mondo)
• Discourses and Mathematical Demonstrations Relating to Two New Sciences (1638; in Italian, Discorsi e Dimostrazioni Matematiche, intorno a due nuove scienze)

Legacy

Galileo’s astronomical discoveries and investigations into the Copernican theory have led to a lasting legacy which includes the categorisation of the four large moons of Jupiter discovered by Galileo (Io, Europa, Ganymede and Callisto) as the Galilean moons. Other scientific endeavours and principles are named after Galileo including the Galileo spacecraft, the first spacecraft to enter orbit around Jupiter, the proposed Galileo global satellite navigation system, the transformation between inertial systems in classical mechanics denoted Galilean transformation and the Gal (unit), sometimes known as the Galileo which is a non-SI unit of acceleration.

To coincide in part with Galileo’s first recorded astronomical observations using a telescope, the United Nations has scheduled 2009 to be the International Year of Astronomy. A global scheme laid out by the International Astronomical Union (IAU), it has also been endorsed by UNESCO – the UN body responsible for Educational, Scientific and Cultural matters. The International Year of Astronomy 2009 is intended to be a global celebration of astronomy and its contributions to society and culture, stimulating worldwide interest not only in astronomy but science in general, with a particular slant towards young people.

The 20th-century German playwright Bertolt Brecht dramatised Galileo’s life in his Life of Galileo (1943).

Life

Ahmed ibn Yusuf was born in Baghdad (today in Iraq) and moved with his father to Damascus in 839. He later moved to Cairo, but the exact date is unknown: since he was also known as al-Misri, which means the Egyptian, this probably happened at an early age. Eventually, he also died in Cairo. He probably grew up in a strongly intellectual environment: his father worked on Mathematics, Astronomy and Medicine, produced astronomical tables and was a member of a group of scholars. He achieved an important role in Egypt, which was caused by Egypt’s relative independence from the Abbasid Caliph.

Work

For some of the work attributed to Ahmed, it is not exactly clear whether he wrote his, whether his father wrote it or whether they wrote it together. It is clear, however, that he worked on a book on ratio and proportion. This was translated to Latin by Gherard of Cremona and was a commentary of Euclid’s Elements. This book influenced early European mathematicians such as Fibonacci. Further, in On similar arcs, he commented on Ptolemy’s Centiloquium. He also wrote a book on the astrolabe, a predecessor of the octant and the sextant. He invented methods to solve tax problems in Liber Abaci. He was also quoted by mathematicians such as Thomas Bradwardine, Jordanus Nemorarius and Luca Pacioli.

en.wikipedia.org

Biography

Abu al-Qasim was born in the city of El Zahra, six miles northwest of Cordoba, Spain. He was descended from the Ansar Arab tribe who settled earlier in Spain. Few details remain regarding his life, aside from his published work, due to the destruction of El-Zahra during later Spanish-Moorish conflicts. His name first appears in the writings of Abu Muhammad bin Hazm (993 – 1064), who listed him among the greatest physicians of Moorish Spain. But we have the first detailed biography of El-Zahrawi from al-Humaydi’s Jadhwat al-Muqtabis (On Andalusian Savants), completed six decades after El-Zahrawi’s death.

In El-Zahra, he lived most of his life. It is also where he studied, taught and practised medicine and surgery until shortly before his death in about 1013, two years after the sacking of El-Zahra.

Works

Abu al-Qasim was a court physician to the Andalusian caliph Al-Hakam II. He devoted his entire life and genius to the advancement of medicine as a whole and surgery in particular. His best work was the Kitab al-Tasrif. It is a medical encyclopaedia spanning 30 volumes which included sections on surgery, medicine, orthopaedics, ophthalmology, pharmacology, nutrition etc.

In the 14th century, French surgeon Guy de Chauliac quoted al-Tasrif over 200 times. Pietro Argallata (d. 1453) described Abu al-Qasim as “without doubt the chief of all surgeons”. In an earlier work, he is credited to be the first to describe ectopic pregnancy in 963, in those days a fatal affliction. Abu Al-Qasim’s influence continued for at least five centuries, extending into the Renaissance, evidenced by al-Tasrif’s frequent reference by French surgeon Jaques Delechamps (1513-1588).

Page from a 1531 Latin translation by Peter Argellata of El Zahrawi’s treatise on surgical and medical instruments.

Kitab al-Tasrif

Abu al-Qasim’s thirty-chapter medical treatise, Kitab al-Tasrif, published in 1000, covered a broad range of medical topics, including dentistry and childbirth, which contained data that had accumulated during a career that spanned almost 50 years of training, teaching and practice. In it he also wrote of the importance of a positive doctor-patient relationship and wrote affectionately of his students, whom he referred to as “my children”. He also emphasised the importance of treating patients irrespective of their social status. He encouraged the close observation of individual cases in order to make the most accurate diagnosis and the best possible treatment.

Al-Tasrif was later translated into Latin by Gerard of Cremona in the 12th century, and illustrated. For perhaps five centuries during the European Middle Ages, it was the primary source for European medical knowledge, and served as a reference for doctors and surgeons.

Not always properly credited, Abu Al-Qasim’s al-Tasrif described both what would later became known as “Kocher’s method” for treating a dislocated shoulder and “Walcher position” in obstetrics. Al-Tasrif described how to ligature blood vessels before Ambroise Pare, and was the first recorded book to document several dental devices and explain the hereditary nature of haemophilia.

Advances in surgery

Al-Qasim was a surgeon and specialized in curing disease by cauterization. He also invented several devices used during surgery, for the purpose of:

• inspection of the interior of the urethra
• applying and removing foreign bodies from the throat
• inspection of the ear

Al-Qasim also described the use of forceps in vaginal deliveries.

Surgical instruments

In his Al-Tasrif (The Method of Medicine), he introduced his famous collection of over 200 surgical instruments. Many of these instruments were never used before by any previous surgeons. Hamidan, for example, listed at least twenty six innovative surgical instruments that Abulcasis introduced.

Catgut

Abu al-Qasim’s use of catgut for internal stitching is still practised in modern surgery. The catgut appears to be the only natural substance capable of dissolving and is acceptable by the body.

Forceps

In the Al-Tasrif (1000), Abu al-Qasim invented the forceps for extracting a dead fetus, as illustrated in the the Al-Tasrif.^[3]

Ligature

In the Al-Tasrif (1000), Abu al-Qasim introduced the use of ligature for the arteries in lieu of cauterization.

Surgical needle

The surgical needle was invented and described by Abu al-Qasim in his Al-Tasrif (1000).

Other instruments

Other surgical instruments invented by Abu al-Qasim and first described in his Al-Tasrif (1000) include the scalpel, curette, retractor, surgical spoon, sound, surgical hook, surgical rod, and specula.

en.wikipedia.org

He wrote some 450 books on a wide range of subjects, many of which concentrated on philosophy and medicine. His most famous works are The Book of Healing and The Canon of Medicine, which was a standard medical text at many Islamic and European universities up until the 18th century. Ibn Sina developed a medical system that combined his own personal experience with that of Islamic medicine, the medical system of Galen, Aristotelian metaphysics, and ancient Persian, Arabian and Indian medicine. Ibn Sina is regarded as the father of modern medicine, particularly for his introduction of systematic experimentation and quantification into the study of physiology, and for his discovery of the contagious nature of diseases. He is also considered the father of the fundamental concept of momentum in physics.

George Sarton, the father of the history of science, wrote in the Introduction to the History of Science:

“One of the most famous exponents of Muslim universalism and an eminent figure in Islamic learning was Ibn Sina, known in the West as Avicenna (981-1037). For a thousand years he has retained his original renown as one of the greatest thinkers and medical scholars in history. His most important medical works are the Qanun (Canon) and a treatise on Cardiac drugs. The ‘Qanun fi-l-Tibb’ is an immense encyclopedia of medicine. It contains some of the most illuminating thoughts pertaining to distinction of mediastinitis from pleurisy; contagious nature of phthisis; distribution of diseases by water and soil; careful description of skin troubles; of sexual diseases and perversions; of nervous ailments.

Biography

Early life

Ibn Sina’s life is known to us from authoritative sources. A biography, which is widely considered by foremost Arabicists to have been composed by a disciple and later redacted, covers his first thirty years, and the rest are documented by his disciple al-Juzjani, who was also his secretary and his friend.

He was born in Persia around 980 (370 AH) in Afshana, his mother’s home, a small city now part of Uzbekistan. His father, a respected Ismaili scholar, was from Balkh of the Persian province of Khorasan, now part of Afghanistan, and was at the time of his son’s birth the governor of a village in one of the Samanid Nuh ibn Mansur’s estates. He had his son very carefully educated at Bukhara. According to the Encyclopedia of Islam his father and his brother were influenced by Isma’ili propaganda; he was certainly acquainted with its tenets, but refused to adopt them. Ibn Sina’s independent thought was served by an extraordinary intelligence and memory, which allowed him to overtake his teachers at the age of fourteen.

Ibn Sina was put under the charge of a tutor, and his precocity soon made him the marvel of his neighbours; he displayed exceptional intellectual behaviour and was a child prodigy who had memorized the Quran by the age of 7 and a great deal of Persian poetry as well. From a greengrocer he learned arithmetic, and he began to learn more from a wandering scholar who gained a livelihood by curing the sick and teaching the young.

However he was greatly troubled by metaphysical problems and in particular the works of Aristotle. So, for the next year and a half, he also studied philosophy, in which he encountered greater obstacles. In such moments of baffled inquiry, he would leave his books, perform the requisite ablutions, then go to the mosque, and continue in prayer till light broke on his difficulties. Deep into the night he would continue his studies, and even in his dreams problems would pursue him and work out their solution. Forty times, it is said, he read through the Metaphysics of Aristotle, till the words were imprinted on his memory; but their meaning was hopelessly obscure, until one day they found illumination, from the little commentary by Farabi, which he bought at a bookstall for the small sum of three dirhams. So great was his joy at the discovery, thus made by help of a work from which he had expected only mystery, that he hastened to return thanks to God, and bestowed alms upon the poor.

He turned to medicine at 16, and not only learned medical theory, but also by gratuitous attendance on the sick had, according to his own account, discovered new methods of treatment. The teenager achieved full status as a physician at age 18 and found that “Medicine is no hard and thorny science, like mathematics and metaphysics, so I soon made great progress; I became an excellent doctor and began to treat patients, using approved remedies.” The youthful physician’s fame spread quickly, and he treated many patients without asking for payment.

Adulthood

His first appointment was that of physician to the emir, who owed him his recovery from a dangerous illness (997). Ibn Sina’s chief reward for this service was access to the royal library of the Samanids, well-known patrons of scholarship and scholars. When the library was destroyed by fire not long after, the enemies of Ibn Sina accused him of burning it, in order for ever to conceal the sources of his knowledge. Meanwhile, he assisted his father in his financial labours, but still found time to write some of his earliest works.

When Ibn Sina was 22 years old, he lost his father. The Samanid dynasty came to its end in December 1004. Ibn Sina seems to have declined the offers of Mahmud of Ghazni, and proceeded westwards to Urgench in the modern Uzbekistan, where the vizier, regarded as a friend of scholars, gave him a small monthly stipend. The pay was small, however, so Ibn Sina wandered from place to place through the districts of Nishapur and Merv to the borders of Khorasan, seeking an opening for his talents. Shams al-Ma’ali Kavuus, the generous ruler of Dailam and central Persia, himself a poet and a scholar, with whom Ibn Sina had expected to find an asylum, was about that date (1052) starved to death by his troops who had revolted. Ibn Sina himself was at this season stricken down by a severe illness. Finally, at Gorgan, near the Caspian Sea, Ibn Sina met with a friend, who bought a dwelling near his own house in which Ibn Sina lectured on logic and astronomy. Several of Ibn Sina’s treatises were written for this patron; and the commencement of his Canon of Medicine also dates from his stay in Hyrcania.

Ibn Sina subsequently settled at Rai, in the vicinity of modern Tehran, (present day capital of Iran), the home town of Rhazes; where Majd Addaula, a son of the last Buwayhid emir, was nominal ruler under the regency of his mother (Seyyedeh Khatun). About thirty of Ibn Sina’s shorter works are said to have been composed in Rai. Constant feuds which raged between the regent and her second son, Amir Shamsud-Dawala, however, compelled the scholar to quit the place. After a brief sojourn at Qazvin he passed southwards to Hamadãn, where another Deylamite emir had established himself. At first, Ibn Sina entered into the service of a high-born lady; but the emir, hearing of his arrival, called him in as medical attendant, and sent him back with presents to his dwelling. Ibn Sina was even raised to the office of vizier. The emir consented that he should be banished from the country. Ibn Sina, however, remained hidden for forty days in a sheikh’s house, till a fresh attack of illness induced the emir to restore him to his post. Even during this perturbed time, Ibn Sina persevered with his studies and teaching. Every evening, extracts from his great works, the Canon and the Sanatio, were dictated and explained to his pupils. On the death of the emir, Ibn Sina ceased to be vizier and hid himself in the house of an apothecary, where, with intense assiduity, he continued the composition of his works.

Meanwhile, he had written to Abu Ya’far, the prefect of the dynamic city of Isfahan, offering his services. The new emir of Hamadan, hearing of this correspondence and discovering where Ibn Sina was hidden, incarcerated him in a fortress. War meanwhile continued between the rulers of Isfahan and Hamadãn; in 1024 the former captured Hamadan and its towns, expelling the Tajik mercenaries. When the storm had passed, Ibn Sina returned with the emir to Hamadan, and carried on his literary labours. Later, however, accompanied by his brother, a favourite pupil, and two slaves, Ibn Sina escaped out of the city in the dress of a Sufi ascetic. After a perilous journey, they reached Isfahan, receiving an honourable welcome from the prince.

Later life

Avicenna’s tomb in Hamedan, Iran

The remaining ten or twelve years of Ibn Sina’s life were spent in the service of Abu Ja’far ‘Ala Addaula, whom he accompanied as physician and general literary and scientific adviser, even in his numerous campaigns.

During these years he began to study literary matters and philology, instigated, it is asserted, by criticisms on his style. He contrasts with the nobler and more intellectual character of Averroes. A severe colic, which seized him on the march of the army against Hamadãn, was checked by remedies so violent that Ibn Sina could scarcely stand. On a similar occasion the disease returned; with difficulty he reached Hamadãn, where, finding the disease gaining ground, he refused to keep up the regimen imposed, and resigned himself to his fate.

His friends advised him to slow down and take life moderately. He refused, however, stating that: “I prefer a short life with width to a narrow one with length”. On his deathbed remorse seized him; he bestowed his goods on the poor, restored unjust gains, freed his slaves, and every third day till his death listened to the reading of the Qur’an. He died in June 1037, in his fifty-eighth year, and was buried in Hamedan, Iran.

Works

Scarcely any member of the Muslim circle of the sciences, including theology, philology, mathematics, astronomy, physics, and music, was left untouched by the treatises of Ibn Sina. This vast quantity of works – be they full-blown treatises or opuscula – vary so much in style and content (if one were to compare between the ‘ahd made with his disciple Bahmanyar to uphold philosophical integrity with the Provenance and Direction, for example) that Yahya (formerly Jean) Michot has accused him of “neurological bipolarity”.

Ibn Sina wrote at least one treatise on alchemy, but several others have been falsely attributed to him. His book on animals was translated by Michael Scot. His Logic, Metaphysics, Physics, and De Caelo, are treatises giving a synoptic view of Aristotelian doctrine, though the Metaphysics demonstrates a significant departure from the brand of Neoplatonism known as Aristotelianism in Ibn Sina’s world; Arabic philosophers have hinted at the idea that Ibn Sina was attempting to “re-Aristotelianise” Muslim philosophy in its entirety, unlike his predecessors, who accepted the conflation of Platonic, Aristotelian, Neo- and Middle-Platonic works transmitted into the Muslim world.

The Logic and Metaphysics have been printed more than once, the latter, e.g., at Venice in 1493, 1495, and 1546. Some of his shorter essays on medicine, logic, etc., take a poetical form (the poem on logic was published by Schmoelders in 1836). Two encyclopaedic treatises, dealing with philosophy, are often mentioned. The larger, Al-Shifa’ (Sanatio), exists nearly complete in manuscript in the Bodleian Library and elsewhere; part of it on the De Anima appeared at Pavia (1490) as the Liber Sextus Naturalium, and the long account of Ibn Sina’s philosophy given by Muhammad al-Shahrastani seems to be mainly an analysis, and in many places a reproduction, of the Al-Shifa’. A shorter form of the work is known as the An-najat (Liberatio). The Latin editions of part of these works have been modified by the corrections which the monastic editors confess that they applied. There is also a حكمت مشرقيه (hikmat-al-mashriqqiyya, in Latin Philosophia Orientalis), mentioned by Roger Bacon, the majority of which is lost in antiquity, which according to Averroes was pantheistic in tone.

Sciences

Medicine

A Latin copy of the Canon of Medicine, dated 1484, located at the P.I. Nixon Medical Historical Library of The University of Texas Health Science Center at San Antonio.

About 100 treatises were ascribed to Ibn Sina. Some of them are tracts of a few pages, others are works extending through several volumes. The best-known amongst them, and that to which Ibn Sina owed his European reputation, is his 14-volume The Canon of Medicine, which was a standard medical text in Europe and the Islamic world up until the 18th century. The book is known for its introduction of systematic experimentation and quantification into the study of physiology, and for the discovery of contagious diseases. It classifies and describes diseases, and outlines their assumed causes. Hygiene, simple and complex medicines, and functions of parts of the body are also covered. In this, Ibn Sina is credited as being the first to correctly document the anatomy of the human eye, along with descriptions of eye afflictions such as cataracts. It asserts that tuberculosis was contagious, which was later disputed by Europeans, but turned out to be true. It also describes the symptoms and complications of diabetes. Both forms of facial paralysis were described in-depth. In addition, the workings of the heart as a valve are described.

A copy of the Canon of Medicine, dated 1593

An Arabic edition of the Canon appeared at Rome in 1593, and a Hebrew version at Naples in 1491. Of the Latin version there were about thirty editions, founded on the original translation by Gerard de Sablonetta. In the 15th century a commentary on the text of the Canon was composed. Other medical works translated into Latin are the Medicamenta Cordialia, Canticum de Medicina, and the Tractatus de Syrupo Acetoso.

It was mainly accident which determined that from the 12th to the 18th century, Ibn Sina should be the guide of medical study in European universities, and eclipse the names of Rhazes, Ali ibn al-Abbas and Averroes. His work is not essentially different from that of his predecessor Rhazes, because he presented the doctrine of Galen, and through Galen the doctrine of Hippocrates, modified by the system of Aristotle, as well as the Indian doctrines of Sushruta and Charaka.^[12] But the Canon of Ibn Sina is distinguished from the Al-Hawi (Continens) or Summary of Rhazes by its greater method, due perhaps to the logical studies of the former.

The work has been variously appreciated in subsequent ages, some regarding it as a treasury of wisdom, and others, like Averroes, holding it useful only as waste paper. In modern times it has been seen of mainly historic interest as most of its tenets have been disproved or expanded upon by scientific medicine. The vice of the book is excessive classification of bodily faculties, and over-subtlety in the discrimination of diseases. It includes five books; of which the first and second discuss physiology, pathology and hygiene, the third and fourth deal with the methods of treating disease, and the fifth describes the composition and preparation of remedies. This last part contains some personal observations.

He is, like all his countrymen, ample in the enumeration of symptoms, and is said to be inferior to Ali in practical medicine and surgery. He introduced into medical theory the four causes of the Peripatetic system. Of natural history and botany he pretended to no special knowledge. Up to the year 1650, or thereabouts, the Canon was still used as a textbook in the universities of Leuven and Montpellier.

In the museum at Bukhara, there are displays showing many of his writings, surgical instruments from the period and paintings of patients undergoing treatment. Ibn Sina was interested in the effect of the mind on the body, and wrote a great deal on psychology, likely influencing Ibn Tufayl and Ibn Bajjah. He also introduced medical herbs.

Alchemy

In alchemy, Ibn Sina discredited the theory of transmutation of substances believed by some alchemists:

“Those of the chemical craft know well that no change can be effected in the different species of substances, though they can produce the appearance of such change.”

Aromatherapy

Ibn Sina used steam distillation to produce the first essential oils. As a result, he is regarded as a pioneer of aromatherapy.

Astronomy

In 1070, Abu Ubayd al-Juzjani, a pupil of Ibn Sina, claimed that his teacher Ibn Sina had solved the equant problem in Ptolemy’s planetary model.

Chemistry

In chemistry, steam distillation was invented by Ibn Sina in the early 11th century, which he used to produce essential oils.

Earth sciences

Ibn Sina wrote on the earth sciences in The Book of Healing. In geology, he hypothesized two causes of mountains:

“Either they are the effects of upheavals of the crust of the earth, such as might occur during a violent earthquake, or they are the effect of water, which, cutting itself a new route, has denuded the valleys, the strata being of different kinds, some soft, some hard… It would require a long period of time for all such changes to be accomplished, during which the mountains themselves might be somewhat diminished in size.”

Physics

In physics, Ibn Sina was the first to employ an air thermometer in his scientific experiments.

In mechanics, Ibn Sina developed an elaborate theory of motion, in which he made a distinction between the inclination and force of a projectile, and concluded that motion was a result of an inclination (mayl) transferred to the projectile by the thrower, and that projectile motion in a vacuum would not cease. He viewed inclination as a permanent force whose effect is dissipated by external forces such as air resistance. His theory of motion was thus consistent with the concept of inertia in Newton’s first law of motion. Ibn Sina also referred to mayl to as being proportional to weight times velocity, a precursor to the concept of momentum in Newton’s second law of motion. Ibn Sina’s theory of mayl was further developed by Jean Buridan in his theory of impetus.

In optics, Ibn Sina provided a sophisticated explanation for the rainbow phenomenon. Carl Benjamin Boyer described Ibn Sina’s theory on the rainbow as follows:

“Independent observation had demonstrated to him that the bow is not formed in the dark cloud but rather in the very thin mist lying between the cloud and the sun or observer. The cloud, he thought, serves simply as the background of this thin substance, much as a quicksilver lining is placed upon the rear surface of the glass in a mirror. Ibn Sina would change the place not only of the bow, but also of the color formation, holding the iridescence to be merely a subjective sensation in the eye.”

en.wikipedia.org

He was a scientist and physicist, an anthropologist, an astronomer and astrologer, an encyclopedist and historian, a geographer, a geodesist and geologist, a mathematician, a pharmacist and physician, a philosopher and Ash’ari theologian, a scholar and teacher, and a traveller, who contributed greatly to all of these fields. He was also the first Muslim scholar to study India and the Brahminical tradition, and has been described as the father of Indology, the father of geodesy, and “the first anthropologist”. Along with Geber and Ibn al-Haytham, al-Biruni was also one of the earliest leading exponents of the experimental method, and the first to conduct elaborate experiments related to astronomical phenomena.

George Sarton, the father of the history of science, described al-Biruni as:

“One of the very greatest scientists of Islam, and, all considered, one of the greatest of all times.”

A. I. Sabra desribed al-Biruni as:

“One of the great scientific minds in all history.”

The Al-Biruni crater, on the Moon, is named after al-Biruni.

Biography

He was born in Khwarazm (formerly north-eastern part of the Persian Samanid dynasty) presently in Khiva, Uzbekistan. He studied mathematics and astronomy under Abu Nasr Mansur.

He was a colleague of the fellow Persian Muslim philosopher and physician Abu Ali ibn Sina (Avicenna), the historian, philosopher and ethicist Ibn Miskawayh, in a university and science center established by prince Abu al-Abbas Ma’mun Khawarazmshah. He also travelled to South Asia with Mahmud of Ghazni (whose son and successor Masud was, however, his major patron), and accompanied him on his campaigns in India (in 1030), learning Indian languages, and studying the religion and philosophy of its people. There, he also wrote his Ta’rikh al-Hind (“Chronicles of India”). Biruni wrote his books in Arabic and his native language Persian, though he knew no less than four other languages: Greek, Sanskrit, Syriac, and possibly Berber.

He was buried in Ghazni in Afganistan.

Works

An illustration from Beruni’s Persian book. It shows different phases of the moon.

Biruni’s works number 146 in total. These include 35 books on astronomy, 4 on astrolabes, 23 on astrology, 5 on chronology, 2 on time measurement, 9 on geography, 10 on geodesy and mapping theory, 15 on mathematics (8 on arithmetic, 5 on geometry, 2 on trigonometry), 2 on mechanics, 2 on medicine and pharmacology, 1 on meteorology, 2 on mineralogy and gems, 4 on history, 2 on India, 3 on religion and philosophy, 16 literary works, 2 books on magic, and 9 unclassified books. Among these works, only 22 have survived, and only 13 of these works have been published. His extant works include:

• Critical study of what India says, whether accepted by reason or refused (Arabic تحقيق ما للهند من مقولة معقولة في العقل أم مرذولة) – a compendium of India’s religion and philosophy
• The Remaining Signs of Past Centuries (Arabic الآثار الباقية عن القرون الخالية) – a comparative study of calendars of different cultures and civilizations, interlaced with mathematical, astronomical, and historical information.
• The Mas’udi Canon (Persian قانون مسعودي) – an extensive encyclopedia on astronomy, geography, and engineering, named after Mas’ud, son of Mahmud of Ghazni, to whom he dedicated
• Understanding Astrology (Arabic التفهيم لصناعة التنجيم) – a question and answer style book about mathematics and astronomy, in Arabic and Persian
• Pharmacy – about drugs and medicines
• Gems (Arabic الجماهر في معرفة الجواهر) about geology, minerals, and gems, dedicated to Mawdud son of Mas’ud
• Astrolabe
• A historical summary book
• History of Mahmud of Ghazni and his father
• History of Khawarazm

Anthropology

Biruni has been described as “the first anthropologist”. He wrote detailed comparative studies on the anthropology of peoples, religions and cultures in the Middle East, Mediterranean and South Asia. Biruni’s anthropology of religion was only possible for a scholar deeply immersed in the lore of other nations. Biruni has also been praised by several scholars for his Islamic anthropology.

Astronomy

A statue of Biruni adorns the southwest entrance of Laleh Park in Tehran, Iran.

Instruments

In astronomy, al-Biruni invented and wrote the earliest treatises on the planisphere and the orthographical astrolabe, as well as the armillary sphere, and was able to mathematically determine the direction of the Qibla from any place in the world.^[15][16]

He also invented an early hodometer, and the first mechanical lunisolar calendar computer which employed a gear train and eight gear-wheels. These were early examples of fixed-wired knowledge processing machines.

Theories

Al-Biruni was the first to conduct elaborate experiments related to astronomical phenomena. He discovered the Milky Way galaxy to be a collection of numerous nebulous stars. In Khorasan, he observed and described the solar eclipse on April 8, 1019, and the lunar eclipse on September 17, 1019, in detail, and gave the exact latitudes of the stars during the lunar eclipse.

In 1030, Biruni discussed the Indian heliocentric theories of Aryabhata, Brahmagupta and Varahamihira in his Indica. Biruni noted that the question of heliocentricity was a philosophical rather than a mathematical problem.

In 1031, al-Biruni completed his extensive astronomical encyclopaedia Kitab al-Qanun al-Mas’udi (Latinized as Canon Mas’udicus), in which he recorded his astronomical findings and formulated astronomical tables. The book introduces the mathematical technique of analysing the acceleration of the planets, and first states that the motions of the solar apogee and the precession are not identical. Al-Biruni also discovered that the distance between the Earth and the Sun is larger than Ptolemy’s estimate, on the basis that Ptolemy disregarded the annual solar eclipses.

Abu Said Sinjari, a contemporary of al-Biruni, suggested the possible heliocentric movement of the Earth around the Sun, which al-Biruni did not reject. Al-Biruni agreed with the Earth’s rotation about its own axis, and while he was initially neutral regarding the heliocentric and geocentric models, he considered heliocentrism to be a philosophical problem. He remarked that if the Earth rotates on its axis and moves around the Sun, it would remain consistent with his astronomical parameters:

“Rotation of the earth would in no way invalidate astronomical calculations, for all the astronomical data are as explicable in terms of the one theory as of the other. The problem is thus difficult of solution.”

Will Durant wrote the following on al-Biruni’s contributions to astronomy:

“He wrote treatises on the astrolabe, the planisphere, the armillary sphere; and formulated astronomical tables for Sultan Masud. He took it for granted that the earth is round, noted “the attraction of all things towards the center of the earth,” and remarked that astronomic data can be explained as well by supposing that the earth turns daily on its axis and annually around the sun, as by the reverse hypothesis.”

Chemistry

Along with al-Kindi and Avicenna, al-Biruni was one of the first chemists to reject the theory of the transmuation of metals supported by some alchemists.

Earth sciences

Biruni made a number of contributions to the Earth sciences. In particular, he is regarded as the father of geodesy,^[7][26] and has made significant contributions to cartography, geography, and geology.

Cartography

By the age of 22, he had written several short works, including a study of map projections, Cartography, which included a method for projecting a hemisphere on a plane.

Geodesy and Geography

At the age of 17, Biruni calculated the latitude of Kath, Khwarazm, using the maximum altitude of the Sun. Biruni also solved a complex geodesic equation in order to accurately compute the Earth’s circumference, which were close to modern values of the Earth’s circumference. His estimate of 6,339.9 km for the Earth radius was only 16.8 km less than the modern value of 6,356.7 km.

John J. O’Connor and Edmund F. Robertson write in the MacTutor History of Mathematics archive:

“Important contributions to geodesy and geography were also made by al-Biruni. He introduced techniques to measure the earth and distances on it using triangulation. He found the radius of the earth to be 6339.6 km, a value not obtained in the West until the 16th century. His Masudic canon contains a table giving the coordinates of six hundred places, almost all of which he had direct knowledge.”

Geology

Among his writings on geology, Biruni wrote the following on the geology of India:

“But if you see the soil of India with your own eyes and meditate on its nature, if you consider the rounded stones found in earth however deeply you dig, stones that are huge near the mountains and where the rivers have a violent current: stones that are of smaller size at a greater distance from the mountains and where the streams flow more slowly: stones that appear pulverised in the shape of sand where the streams begin to stagnate near their mouths and near the sea – if you consider all this you can scarcely help thinking that India was once a sea, which by degrees has been filled up by the alluvium of the streams.”

History

Chronology

By the age of 27, in the year 1000, he had written a book called Chronology which referred to other works he had completed (now lost) that included one book about the astrolabe, one about the decimal system, four about astrology, and two about history.

He discussed more on his idea of history in another work, The Chronology of the Ancient Nations.

Indology

Until the 10th century, history most often meant political and military history, but this was not so with Persian historian Biruni (973-1048). In his Kitab fi Tahqiq ma l’il-Hind (Researches on India), he did not record political and military history in any detail, but wrote more on India’s cultural, scientific, social and religious history. Biruni is now regarded as the father of Indology.

Mathematics

He made significant contributions to mathematics, especially in the fields of theoretical and practical arithmetic, summation of series, combinatorial analysis, the rule of three, irrational numbers, ratio theory, algebraic definitions, method of solving algebraic equations, geometry, and the development of Archimedes’ theorems.

Medicine

Al-Biruni’s Kitab-al-Saidana was an extensive medical encyclopedia which synthesized Islamic medicine with Indian medicine. His medical investigations included one of the earliest descriptions on Siamese twins.

Physics

Celestial mechanics

In the celestial mechanics field of physics, al-Biruni described the Earth’s gravitation as:

“The attraction of all things towards the centre of the earth.”

He also discovered that gravity exists within the heavenly bodies and celestial spheres, and he criticized Aristotle’s views of them not having any levity or gravity and of circular motion being an innate property of the heavenly bodies.

Dynamics and kinematics

In the dynamics and kinematics fields of mechanics, al-Biruni was the first to realize that acceleration is connected with non-uniform motion, which is part of Newton’s second law of motion.

Natural philosophy

Al-Biruni and Abu Ali ibn Sina (Avicenna), who are regarded as two of the greatest polymaths in Persian history, were both colleagues and knew each other since the turn of the millenium. Al-Biruni later engaged in a written debate with Avicenna, with al-Biruni criticizing Aristotelian natural philosophy and the Peripatetic school, while Avicenna and his student Ahmad ibn ‘Ali al-Ma’sumi respond to al-Biruni’s criticisms in writing. Al-Biruni began by asking Avicenna eighteen questions, ten of which were criticisms of Aristotle’s On the Heavens, with his first question criticizing Aristotle’s reasons for denying the existence of levity or gravity in the celestial spheres and the Aristotelian notion of circular motion being an innate property of the heavenly bodies.

Al-Biruni’s second question criticizes Aristotle’s over-reliance on more ancient views concerning the heavens, while the third criticizes the Aristotelian view that space has only six directions. The fourth question deals with the continuity and discontinuity of physical bodies, while the fifth criticizes the Peripatetic school’s denial of the possibility of there existing another world completely different from the world known to them. In his sixth question, al-Biruni rejects Aristotle’s view on the celestial spheres having circular orbits rather than elliptic orbits. In his seventh question, he rejects Aristotle’s notion that the motion of the heavens begins from the right side and from the east, while his eighth question concerns Aristotle’s view on the fire element being spherical. The ninth question concerns the movement of heat, and the tenth question concerns the transformation of elements. The eleventh question concerns the burning of bodies by radiation reflecting off a flask filled with water, and the twelveth concerns the natural tendency of the classical elements in their upward and downward movements. The thirteenth question deals with vision, while the fourteenth concerns habitation on different parts of Earth. His fifteenth question asks how two opposite squares in a square divided into four can be tangential, while the sixteenth question concerns vacuum. His seventeenth question asks “if things expand upon heating and contract upon cooling, why does a flask filled with water break when water freezes in it?” His eighteenth and final question concerns the observable phenomenon of ice floating on water.

After Avicenna responded to the questions, al-Biruni was unsatisfied with some of the answers and wrote back commenting on them, after which Avicenna’s student Ahmad ibn ‘Ali al-Ma’sumi wrote back on behalf of Avicenna.

Optics

In optics, al-Biruni was one of the first, along with Ibn al-Haytham, to discover that the speed of light was finite. Al-Biruni was also the first to discover that the speed of light is much faster than the speed of sound.

Statics

In statics, al-Biruni measured the specific gravities of eighteen gemstones, and discovered that there is a correlation between the specific gravity of an object and the volume of water it displaces. He also introduced the method of checking tests during experiments, measured the weights of various liquids, and recorded the differences in weight between fresh water and salt water, and between hot water and cold water.

During his experiments, he invented the conical measure, in order to find the ratio between the weight of a substance in air and the weight of water displaced, and to accurately measure the specific weights of the gemstones and their corresponding metals, which are very close to modern measurements.

Theology

Islamic theology

Al-Biruni was a supporter of the Ash’ari school of Islamic theology. He assigned to the Qur’an a separate and autonomous realm of its own and held that:

“[the Qur'an] does not interfere in the business of science nor does it infringe on the realm of science.”

Comparative religion

He wrote works on both Islamic theology and Indian theology, and wrote on the topic comparative religion, comparing both religions. His comparisons included the following comparison between the Qur’an and the Indian religious scriptures in the “On the Configuration of the Heavens and the Earth According to [Indian] astrologers” chapter of the Indica:

“[The views of Indian astrologers] have developed in a way which is different from those of our [Muslim] fellows; this is because unlike the scriptures revealed before it, the Qur’an does not articulate on this subject [of astronomy], or any other [field of] necessary [knowledge] any assertion that would require erratic interpretations in order to harmonize it with that which is known by necessity.”

“[In contrast, the religious and transmitted books of the Indians do indeed speak] of the configuration of the universe in a way which contradicts the truth which is known to their own astrologers.”

en.wikipedia.org

Ibn al-Haytham is regarded as the father of optics, for his influential Book of Optics, which correctly explained and proved the modern intromission theory of vision, and for his experiments on optics, including experiments on lenses, mirrors, refraction, reflection, and the dispersion of light into its constituent colours. He also explained binocular vision and the moon illusion, speculated on the finite speed, rectilinear propagation and electromagnetic aspects of light, and argued that rays of light are streams of energy particles travelling in straight lines. Due to his quantitative, empirical and experimental approach to physics and science, he is considered the pioneer of the modern scientific method and experimental physics, and some have described him as the “first scientist” for this reason. He is also considered by some to be the founder of psychophysics and experimental psychology, for his experimental approach to the psychology of visual perception, and a pioneer of the philosophical field of phenomenology. His Book of Optics has been ranked alongside Isaac Newton’s Philosophiae Naturalis Principia Mathematica as one of the most influential books ever written in the history of physics.

Among his other achievements, Ibn al-Haytham described the pinhole camera and invented the camera obscura (a precursor to the modern camera), discovered Fermat’s principle of least time and Newton’s first law of motion, described the attraction between masses and was aware of the magnitude of acceleration due to gravity, discovered that the heavenly bodies were accountable to the laws of physics, presented the earliest critique and reform of the Ptolemaic model, first stated Wilson’s theorem in number theory, pioneered analytic geometry, formulated and solved Alhazen’s problem geometrically, developed and proved the earliest general formula for infinitesimal and integral calculus using mathematical induction, and in his optical research, laid the foundations for the later development of telescopic astronomy, as well as the microscope and the use of optical aids in Renaissance art.

Biography

Abu ‘Ali al-Hasan ibn al-Hasan ibn al-Haytham was born in the Arab city of Basra, Iraq (Mesopotamia), then part of the Shia Muslim Buyid dynasty of Persia, and he probably died in Cairo, Egypt. Known in the West as Alhacen or Alhazen, Ibn al-Haytham was born in 965 in Basra, and was educated there and in Baghdad. He was a supporter of the Ash’ari school of Islamic theology.

One account of his career has him summoned to Egypt by the mercurial caliph Hakim to regulate the flooding of the Nile. After his field work made him aware of the impracticality of this scheme, and fearing the caliph’s anger, he feigned madness. He was kept under house arrest until Hakim’s death in 1021. During this time, he wrote his influential Book of Optics and scores of other important treatises on physics and mathematics. He later traveled to Spain and, during this period, he had ample time for his scientific pursuits, which included optics, mathematics, physics, medicine, and the development of scientific methods on each of which he has left several outstanding books.

Legacy

Ibn al-Haytham was one of the most eminent physicists, whose development of optics and the scientific method are outstanding. Ibn al-Haytham’s work on optics is credited with contributing a new emphasis on experiment. His influence on physical sciences in general, and optics in particular, has been held in high esteem and, in fact, it ushered in a new era in optical research, both in theory and practice. The scientific method is considered to be so fundamental to modern science that some – especially philosophers of science and practicing scientists – consider earlier inquiries into nature to be pre-scientific. Due to its importance in the history of science, some have considered his development of the scientific method to be the most important scientific development of the second millenium.

Rosanna Gorini wrote the following on Ibn al-Haytham’s development of the scientific method:

“According to the majority of the historians al-Haytham was the pioneer of the modern scientific method. With his book he changed the meaning of the term optics and established experiments as the norm of proof in the field. His investigations are based not on abstract theories, but on experimental evidences and his experiments were systematic and repeatable.”

Roshdi Rashed wrote the following on Ibn al-Haytham:

“His work on optics, which includes a theory of vision and a theory of light, is considered by many to be his most important contribution, setting the scene for developments well into the 17th century. His contributions to geometry and number theory go well beyond the archimedean tradition. And by promoting the use of experiments in scientific research, al-Haytham played an important part in setting the scene for modern science.”

Nobel Prize winning physicist Abdus Salam wrote:

“Ibn-al-Haitham (Alhazen, 965-1039 CE) was one of the greatest physicists of all time. He made experimental contributions of the highest order in optics. He enunciated that a ray of light, in passing through a medium, takes the path which is the easier and ‘quicker’. In this he was anticipating Fermat’s Principle of Least Time by many centuries. He enunciated the law of inertia, later to become Newton’s first law of motion. Part V of Roger Bacon’s “Opus Majus” is practically an annotation to Ibn al Haitham’s Optics.”

George Sarton, the “father of the history of science”, wrote in the Introduction to the History of Science:

“[Ibn al-Haytham] was not only the greatest Muslim physicist, but by all means the greatest of mediaeval times.”

“Ibn Haytham’s writings reveal his fine development of the experimental faculty. His tables of corresponding angles of incidence and refraction of light passing from one medium to another show how closely he had approached discovering the law of constancy of ratio of sines, later attributed to Snell. He accounted correctly for twilight as due to atmospheric refraction, estimating the sun’s depression to be 19 degrees below the horizon, at the commencement of the phenomenon in the mornings or at its termination in the evenings.”

Robert S. Elliot wrote the following on the Book of Optics:

“Alhazen was one of the ablest students of optics of all times and published a seven-volume treatise on this subject which had great celebrity throughout the medieval period and strongly influenced Western thought, notably that of Roger Bacon and Kepler. This treatise discussed concave and convex mirrors in both cylindrical and spherical geometries, anticipated Fermat’s law of least time, and considered refraction and the magnifying power of lenses. It contained a remarkably lucid description of the optical system of the eye, which study led Alhazen to the belief that light consists of rays which originate in the object seen, and not in the eye, a view contrary to that of Euclid and Ptolemy.”

The Biographical Dictionary of Scientists wrote the following on Ibn al-Haytham::

“He was probably the greatest scientist of the Middle Ages and his work remained unsurpassed for nearly 600 years until the time of Johannes Kepler.”

The Latin translation of his main work, Kitab al-Manazir, exerted a great influence upon Western science e.g. on the work of Roger Bacon, who cites him by name, and Kepler. It brought about a great progress in experimental methods. His research in catoptrics centered on spherical and parabolic mirrors and spherical aberration. He made the important observation that the ratio between the angle of incidence and refraction does not remain constant and investigated the magnifying power of a lens. His work on catoptrics also contains the important problem known as Alhazen’s problem.

The list of his books runs to 200 or so, yet very few of the books have survived. Even his monumental treatise on optics survived only through its Latin translation. During the Middle Ages his books on cosmology were translated into Latin, Hebrew and other languages.

The Alhazen crater on the Moon was named in his honour. Ibn al-Haytham is also featured on the obverse of the Iraqi 10,000 dinars banknote issued in 2003. The asteroid “59239 Alhazen” was also named in his honour, while Iran’s largest laser research facility, located in the Atomic Energy Organization of Iran headquarters in Tehran, is named after him as well.

en.wikipedia.org