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.

Manuscript tradition

For a long time, only an incomplete version of the account was known, as transmitted in the geographical dictionary of Yaqut (under the headings Atil, Bashgird, Bulghar, Khazar, Khwarizm, Rus), published in 1823 by Fraehn. Only in 1923 was a manuscript discovered by the Turkish scholar of Bashkir origin Zeki Validi Togan in the library of the Iranian city of Mashhad. The manuscript MS 5229 dates from the 13th century (7th cent. Hijra) and consists of 420 pages (210 folia). Besides other geographical treatises, it contains a fuller version of Ibn Fadlan’s text (pp. 390-420). Additional passages not preserved in MS 5229 are quoted in the work of the 16th century Persian geographer Amin Razi called Haft Iqlim “Seven Climes”.

The Embassy

Ibn Fadlan was sent from Baghdad in 921 to serve as the secretary to an ambassador from the Abbasid Caliph al-Muqtadir to the iltabar (vassal-king under the Khazars) of the Volga Bulgaria, Almış.

The embassy’s objective was to have the king of the Bolğars pay homage to Caliph al-Muqtadir and, in return, to give the king money to pay for the construction of a fortress. Although they reached Bolğar, the mission failed because they were unable to collect the money intended for the king. Annoyed at not receiving the promised sum, the king refused to switch from the Maliki rite to the Hanafi rite of Baghdad.

The embassy left Baghdad on June 21, 921 (11 Safar 309). It reached the Bulghars after much hardship on May 12, 922 (12 Muharram 310) (This day is an official religious holiday in modern Tatarstan). The journey took Ibn Fadlan from Baghdad to Bukhara, to Khwarizm (south of the Aral Sea), to Jurjaniya (where his party spent the winter), north across the Ural River until they reached the towns of the Bulghars at the three lakes of the Volga north of the Samara bend.

After arriving in Bolğar, Ahmad ibn Fadlan made a trip to Wisu and recorded his observations of trade between the Volga Bolğars and local Finnic tribes.

The Rus

A substantial part of Ibn Fadlan’s account is dedicated to the description of a people he called the Rus روس or Rusiyyah. Most scholars identify them with the Rus’ or Varangians, which would make Ibn Fadlan’s account one of the earliest portrayals of Vikings.

The Rus appear as traders that set up shop on the river banks nearby the Bolğar camp. They are described as having the most perfect bodies, tall as palm-trees, with blond hair and ruddy skin. They are tattooed from “fingernails to neck” with dark blue “tree patterns” and other “figures” and that all men are armed with an axe and a long knife.

Ibn Fadlan describes the hygiene of the Rusiyyah as disgusting (while also noting with some astonishment that they comb their hair every day) and considers them vulgar and unsophisticated. In that, his impressions contradict those of the Persian traveler Ibn Rustah. He also describes in great detail the funeral of one of their chieftains (a ship burial involving human sacrifice). Some scholars believe that it took place in the modern Balymer complex.

Fiction

Elements of Ibn Fadlan’s account are used in the novel Eaters of the Dead by Michael Crichton (filmed as The 13th Warrior with Antonio Banderas as Ibn Fadlan), in which the Arab ambassador is taken even further north and is involved in adventures inspired by the Old English epic Beowulf. Indeed Crichton designed “Eaters of the Dead” as being a fictional version of the historic events which created the basis of the epic “Beowulf”.

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.”

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