Thabit ibn Qurra: A pioneering Muslim polymath of the 9th century

Born in Harran, in Turkey’s Sanliurfa province in 836, Abu al-Hasan Thabit ibn Qurra al-Harrani al-Sabi, also known as Thabit Ibn Qurra, was a prolific scientist of the ninth century whose contributions have shaped modern mathematics, astronomy, mechanics, physics and more. 

He belonged to a family that raised many scholars. They were part of the Sabian community, mentioned in the Quran; the Sabians descended from the Babylonian star worshippers and their beliefs are what led them to produce so many astronomers and mathematicians.

Between 892 and 902, he was a distinguished scientist and physician in Baghdad, mainly under the reign of the Abbasid Caliph al-Mu‘tadid. 

There he studied philosophy and he translated the works of Greek mathematicians into Arabic. Thabit Ibn Qurra also wrote volumes on mathematics and astronomy, and was engaged in medicine. Besides this, Thabit also corrected some works that had been translated before him. Most of his scientific works were written in Arabic, but some in Syriac, too. 

He mainly contributed to science with translations in the fields of philosophy, mathematics, astronomy, medicine and natural sciences. According to some sources, Sabit has about 150 works in these fields.

Along with Hunayn ibn Ishaq al-Ibad, he is considered one of the two greatest translators in Islamic history.

Qurra’s contributions to mathematics can be summarised in three stages. The first is the translation of important works of Greek mathematicians into Arabic, or the correction of previous translations. In particular, Sabit translated all of Archimedes' mathematics into Arabic. Today, since the Greek originals belonging to Archimedes’ have been lost, they have hugely benefited from Thabit’s translations.

Qurra translated or edited, in full or in part, many of the Greek works by Euclid, Archimedes, Apollonius, Theodosius, and Menelaus. He also wrote commentaries on Euclid’s Elements and Ptolemy’s Almagest.

The second stage is Sabit's contribution to the formation of an Arabic mathematical language through translation and corrections. With the efforts of Thabit, Arabic, Greek or Syriac works of fixed mathematics found appropriate Arabic equivalents.

Some of the concepts he identified were replaced by Muslim mathematicians who lived after him, but many remained in use. Thabit Ibn Qurra’s contributions to in the third stage are original works that he authored in the fields of mathematics such as arithmetic (number theory), algebra, geometry, cone sections and trigonometry.

His work on integral calculus, some theorems of spherical trigonometry, analytic geometry, and non-Euclidean geometry, left lasting traces, especially in the expansion of the concept of numbers to include positive real numbers.

One of Thabit’s most important contributions to the theory of numbers was his translation of the Greek mathematician Nicomachus's introduction to arithmetic. Later, Euler generalised the formula developed by Thabit for friendly numbers with new possibilities given by modern Western European mathematics.

Furthermore, there is some evidence that shows Thabit was the first to solve the Menelaus problem. As it’s known, Menelaus' theorem relates ratios obtained by a line cutting the sides of a triangle. The converse of the theorem is also true and is extremely powerful in proving that three points are collinear.

Ptolemy was the one who also used Menelaus' complete spherical quadrilateral theorem to solve problems of spherical astronomy. Thabit Ibn Qurra revisited the subject in his own work and gave perfect proof of Menelaus' theorem.

He used a method similar to the integral calculation technique used in modern “calculus” during this calculation. Therefore, Thabit was introduced by David E. Smith (History of Mathematics) as one of the first founders of calculus.

As one of the first reformists to attempt to correct Ptolemy's system in the history of astronomy, he put forward the assumption of kinematics and tried to explain the phenomenon of motion with the eighth stroke.

Considered the founder of statics in the science of mechanics, he dealt with the issue of weights and reformulated Aristotle's dynamic principle, studying the problem of equilibrium. 

In astronomy, Thabit was the author of many treatises on the movement of the sun and moon, sundials, visibility of the new moon, and celestial spheres. In a well-known treatise extant only in a Latin version (De motu octave sphere), he added an eighth sphere, that of the fixed stars to Ptolemy’s spheres (those of the sun, moon, and five planets). He proposed the theory of “trepidation” to explain the precession of the equinoxes. This theory first appeared in Islamic astronomy in connection with his name.

In addition to all these, in other pieces he covered general medicine, diseases, embryology, blood circulation, anatomy of birds and veterinary medicine. 

After a decades filled with science and contributions to several disciplines, Thabit Ibn Qurra passed away on 19 February 901, in Baghdad.