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History of Islamic Science 3
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Introduction to the History of Scienceby George Sarton
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The Time of Al-Razi
Second Half of Ninth Century

The whole ninth century was essentially a Muslim century. This more clear in the second half than of the first, since all the scientific leaders were Muslims, or at any rate were working with and for Muslims and wrote in Arabic.


Cultural Background

Abbasid Caliph Al-Mutawakkil (847-861) continued to protect men of science, chiefly the physicians, and he encouraged the school of translators headed by Hunain ibn Ishaq.
Da ud al-Zahiri founded a new school of theology, based upon a more literal interpretation of the Qur'an; however, did not survive very long. Muslim published a new collection of traditions, arranged according to legal topics, like Bukhari's, but more theoretical.
The Egyptian Dhul-Nun is generally considered the founder of Sufism, that is, of Muslim mysticism.



Arabic Mathematics and Astronomy

G. Sarton clarify that when he said  "Arabic" instead "Muslim" he means that some of the most important work accomplished under Muslim tutelage was actually done by non-Muslims but in Arabic language.
There were so many mathematical and astronomers in Islam that is necessary to divide them into four groups as he did before: geometers; arithmeticians; astronomers and trigometricians; astrologers.

Geometers: Al-Mahani wrote commentaries on Euclid and Archimedes, and tried to vain and divide a sphere into two segments, being in a given ratio.  Archimedian problem became a classical Muslim problem; it led to a cubic equation which was called al-Mahani's equation. Hilal al-Himsi translated the first four books of Apolloinos into Arabic.  Ahmed ibn Yusuf wrote a book on proportions which are of special importance, because through it Western mathematicians became acquainted with the theorem of Menelaos. Al-Nairizi wrote commentaries on Ptolemy and Euclid. Thabit ibn Qurra made very remarkable measurements of parabolas and paraboids, but is best known as the leader of a school of translators which produced Arabic versions of some of the mathematical classics: Euclid, Archimedes, Apollonios, Theodosios, Ptolemy, Thabit himself was the foremost translator and revised some of the translations made by others. The two most important translators of his school, outside of himself, were Yusuf al-Khuri and Ishaq ibn Hunain. A comparison of this brief account with the similar section in the previous chapter will show that much progress had already been made in geometry since the beginning of the century.

Arithmeticians: I mentioned in the previous chapter the writings of al-Kindi and al-Khwarizmi were in probability the main channels through which the Hindu numerals known in Islam and later in the West. The earliest Muslim documents bearing such numerals date from 874 and 888. The propagation of these numerals may have been accelerated by the fact that the Muslim trade was exceedingly active in those very days and reached every part of the world.
Thabit ibn Qurra developed the theory of amicable numbers. Qusta ibn Luqa translated Diophantos.

Astronomers and Trigonometricians: Al-Mahani made a series of astronomical observations from 855 to 866. Al-Nairizi compiled astronomical tables and wrote an elaborate treatise on the spherical astrolabe; he made systemic use of the tangent. Hamid ibn Ali became famous as a constructor of astrolabes. Thabit ibn Qurra published solar observations; he tried to improve the Ptolematic theory in planetary motions by the addition of a ninth sphere to account for the (imaginary) trepidation of the equinoxes. Qusta ibn Luqa wrote a treatise on the spherical astrolabes. Jabir ibn Sinan, of whom we know nothing, but who may have been al-Battani's father, constructed astronomical instruments, notably a spherical astrolabe.
The greatest astronomer of the age and one of the greatest of Islam was al-Battani (Albategnius). He made a number of observations from 877, on, compiled a catalogue of stars for the year 880, determined various astronomical coefficients with great accuracy, discovered the motion of the solar apsides, and made an elaborate astronomical treatise which remained authoritative until the Sixteen Century. That treatise included naturally a trigonometical summary wherein not only sines, but tangents and cotangents, are regularly used. It contains a table of contangents by degrees and theorem equivalent to our formula giving the cosine of a side of a spherical triangle in function of the cosine of the opposite angle and of the sines and cosines of the other side.

Astrologers: The most famous astrologers  were Abu Bakr (Albubather), Ahmed ibn Yusuf, and Ibn Qutaiba.
The whole mathematical and astronomical work was far more original than in the first half of the century and on a relatively high level. It is true, Thabit ibn Qurra introduced an unfortunate error of which a great many later astronomers (including Copernicus!) remained prisoners, but original research always implies the possibility of error. Thabit's error was no discreditable. The elaboration of trigonometry was continued with great skill and originality. Much attention was paid to astronomical instruments and especially to a new one, the spherical astrolabe, al-Battani's masterly work was a fitting climax to this wonderful activity.
So much for Islam. What was being done at the same time at the rest of the World? Nothing.



Muslim Alchemy and Physics

Al-Jahiz seems to have some chemical knowledge, for instance, he knew how to obtain ammonia from animal offals by dry distillation, but it would be absurd to call him a chemist. On the other hand, the great physician Al-Rhazi was undoubtedly a genuine chemist: he wrote various chemical treatises, described a number of chemical instruments, attempted to classify mineral substances, and even tried to apply his chemical knowledge to medical purposes. He may be considered a distant ancestor of the iatrochemists of the Sixteenth Century. He was also a physicist; he used the hydrostatic balance to make investigations on specific gravity. The mathematician al-Nairizi wrote a treatise on atmospheric phenomena.

Muslim Biology: The Muslims had little interest in natural history; they were certainly not tempted to study it for its own sake, but many of their current views on biological subjects may be found in their literary and historical compilations. The most remarkable example is "The Book of Plants" composed by the historian al-Dinawari. The purpose of that book was primarily philological, but contains much valuable information for the historian of botany. Al-Jahiz's "Book of Animals" is also a mine of information though most of it is folkloric rather than zoological.



Muslim Medicine

So much medical work was accomplished in Islam that is expedient to divide the physicians into two groups: those who were primarily practitioners and those who were primarily scholars and those who were engaged in translating the Greek medical classics into Syriac and Arabic. Of course, those of the second group were, all of them were for foreigners, non Muslims,; but even in the first group, one-half of the physicians was christians. thus the activity was christian rather than Muslim, but we must not forget that by far the greatest of all of them, al-Razi, was a Muslim.
The Persian al-Razi was simply the greatest clinician of Islam and of the whole middle ages; he was also, as we have seen, a chemist and physicist. It would be difficult to choose between him and his contemporary al-Battani: both were very great scientist who would have been conspicuous in any age. I decide to call this period "The Time of al-Razi" because the physician is known to the larger public than the astronomer, and also because his influence can be traced more directly throughout many centuries of human effort, East and West. I have already remarked that al-Razi might be considered to be one of the forerunners of the iatrochemists of the Renaissance. He wrote an immense medical encyclopaedia called Al-hawi ("Continens") and a monograph on measles and smallpox which is the masterpiece of Muslim medicine. Ya'qub ibn akhi Hizam was the author of a treatise on horsemanship, which contains some rudiments of veterinary art, the earliest work of its kind in Arabic.
The greatest of the translators was Hunain ibn Ishaq (Joannitius). He collected great medical manuscripts, translated many of them, supervised the activities of other scholars, and revised their translations. His role as regard to medical literature was very similar to that of Thabit ibn Qurra with regard to the mathematical and astronomical texts. The school of nestorian translators beaded by Hunain must have been quite considerable, for between them they managed to translate the greatest part of the Hippocratic and Galenic writings into Syriac and into Arabic. Hunain wrote also original works, notably a treatise on ophthalmology and the introduction to Galen's Ars parva which was immensely medical writings: Hunain's son Ishaq, Hubaish ibn al-Hassan, Isa ibn Yahia, Stephen son of Basil, Musa ibn Khalid, Thabit ibn Qurra, Yusuf al-Khuri. Hunain was a very great man, but he was more of a scholar than a scientist proper and his activity, which already had begun in the middle of the previous period, ended in the middle of this one; in other words al-Razi and al-Battani were one generation ahead of him. The time of Hunain, extending from 826 to 877, falls just between that of al-Khawarizimi and that of al-Razi.



AL-MAHANI
Abu Abdallah Mohammed ibn Isa al-Mahani, that is, from Mahana, Kirman, Persia. Flourished c. 860, died c. 874 to 884. Mathematician, astronomer. A series of observations of lunar and solar eclipses and planetary conjunctions, made by him from 853 to 866, was used by Ibn Yunus. He wrote commentaries on Euclid and Archimedes, and improved Ishaq ibn Hunain's translation of Menelaos's spherics. He tried vainly to solve an Archimedian problem: to divide a sphere by means of a plane into two segments being in a given ratio. That problem led to a cubic equation, x3 + c2b = cx2, which Muslim writers called al-Mahani's equation.
H. Suter: Die Mathematiker und Astronomen der Araber (26, 1900. His failure to solve the Archimedian problem is quoted by 'Omar al-Khayyami'). See Fr. Woepcke: L'algebra d'Omar Alkhayyami (2, 96 sq., Paris, 1851).

AHMED IBN YUSUF
Abu Ja'far Ahmed ibn Yusuf ibn Ibrahim al-Daya al Misri, i.e., the Egyptian.  Flourished in Egypt in the second half and died about the Third Century H., c. 912. Mathematician. Secretary of the Tulunids, who ruled in Egypt from 868 to 905. He wrote a book on similar arcs (De Similibus arcubus), commentary on Ptolemy's Centiloquium, and a book on proportions ("De proportione et Proportionalitate"). The latter book is important because it influenced mediaeval thought through Leonardo de Pisa and Jordanus Nemorarius (theorem of Menelaos about the triangle cut by a transversal; al-qatta, sector; hence figura cata, regula catta).
M. Cantor: Ahmed und sein Buch Uber die Proportionen (Bibliotheca Mathematica, 7-9, 1888).

AL-NAIRIZI
Latin name: Anaritius. Abu-l-Abbas al-Fadl ibn Hatim al-Nairizi (i.e., from Nairiz, near Shiraz). Flourished under al-Mu'tadid, Caliph from 892 to 902, died c. 922. Astronomer, Mathematician. He compiled astronomical tables and wrote for al-Mu'tadid a book on atmospheric phenomena, He wrote commentaries on Ptolemy and Euclid. The latter were translated by Gherardo da Cermona. Al-Nairizi used the so-called umbra (versa), the equivalent to the tangent, as a genuine trigonometric line (but he was anticipated in this by Habash, q. v., first half of ninth century). He wrote a treatise on he spherical astrolabe, which is very elaborate and seems to be the best Arabic work on the subject. It is divided into four books: (1) Historical and critical introduction; (2) Description of the spherical astrolabe; its superiority over plane astrolabes and all other astronomical instruments; (3 and 4) Applications.
H. Suter: Die Mathematiker und Astronomen der Araber (45, 1900); Nachtrage (164, 1902).

THABIT IBN QURRA
Abu Hassan Thabit ibn Qurra Marawan al-Harrani, that is, from Harran, Mesopotamia, born 826-27 (or 835-36), flourished in Bagdad, died in 901. Harranian physician, astronomer, mathematician. one of the greatest translators from Greek and Syriac into Arabic; the founder of a school of translators, in which many of his own family we remembers. apollonios (Books 5 to 7), Archimedes, Euclid, Theodosios, Ptolemy (geography), Galen, Eutocios were translated by him or under his direction, or translations made by others (e.g., Ishaq ibn Hunain) were revised by him. He published solar observations, explaining his methods. to the eight Ptolemaic spheres he added a ninth one (primum mobile) to account for the imaginary trepidation of the equinoxes (he is chiefly responsible for the introduction of this erroneous theory). His mensurations of parabolas and paraboloids are very remarkable. He improved the theory of amicable numbers (if p = 3.2n - 1; q = 3.2n-1-1; r = 9.22n-1-1; and if p, q, and r are prime together, 2npq and 2nr are amicable numbers). Many mathematical, astronomical, also anatomical and medical, writings are ascribed to him (most of them in Arabic, some in Syriac).
Fihrist (272, and comment. by index). F. Wustenfled: Geschichte der arabischen Aerzte (34-36, 1840. Followed by notices on other members of the same family).

YUSUF AL-KHURI
Joseph the Priest. Also called Yusuf al-Qass (same meaning) or al-Sahir (the vigilant). He was still living under the caliphate of al-Muqtafi (902 to 908). Physician and mathematician. Translator from Syriac into Arabic. He translated Archimedes's lost work on the triangles and Galen's "De simlicium temperamentis et facultatibus." That the first translation was revised by Sinan ibn Thabit ibn Qurra (q. v., first half of first century), the second by Ishaq.
H. Suter: Die Mathematiker der Araber (52, 224, 1900). Max Meyerhof: NewLight on Hunain ibn Ishaq (Isis, VIII, 704, 1926).

HAMID IBN ALI
Abu-l-Rabi Hamid ibn Ali al-Wasiti. From Waist in Lower Mesopotamia. Flourished in the ninth century, probably toward the end. Muslim astronomer. According to Ibn Yunus, Ali ibn Isa and Hamid were the foremost constructors of astrolabes. Ibn Yunus compares them to Ptolemy and Galen! This proves the importance which Muslims attached to good instruments.
H. Suter: Mathematiker (40, 1900).



MUSLIM (OR ARABIC) MEDICINE

SABUR IBN SAHL
Flourished at Jundishapur. Died Dec. 3, 860. Christian physician. He wrote an antidotary (Aqrabadhin), divided into 22 books, which was possibly the earliest of its kind to influence Muslim medicine, and other medical works. This antidotary enjoyed much popularity until it was superseded Ibn al-Tilmidh's new one (q. v., first half of twelfth century).
 F. Wustenfled:  arabische Aerzte (25, 1840).

YAHYA IBN SARAFYUN
Separion the elder. Yahya ibn Sarafyun. Flourished in Damascus in the second half of the ninth century. Christian physician who wrote in Syriac two medical compilations (Kunnash, pandects), one in 12 books, the other in 7 books. the latter was translated into Arabic by various writers and into Latin by Gherardo da Cermona (Practica sive breviarium). It was very popular during the middle ages. Its last book deals with antidotes. Ibn Srarfyun attached great importance to venesection and gave subtle prescriptions concerning the choice of the veins to be opened.
Fihrist (29; 303,1. 3; and comm. 296, note 1). Wustenfeld: Geschichte der arabischen Aerzte (49, 1840).

AL-RAZI
In Latin: Rhazes. Abu Bakr Mohammed ibn Zakaria al Razi. Born in Ray, near Tehran, Persia, about the middle of the ninth century. Flourished in Ray and in Bagdad. died 923-24. Physician, physicist, alchemist. The greatest clinician of Islam and middle ages. Galenic in theory, he combined with his immense learning true Hippocratic wisdom. His chemical knowledge was applied by him to medicine; he might be considered an ancestor of the iatrochemists. Of his many writings, the most important are the "Kitab al Hawi" (Continens), an enormous encyclopaedia containing many extracts from Greek and Hindu authors and also observations of his own; the "Kitab al Mansuri" (Liber Almansoris), a smaller compilation in ten books based largely on Greek science, and finally his famous monograph on smallpox and measles "Kitab al-jadari wal-hasba" (De variolis et morbiliis; de peste, de pestilentia), the oldest description of variola and the masterpiece of Muslim medicine. many contributions to gynaecology, obstetrics, and ophthalmic surgery can be traced back to him.
He made investigations on specific gravity by means of the hydrostatic balance, which he called al-mizan al-tabi'i. Various chemical treatises are ascribed to him, and one of them (Arcandorum liber, apocryphal?) contains a list of 25 pieces of chemical apparatus. He also made an attempt to classify chemical substracts.
The al-Hawi has not been published, and there is not even a single complete manuscript in existence. A latin translation, Liber dictus Elhavi, appeared in Brescia (1486), followed by various Ventian editions. The liber ad Almansurem, in ten books was first published in Milano (1481) and was frequently republished.

HUNAIN IBN ISHAQ
In Latin, Joannitius. Abu Zaid Hunain ibn Ishaq al-Ibadi. Born in Hira, 809-10. Flourished at Jundishapur, then in Bagdad, where he died in October 877. Famous Nestorian physician; one of the greatest scholars and of the noblest men of his tome. Pupil of Ibn Masawiah. Employed by the Banu Musa to collect Greek manuscripts and translate them into arabic, he became the foremost translator of medical works. These translations were made partly with the assistance of other scholars.
It is reported that the Abbasid caliph al-Mutawakkil created (or endowed) a school where translations were made under Hunain's supervision. It is not too much to say that the translations made by Hunain and his disciplines marked a considerable progress in the history of scholarship. He took infinite pains to obtain manuscripts of the Greek medical texts; he collated them, examined the existing Syriac and Arabic versions, and translated them as accurately and as well as possible. His methods remind one of modern methods. to appreciate more the value of his efforts, one must realize that the Syriac versions were very unsatisfactory and the Arabic versions already available were hardly better. Hunain carefully compared these versions with the great text to prepare his new arabic translations. His activity was prodigious; it began as early as c.826 and lasted till the end of his days. It is typical of his scientific honesty that he very severely criticized the translations made by himself early in life. As his experience increased, his scientific ideal became more exacting. He translated a great many of Galen's works, also various writings of Hippocrates, Plato, Aristotle, Dioscordies, and Ptolemy's Quadripartitum. The importance of his activity can be measured in another way by stating that the translations prepared by Hunain and his school were the foundation of that Muslim canon of Knowledge which dominated medical thought almost to modern times.
Various medical and astronomical writings are ascribed to him (e. g., on the tides, on meteors, on the rainbow). His most Important work is his introduction to Galen's "Ars prava" ("Isagoge Johannitii ad Tegni Galeni") which was mensly popular during the Middle Ages and played the same part in the teaching of medicine as Porphyry's "Isagoge" in that of logic. Galenic classification extended and elaborated.
Fihrist (294 f and by index). Ferdinand Wustenfeld: Geschichte der arabischen Aerzte und Naturforscher.

QUSTA IBN LUQA
Qusta ibn Luqa al-Ba'labakki, i. e. from Baalbek or Heliopolis, Syria. Flourished in Bagdad, died in Armenia about the end of the third century H., i. e., c. 912. A Christian of Greek origin. Philosopher, Physician, mathematician, astronomer, Translations of Diophantos, Theodosios, Autolycos, Hypsicles, Aristarchos, Heron were made or revised by him, or made under his direction, He wrote commentaries on Euclid and a treatise on the spherical astrolabe.
Fihrist (295 and by index). C. Brockelmann : Geschichte der arabischen Litteratur (Vol. I, 204-205, 512, 1898).

JABIR IBN SINAN
Jaber ibn Sinan al-Harrani is one of the makers of astronomical instruments mentioned in the Fihrist at the end of the mathematical section. Nothing else is said of him, but al-Battani's full name suggests that this Jaber may have been his father. According to al-Biruni, this Jaber was the first to make a spherical astrolabe.
Fihrist (p. 284). Sutre's translation (p. 41). H. Suter : Die Mathematiker (68, 224, 1900).

AL-BATTANI
In Latin: Albategnius, Albatenius. The origin of that nisba is unknown. Abu Abdallah Mohammed ibn Jabir ibn Sinan al-Battani, al-Harrani, al-Sabi, born before 858 in or near Harran. Flourished at al-Raqqa, in the Euphrates, died in 929 near Samarra. Of Sabin origin, though himself a Muslim. The greatest astronomer of his race and time and one of the greatest of Islam. Various astrological writings, including a commentary on Ptolemy's "Tetrabiblon" are ascribed to him, but his main work is an astronomical treatise with tables ("De scientia stellarum," " De numeris stellarum et motibus") which was extremely influential until the Renaissance. He made astronomical observations of remarkable range and accuracy from 877 on. His tables contain a catalogue of fixed stars for the years 880-81 (not 911-12). He found that the longitude of the sun's apogee had increased by 16o47` increase since Ptolemy, that implied the discovery the motion of the solar apsides and of a slow variation in the equation of time. He determined many astronomical coefficients with great accuracy: precession 54.5`` a year; inclination of the ecliptic, 23o35`. He did not believe in the trepidation of the equinoxes. (Copernicus believed in it!)
The third chapter of his astronomy is devoted to trigonometry. He used sines regularly with a clear consciousness of their superiority over the Greek chords. He completed the introduction of the functions umbra extensa and umbera versa (hence our contangents and tangents) and gave a table of contangents be degrees. He knew the relation between the sides and angles of a spherical triangle which we express by the formula
                                cos a = cos c cos c + sin b sin c cos A.
 H. Suter : Die Mathematiker und Astronomen der Araber (45-47, 1900).

ABU BAKR
In Latin: Albubather. Abu Bakr al-Hassan ibn al-Khasib. Of Persian origin. Flourished probably in the third quarter of the ninth century. astrologer who wrote in Persian and arabic and would hardly deserve to be quoted but for the importance given to him in the middle ages. The work he is best known by ("De nativitatibus") was translated into Latin by one canonicus Salio in Padua 1218; it was also translated into Hebrew.
Fihrist (p. 276 and Commentary, p. 131). H. Suter : Die Mathematiker und Astronomen der Araber (32, 1900); Nachtrage (162, 1902); encycl. of Islam, II, 274, 1916.