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.
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 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.
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).
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.