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"O Allah! We seek goodness from Your Knowledge and with Your Power (and Might) We seek strength, and We ask from You Your Great Blessings, because You have the Power and We do not have the power. You Know everything and I do not know, and You have knowledge of the unseen. Oh Allah! If in Your Knowledge this action (We are about to take) is better for my religion and faith, for our life and end [death], for here [in this world] and the hereafter then make it destined for us and make it easy for us and then add blessings [baraka'] in it, for us. O Allah! In Your Knowledge if this action is bad for us, bad for our religion and faith, for our life and end [death], for here [in this world] and the hereafter then turn it away from us and turn us away from it and whatever is better for us, ordain [destine] that for us and then make us satisfied with it."

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Importance of a good shaykh by Shaykh Abd'al-Qadir al-Jilani Radi Allahu anhu

Al Ghawth al-Adham Shaykh Sayyad Abd'al-Qadir al-Jilani Radi 'Allahu anhu said: You must work hard to ensure that your hearts are not locked out of the door of His nearness. Be sensible! You are getting nowhere. You must seek the company of a Shaykh who is learned in the law [hukm] and knowledge ['ilm] of Allah (Almighty and Glorious is He), and who will show you the way toward Him. Without seeing the successful [muflih], one cannot succeed. If a person does not seek the company of scholars who put their knowledge into practice ['ulama 'ummal], he is a chicken from an egg abandoned by the rooster and the mother hen.

Seek the fellowship of those who enjoy fellowship with the Lord of Truth (Almighty and Glorious is He). What each of you should do, when the night has grown dark and people have gone to bed and their voices are silent, is get up, take an ablution [yatawadda'], perform two cycles of ritual prayer [yusalli rak'atain] and say: "O my Lord, guide me to one of Your righteous servants near to You, so that he may guide me toward You and make me familiar with Your path." The instrument [sabab] is necessary. Allah (Almighty and Glorious is He) was quite capable of guiding [His servants] to Him without the Prophets [anbiya']. Be sensible! You are getting nowhere. You must awaken from your heedless folly. As the Beloved Prophet Salla Allahu ta'ala 'alayhi wa Sallam has said: If someone relies entirely on his own subjective judgement, he will go astray. Try to find someone who will be a mirror for the face of your religion [din], just as you look in the mirror to check the appearance of your outer face, your turban and your hair. Be sensible! What is this crazy foolishness? You say, "I don't need anyone to teach me," and yet the Beloved Prophet Salla Allahu ta'ala 'alayhi wa Sallam has said: The believer is the believer's mirror [al-mu'minu mir'atu 'l-mu'min].

When the believer's faith is sound, he comes to be a mirror for all creatures. They behold their religious faces [wujuh adyanihim] reflected in the mirror of his speech, every time they see him and get close to him. What is this craziness? Not a moment goes by without your begging Allah (Almighty and Glorious is He) to provide you with more than you already have to eat, to drink, and to wear, with more sexual opportunities and more income. These are not things that could increase or decrease, even if you were to be joined in your plea by every supplicant whose prayers are answered [da 'in mujab].

Supplication [da 'wa] will neither increase one's sustenance by so much as an atom, nor reduce it by an atom. This is a foregone conclusion [mafrugh minhu]. You must devote your attention to doing what you have been commanded to do, and to avoiding what you have been forbidden to do. You should not worry about that which is bound to come your way, because He guarantees that it will come to you. Allotted shares [aqsam] arrive at their appointed times, whether they be sweet or bitter, whether you like them or dislike them.

The people [of the Way] attain to a condition in which they no longer have any prayer of supplication [du'a] or request [su'al] to make. They do not beg [in their prayers] to gain advantages, nor to get rid of disadvantages. Their supplication comes to be a matter concerning their hearts, sometimes for their own sake and sometimes for the sake of all creatures, so they utter the prayer of supplication without conscious premeditation [fi ghaiba].
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"O '' Allah, endow us with good behaviour in Your company under all circumstances!
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[When the believer's faith is sound], fasting [sawm], prayer [salat], remembrance [dhikr] and all acts of obedience [ta 'at] become second nature to him, mingled with his flesh and blood. Then he receives protection from Allah (Almighty and Glorious is He) under all circumstances. The restraint of the law [hukm] does not desert him, not for an instant, while he is on this course. The law comes to be like the vessel in which he sits, as he travels over the ocean of the power [qudra] of his Lord (Almighty and Glorious is He). He goes on traveling over it until he arrives at the shore of the hereafter, at the shore of the ocean of grace and the hand of nearness. Thus he is sometimes in the company of creatures and at certain times in the company of the Creator. His work and toil are with creatures, while his relaxation is with the Creator.
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From Shaykh 'Abd al-Qadir al-Jilani, "The Sublime Revelation (Al-Fath ar-Rabbani)," translated by Muhtar Holland (Al-Baz Publishing, Houston, 1992), p. 426-8.
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On the authority of Abu Hurayrah r.a., who said that Prophet Muhammad S.A.W. said: Allah SWT said:

Whosoever shows enmity to someone devoted to Me, I shall be at war with him. My servant draws not near to Me with anything more loved by Me than the religious duties I have enjoined upon him, and My servant continues to draw near to Me with supererogatory works so that I shall love him. When I love him I am his hearing with which he hears, his seeing with which he sees, his hand with which he strikes and his foot with which he walks. Were he to ask [something] of Me, I would surely give it to him, and were he to ask Me for refuge, I would surely grant him it. I do not hesitate about anything as much as I hesitate about [seizing] the soul of My faithful servant: he hates death and I hate hurting him. (It was related by al-Bukhari)
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“Allah! There is no God save Him, the Alive, the Eternal. Neither slumber nor sleep overtaketh Him. Unto Him belongeth whatsoever is in the heavens and whatsoever is in the earth. Who is he that intercedeth with Him save by His leave? He knoweth that which is in front of them and that which is behind them, while they encompass nothing of His knowledge save what He will. His throne includeth the heavens and the earth, and He is never weary of preserving them. He is the Sublime, the Tremendous.”

Tuesday, May 27, 2008

MUSLIM ANCIENT SCIENTIST PART 4

ORIGINAL SOURCE

Based on the book Introduction to the History of Science by George Sarton (provided with photos and portraits)Edited and prepared by Prof. Hamed A. Ead

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

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.

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.