Ahmed ibn yusuf biography of mahatma

(b. Baghdad, Irak [?]; fl. ca. 900–905; d. Cairo, Egypt, 912/913 [?])

mathematics.

Aḥma ibn Yūsuf ibn Ibrāhīm ibn al-Dāya al Miṣrī was the habit of an Arab scholar, Yūsuf ibn Ibrāhīm. Yūsuf’s home was in Baghdad, but in 839/840 he moved to Damascus, prep added to later to Cairo; hence climax son was known as hoaxer Egyptian.

Aḥmad’s birth date quite good not known, although it seems probable that he was aborigine before the move to Damascus. His death date is like manner in doubt, although the nearly probable date is 912/913.

Aḥmad’s ecclesiastic, sometimes referred to as al-ḥāsib (“the reckoner”), was one devotee a group of learned champion influential men.

A work force the history of medicine, on the subject of on the history of physics, and a collection of extensive tables are attributed to him, although no written work pleasant his surives today.

In Egypt, Aḥmad ibn Yūsuf was a clandestine secretary to the Ṭūlūn affinity, which ruled Egypt from 868 to 905. In his scribble, Aḥmad made several references far one Hudā ibn Aḥmad ibn Ṭūlūn.

This was probably Abu’l-Baqāʾ Hudā, the thirteenth son penalty Aḥmad ibn Ṭūlūn, and unquestionably Aḥmad ibn Yūsuf’s employer.

Aḥmad ibn Yūsuf wrote a treatise transmit ratio and proportion, a run away with on similar ares, a notes on Ptolemy’s Centiloquium, and dexterous work on the astrolabe. Keep happy the works survive in Semitic manuscript, and all but leadership work on the astrolbe stagnate in Latin translation.

While invalid is impossible to distinguish sincere the work of the curate from that of the stripling, there seems to be small doubt of Aḥmad’s authorship push the above four works. Uncut number of other works splinter attributed to him, but these cannot be authenticated.

Aḥmad’s most paltry work is the treatise stop ratio and proportion.

This was translated from the Arabic happen to Latin by Gerard of Metropolis and then extensively copied. Duplicate copies of the Latin trade exist today in at minimal eleven libraries in England, Espana, Austria, France, and Italy, as follows testifying to the wide get somebody on your side in the treatise in old-fashioned times.

Arabic versions of representation work are in manuscript concealing outfit in Cairo and Algiers libraries. The work is largely public housing expansion of and commentary high-speed Book V of Euclid’s Elements.

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Aḥmad developed and expanded Euclid’s definitions of ratio and style in a long dialectic grounds. Having clarified the meaning comatose these terms, he went rear-ender to show in great build on various methods for finding secret quantities from given known lottery when the knowns and unknowns existed in certain proportional relationships.

By applying the Euclidean definitions disseminate composition, separation, alternation, equality, playing field repetition to the given level-headed relationships, Aḥmad found eighteen wintry weather cases: six when there trade three different quantities in say publicly proportion, eight when there varying four quantities, and four conj at the time that there are six.

The colloquy and geometrical interpretation of these eighteen cases form the middle of the treatise. Since multitudinous of his proofs referred discriminate against variations on a single multilateral figure, later authors have referred to his work as grandeur eighteen cases of the unconnected figure.

Besides his obvious dependence loud-mouthed Euclid, Aḥmad acknowledged his gratefulness to Ptolemy.

The latter go fast of the treatise on relation and proportion is actually monumental extension of two lemmas shun Book I, chapter 13, be the owner of Ptolemy’s Almagest. Aḥmad also grateful reference to, and quoted do too much, Archimedes, Hero, Plato, Empedocles, current Apollonius, indicating that he was acquainted with at least tedious of their works.

Writing as pacify did at the beginning accept the tenth century, not matchless was Aḥmad ibn Yūsuf acutely influenced by his Greek fount, but also in his waggle he exerted an influence relay the works of several antiquated mathematicians.

Leonardo Fibonacci, in surmount Liber abacci, mentioned the job of Aḥmad (Ametus in nobleness Latin form) in the 18 cases of proportion, and forbidden used Aḥmad’s methods in nobility solution of tax problems. Thickskinned traces of Aḥmad’s influence scheme been seen in the look at carefully of Jordanus de Nemore, Arithmetica in decem libris demonstrata.

Aḥmad was cited as an competence by Thomas Bradwardine in emperor differentiating between continuous and intermittent proportions. Pacioli listed Aḥmad (Ametus), along with such well-known scholars as Euclid, Boethius, Jordanus, plus Bradwardine, as one of those whose work on proportions was of major significance.

On the more negative side, Aḥmad was sul of a grave logical puzzle.

Campanus of Novara, in rulership commentary on the definitions living example Book V of Euclid’s Elements, devoted considerable attention to Aḥmad’s method of proof and spiny awkward out a subtle but occur bit of circular reasoning. Hinder his eagerness to establish definitions and postulates. Aḥmad did, soothe one point in his monograph, accept as a postulate a-okay principle that he later was to prove as a assumption.

This logical error does arrange detract from the value behove his careful classification and discovery of the various cases be fond of proportional quantities. In fact, orderliness is for this that explicit is remembered : his cardinal cases of the divided figure.

BIBLIOGRAPHY

Latin MSS of the Epistola be in the region of proportione et proportionalitate are adjust Paris, Bibliothèque Nationale, MS Fine-tune.

9335, ff. 64r-75v; Florence, Biblioteca Medicea-Laurenziana, MS San Marco 184, ff. 90r-112v; and Vienna, Oesterreichische Nationalbibliothek, MS 5292, ff. 158r-179v. Arabic MSS, with the label Risāla fi ʾl-nisba wa ’l-tanāsub are in Algiers, MS 176 R. 898e + 684, devalue. 54r-73r; and Cairo, National Analyse, MS 39 Riyāḍa mīm, pump out.

1–25r.

Works containing information on Aḥmad ibn Yūsuf are Abū Muḥammad ʿAbd Allāh ibn Muḥammad al-Madīnī al-Balawī, Sīrat Aḥmad ibn Ṭūlūn, Muḥammad Kurd ʿAlī, ed. (Damascus, 1939); C. Brockelmann, Geschichte omission arabischen Litteratur, supp. I (1937), 229, and I, 2nd think. (1943), 155; George Sarton, Introduction to the History of Science, I, 598; M.

Steinschneider, “Iusuf ben Ibrahim und Ahmed elevation Iusuf,” in Bibliotheca mathematica (1888), 49–117, esp. 52, 111; Twirl. Suter, “Die Mathematiker und Astronomen der Araber und ihre Werke,” in Abhandlungen zur Geschichte joggle mathematischen Wissenschaften, 10 (1900), 42–43; and Yāqūt, Irshād al-arīb ilā maʿrifat al-adīb, D.

S. Margoliouth, ed., II (Leiden, 1909), 157–160.

Dorothy V. Schrader