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AL-SHĪRĀZĪ AND THE EMPIRICAL ORIGIN OF PTOLEMY'S EQUANT IN HIS MODEL OF THE SUPERIOR PLANETS

Published online by Cambridge University Press:  12 March 2013

Amir Mohammad Gamini*
Affiliation:
Iranian Institute of Philosophy, No. 4, Araklyan St., Neauphle-le-Château St., Vali-Asr Ave., P.O. Box: 14155-7166, Tehran 11336-14816, Iran
Hossein Masoumi Hamedani*
Affiliation:
Iranian Institute of Philosophy, No. 4, Araklyan St., Neauphle-le-Château St., Vali-Asr Ave., P.O. Box: 14155-7166, Tehran 11336-14816, Iran

Abstract

Ptolemy presents only one argument for the eccentricity in his models of the superior planets, while each one of them has two eccentricities: one for center of the uniform motion, the other for the center of the constant distance. To take into account the first eccentricity, he introduces the equant point, but he provides no argument for the eccentricity of the center of the deferent. Why is the second eccentricity different from the first one? The 13th century astronomer Quṭb al-Dīn al-Shīrāzī, a member of the famous school of Marāgha, who was interested in this problem, suggests the “retrograde arcs” as the empirical origin of the second eccentricity and develops an argument to justify this conjecture. Although his argument is not without difficulty, his suggestion is in line with the suggestions made by some historians of astronomy in recent decades.

Résumé

Ptolémée ne donne qu'un seul argument pour expliquer dans son système l'excentricité des planètes supérieures, alors que chacune d'elles a deux excentricités: l'une par rapport au centre du mouvement uniforme, l'autre par rapport au centre de la distance constante. Pour rendre compte de la première excentricité, il introduit le point équant, mais il ne donne en revanche aucun argument pour l'excentricité par rapport au centre du cercle déférent. Or, pourquoi la seconde excentricité est-elle différente de la première? Quṭb al-Dīn al-Shīrāzī, astronome du xiiie siècle membre de l'école de Marāgha, qui s'est intéressé à cette question, a fait l'hypothèse que les “arcs de rétrogradation” constituent l'origine empirique de cette seconde excentricité. Bien que l'argument sur lequel il appuie cette hypothèse ne soit pas exempt de difficultés, sa suggestion rejoint celles faites par des historiens de l'astronomie durant les dernières décennies.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2013

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