A short note on the possible empirical origin of Ptolemy’s equant (Almagest X). This is Section II.8 of Quṭb al-Dīn al-Shīrāzī’s Nihāyat al-idrāk fī dirāyat al-aflāk, but in Edinburgh, EUL, Or. 397 and Mashhad, Holy Shrine, 5452 it is found as an independent work appended to al-Ṭūsī’s Taḥrīr al-Majisṭī (C.1.18). The version that is extant in the Edinburgh manuscript differs slightly from that in the other witnesses: it lacks a heading, but provides some additional lines at the end (cf. the edition in Gamini & Masoumi Hamedani, p. 67). Full title: Faṣl fī l-Ṭarīq alladhī bi-hī ʿalima Baṭlamyūs anna markaz al-ḥāmil fī kulli wāḥid min al-kawākib al-ʿulwiyya ʿalā muntaṣaf mā bayna markazay l-burūj wa-muʿaddil al-masīr.

Origin: Al-Shīrāzī finished his Nihāyat al-idrāk in Sivas in Shaʿbān 680/November-December 1281 (Niazi). However, the manuscript Oxford, BL, Thurston 3 is dated to 1262 and 1277 ce. It was written by al-Shīrāzī’s disciple or close collaborator Suhrāb ibn Amīr al-Ḥājj, the same scribe who also copied MS Leiden, UB, Or. 203, which contains a copy of the Nihāyat al-idrāk and is dated to 1283 ce. In Thurston 3 as well as in Mashhad, Holy Shrine, 5452, the method presented in this treatise is ascribed to Thābit b. Qurra (for which, however, there seems to be no evidence in the extant works by Thābit, see Gamini & Masoumi Hamedani, p. 61). Supposing that Suhrāb was well informed about the treatises of al-Shīrāzī, the following account seems most plausible: early on al-Shīrāzī wrote a short treatise on Ptolemy’s equant following a method already employed by Thābit b. Qurra, and later he inserted this into his Nihāyat al-idrāk.

Text: [Oxford, BL, Thurston 3]

[Incipit] (101v) إنّ بطلميوس أخذ بالرصد في سنين متوالية مقدار الرجوع أعني الدرج التي يرجع فيها الكوكب من فلك البروج من الوقوف الأوّل إلى الوقوف الثاني. [Explicit] (102r) ولأنّه استخرج الحركات والنسبة المذكورة من جداول القدماء قبل التصحيح قال في كتابه إنّه وجد هذا الخطّ ضعف هذا الخطّ بالتقريب. وهو أعلم بالسرائر إنّه هو العليم الحكيم.

[Edinburgh, EUL, Or. 397

[alternative Explicit] (235r) إنّ بطلميوس إنّما حكم بكون مركز الحاملين مركزي المعدّل ومعدّل المسير. ظنّا منه بأن فرضه بينهما وهو عليه فلمّا وافق محسوبة المرصود إطمان إلى ذلك وسبب ذلك أنّ هذا البرهان لم يذكر في المجسطي ولم يشتهر اشتهارًا غيره. تمّت والحمد لله شكرًا له.

Bibl.: SuterHeinrich Suter, Die Mathematiker und Astronomen der Araber und ihre Werke, Leipzig: Teubner, 1900, pp. 158–159 (no. 387); GAS VIFuat Sezgin, Geschichte des arabischen Schrifttums. Vol. VI: Astronomie bis ca. 430 H., Leiden: Brill, 1978, pp. 90 (no. 5c) and 168; F. Jamil Ragep, ‘Shīrāzī’s Nihāyat al-Idrāk: Introduction and Conclusion’, Tarikh-e Elm 11 (2013), pp. 41–57; Amir Mohammad Gamini and Hossein Masoumi Hamedani, ‘Al-Shīrāzī and the Empirical Origin of Ptolemy’s Equant in His Model of the Superior Planets’, Arabic Sciences and Philosophy 23 (2013), pp. 47–67; Kaveh Niazi, Quṭb al-Dīn Shīrāzī and the Configuration of the Heavens. A Comparison of Texts and Models, Dordrecht: Springer, 2014, esp. p. 85; Fateme Savadi, The Historical and Cosmographical Context of Hayʾat al-arḍ with a Focus on Quṭb al-Dīn Shīrāzī’s Nihāyat al-Idrāk, PhD dissertation, Montreal: McGill University, 2018, esp. pp. 21–44 and 107–108.

Ed.: Edition and English translation in Gamini & Masoumi Hamedani, pp. 61–67.