The title of this work, covering three pages in its unique manuscript, states that it completes (yatimma) the proof of Proposition 4 of Book IX of the Almagest. It can therefore be considered to be a complement to the same author’s C.1.20, whose title states that it is a ‘correction’ (taṣḥīḥ) of the proof of that proposition. The present treatise sets off by proving a method for bisecting the angle between two equal straight lines. After this, the author returns to the fourth proposition of Book IX following a very different path from C.1.20. Two similar diagrams with different labelling are included in the first part of the text, and space for a large third diagram has been left empty at the top of the last page in the unique manuscript. The explicit mention of al-ʿUrḍī as the author suggests that this text is close to C.1.20, but its occurrence in a manuscript with several other reworked treatises stemming from the Maragha environment (especially, C.1.25, C.1.33, and Ibn al-Ṣalāḥ’s Muqaddima li-ʿamal murabbaʿ as copied by Quṭb al-Dīn al-Shīrāzī into MS Istanbul, Topkapı, Ahmet III 3455, ff. 82r–v) may place it closer to the revised version C.1.29.

Text: [Mashhad, Holy Shrine, 5452]

(97r–98r) هذه مقدّمة حرّرها الشيخ الإمام أفضل المهندسين مؤيّد الملّة والدين العرضي أدام الله أيّامه وبها يتمّ برهان الشكل الرابع من المقالة التاسعة من كتاب المجسطي. كلّ خطّين مستقيمين متساويين تحيطان بزاوية ليست قائمة و يخرج من طرف كلّ واحد منهما عمود على الآخر — فيبقى خطّا ب د ب ه متساويين وزاويتا د ف ك ه ف ط متساويتان فخطّ ك د مثل ف ط ه ط ويرجع الشكل إلى أصله.

Bibl.: Aḥmad Gulchīn Maʿānī, Fihrist-i kutub-i khaṭṭī-i Kitābkhāna-i Āstān-i Quds-i Raḍawī, vol. VIII, Mashhad: Intishārāt-i Kitābkhāna-i Āstān-i Quds-i Raḍawī, 1971 (1350 H.S.), p. 67 (no. 1); FankhāMuṣṭafā Dirāyatī, Fihristgān-i nuskhahā-yi khaṭṭī-yi Īrān (Fankhā), 45 vols, Tehran: Library, Museum and Documentation Center of The Islamic Consultative Assembly, 20 2011, vol. XXXI, p. 216.

Ed.: None.