Abstract
In the preface to the Completion Ibn al-Haytham concludes his observations on the supposed contents of the lost Conics VIII as follows (0i):
We decided that these notions and similar ones were the notions contained in the eighth Book (of the Conics). When our judgement about that had been established, we started to derive these notions, to explain them and to collect them in a book containing them,to replace the eighth Book and to be the Completion of the Conics.
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Reference
Printed in Opera, ed. F. van Schooten, 325–338. Biographical details on Vieta are in DSB XIV, 18–25.
Pappi Alexandrini Mathematicae Collectiones, a Fed. Commandino Urbinate in latinum conversae et commentariis illustratae: dated at the end Pisauri 1588, 2nd printing Venice, 1589. For Commandinus (1509–1575) see DSB II1,363–365.
See D. E. P. Jackson, the Arabic translation of a Greek manual of mechanics, Islamic Quarterly 16/1972/96–103.
Some of the works which were reconstructed in Western Europe were still extant in the Middle Ages in Arabic translation, for example, On Cutting-Off an Area (GAS V,143,4), and On Tangencies (GAS V,143,6).
The Greek text was transmitted to Europe and is extant; Archimedes ed. Heiberg I1, 262–314.
GAS V,260,10, German translation in H. Suter Ausmessung… Thâbit.
GAS V,293,1, printed in Ibrahim ibn Sinan, Rasâ’il no. 5, German translation in H. Suter, Abhandlung… Ibrahim.
The extant text does not provide the analyses of the constructions in Conics 1:52–60,11:4, V:44–63, VI:28–33. The only analyses are in II:49–53.
There is considerable confusion in the modern literature on Al-Kuhi’s letter on Filling the Gap in the Second Book of Archimedes (fi suddi l-khalal fi l-maqalati l-thaniya min kitab Arshimidis). Only part of this letter is extant,in a quotation by Nasir al-Din al-Tusi(1201–1274,DSB XIII,508–517), at the end of his edition (tahrir) if on the Sphere and Cylinder II of Archimedes. For a summary of the contents of the Al-Kuhi fragment see Juschkewitsch,Mathematik im Mittelalter, 258. Woecke discussed the fragment in Algebre, 103–114. He noted that it was appended ot on the Sphere and Cylinder II by a commentator,but he did not know that the commentator was Nasir al-Din al-Tusi. Sezgin in gas v,320,24 does not give the correct title, and he only mentions three manuscripts of the extant fragment.But it is likely that the fragment is also found in all or most of the manuscripts of Al-Tusi’s edition of on the Sphere and cylinder mentioned in gas v,129b. it is not generally known among historians of mathematics that the Arabic text of the fragment has been printed in the Haydarabad edition of Al-Tusi’s revisions of Greek works (Al-Tusi, Rasa’il II, no.5, 115:8–127:15).As far as on the sphere and cylinder is concerned, the Haydarabad edition seems to be based on a manuscript in Rampur(see p. 133:14),which must contain the fragment by Al-Kuhi.
suter,ermittlung,36;Al-Biruni,Istikhraj al-Awtar,ed.Dimirdash 100; Al-Biruni, Rasa’il no. 1, 49–57.
wa-hadhihi l-ashya’u llati dhakarna nafi’atun aydan fi tahlili l-taqsim wa-hiya mustahiqqatun li-l-qubul wa-li’an yu’na bi-ma’rifatiha wa-law lam yakun laha hadhihi l-manafi li-haliha fi-anfusiha wa-ma fiha min al-barahin fa-inna qad naqbalu adhya a akhara kathiratan min al-u’lumi l-ta’limiyya li-hadha l-sabab(ms.oxford, Bodleian library, marsh 667 f. 70a:17–19, ms. Aya sofya 2762, 138a: 14–18; Greek text in conics ed.heiberg II, 4:16–21, tr. By Heath in Hgm II, 131 ).
Preface to Conics I ed. Heiberg I,2:9–22, tr. in Heath, HGM II,129: The passage is also in the Arabic version of the Conics; ms. Oxford, Bodl. Marsh 667,5a:10–14.
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Hogendijk, J.P. (1985). The Completion as a Reconstruction of Conics VIII. In: Ibn al-Haytham’s Completion of the Conics . Sources in the History of Mathematics and Physical Sciences, vol 7. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4059-2_6
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