Abstract
For a long time the history of Arabic philosophy was limited to the history of the philosophy of individual philosophers. Two series of problems predominated: the first series, of a philosophical nature, was concerned in one way or another with reconciling philosophical and revealed knowledge, that is philosophy and religion. The other series, more historical, dealt with the survival and development of traditional Greek philosophy in the new philosophy. It is true some historians did not fail to appreciate the innovating contributions of this philosophy in the fields of ontology, psychology or logic. But for them, as for other historians, its history centred on a few great names: al-Kindī, al-Fārābī, Ibn Sīnā, Ibn Rushd, Ibn Bāja, etc.
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Notes
The proposition is stated as follows: “The asymptotes and the hyperbola, as they pass on to infinity, approach continually nearer, and will come within a distance less than any assignable length”: see Apollonius of Perga, Treatise on Conic Sections, edited by T.L. Heath, Cambridge, 1896, p. 61.
Procli Diadochi, In Primum Euclidis Elementorum Librum Commentarii, edited by G. Friedlein, Leipzig. 1873 (reproduced in Olms, 1967), p. 177; and G.R. Morrows’ translation, Proclus, A Commentary on the First Book of Euclid:r Elements, Princeton. 1970. p. 139.
Proclus, trad. Morrow, op. cit., p. 222.
Op. cit., p. 223.
See M. Clagett, Archimedes in the Middle Ages, Philadelphia, 1980, t. IV.
See Sharaf al-Din al-Tûsi, Oeuvres mathématiques - Algèbre et géométrie au XII’ siècle, edition, translation and commentary by R. Rashed, Paris, Les Belles Lettres. 1986; t.I, pp. cxxviii-cxxi, 710 and 126; t.II, p. 130 sq.
See note 6.
See the edition of the Arabic text and its French translation in Archives Internationales d’Histoire des Sciences, vol. 37, no. 119 (1987), pp. 280–296.
In fact our knowledge of the existence of an Arabic version of Proclus’ Elements of Physics had been based until now on an isolated reference to the title by a 10th century bibliographer, Ibn alNadim [cf. Al-Fihrist, ed. R. Tajaddud, Tehran 1971, p. 312]. We have recently learned that some theorems appear “in the Stoicheiasis Physikr that is reflected or partially reflected in Ms Haci Mahmud’s texts,” i.e. manuscript 5683 in this collection in Istambul [cf. Pines, Studies in Arabic Versions of Greek Texts and in Medieval Science, Leiden, E.J. Brill, 1986, p. 287 sqq.]. According to S. Pines, it concerns theorems 10, 15, 17, 18, 19 and 21 in the second part of Proclus’ work. In his Opuscula, al-SijzTs reference corroborates the bibliographer’s reference and accounts for the inclusion of the preceding theorems. He recalls the title mentioned by the latter: Kitäb Hudüd awd’i! al-Tabi ‘cyat, i.e. Elements of Physics, and moreover indicates the purpose of the work: demonstrate the infinite divisibility of magnitude by the philosophical method. However, an anonymous text (according to G. Endress this text is by Yahyâ ibn ‘MI-0–363/974); cf. “Yahyâ ibn `Adis critique of atomism” in Zeitschrift für Geschichte der arabisch — islamischen Wissenschaften, Band 1 (1984), Frankfurt, pp. 155–179) from one of the oldest manuscripts in the Bibliothèque Nationale (Paris), makes it possible to show that Proclus’ work had been translated, at least partially, into Arabic. (Several sheets date back to the 10th century, in all probability written by al-Sijzi himself, and frequently consulted since the mid-19th century.) Ms 2457 in the Arabic collection includes an anonymous text entitled: Any continuum may be divided into things that have infinite divisibility. It reproduces the translation of several propositions from the Greek text of Proclus, as they survived in the Greek manuscript tradition (which is not necessarily the same version used for the Arabic translation). Here we present the English translation of Greek fragments translated into Arabic as conclusive proof for the existence of an Arabic version of Proclus’ work. Brackets indicate passages where the translater gave the meaning but not a faithful translation. Asterisks indicate passages omitted in the Arabic translation. Proclus, Elements of Physics Def. I: Are continuous things whose extremities are the same. Def. I I: Are contiguous things whose extremities are together. Def. III: Are successive things between which there is nothing of the same kind.
Two indivisible things will not touch each other. If in fact it were possible, let the two indivisibles AB touch each other. But things which touch each other are things whose extremities are together. *From two indivisibles there will be extremities, and therefore A and B are not indivisibles.*
Two indivisible things do not form a continuum. If it were in fact possible (let A and B be two indivisibles and let there be from these two a continuous thing). However all continuous things are first of all contiguous; therefore A and B are contiguous, while being at the same indivisible; which is impossible. *Otherwise…*
What lies between two indivisible things in a continuum is continuous.) Let in fact AB be two indivisible things, I say that the intermediary between A and B is continuous. *If in fact this were not so, indivisible A is contiguous to indivisible B, *which is impossible*; therefore the intermediary between them is continuous.
Two indivisible things are not successive to each other. Let in fact AB be two indivisible things; I say that A is not successive to B. Because in fact it has been demonstrated that the intermediary between two indivisible things is continuous; now let their intermediary be CD and let it be divided by E; therefore E is indivisible *as it is an intermediary between A and B.* However, are successive things between which there is nothing of the same kind; therefore A and B are not successive.
A continuum is divided into parts that are continuously divisible. Let in fact AB be a continuum. I say that AB is divided into continuously divisible parts. Let AB be divided into AE and EB. AE and EB are now either indivisible or continuously divisible. If, therefore, on the one hand, they are indivisible, then there is a continuum from indivisible things, *which is impossible;* if, on the other hand, they are divisible, *then let them be divided into parts again and these subdivided in turn. If, on the other hand, they are indivisible, the indivisible parts will be continuous to each other; if, on the other hand, they are divisible, let them be divided as well, and so into infinity. Therefore any continuum is divided into things that are continuously divisible.*
See, for example, his work “Solution of a problem in the work of Yûhanna ibn Yûsuf: the division of two halves of a straight line and the explanation of Yûhanna’s book on this subject.” Mss BN 2417, ff. 52“-53”.
l Let us quote the famous philosopher al-Farabi, al-Sijzi s predecessor. This is what he wrote in On demonstration: “the name of science, as we said earlier, is usually given to two notions, that of judgement and that of conception,” f. 1“. Al-Farabi developed this doctrine in his work. We may also mention later philosophers such as Avicenne; AI-Shifa’; La Logique vol. V, edited by A.E. Affifi, Cairo, 1952, pp. 51 sqq. In his work, Reply to Logicians, Ibn Taymiyya made an appropriate summary of this philosophical doctrine: cf. Kitah al-Radd âla al-mantigiyyin, Bombay, 1949, p. 4 sqq.
Cf. for example al-Farabi, op. cit.
Posterior Analytics, I1, 3, 91a.
See al-Sijzi s text, cited note 8.
Proclus, Elements of Physics, op. cit., p. 30–32.
Ibn al-Haytham, On the solution of doubts concerning Euclid’s book of Elements and an explanation of his ideas, fhall Shukak kitab Uglidisfal-Usûl xa sharp ma ‘am7t, Istambul University Library, ms 800.
Euclid’s Elements, translation, introduction and commentary by Sir Thomas L. Heath, vol. I (Dover, ed. 1956 ), p. 235.
Op. cit., pp. 235–236.
Proclus, Commentary…, op. cit., p. 251.
Idem.
Idem.
Euclid’s Elements, op. cit., p. 300.
B. Russell, Principles of Mathematics (second edition), London, 1937, p. 405.
Euclid’s Elements, op. cit., p. 249.
Posterior Analytics, I, 4, 74 a.
Proclus, Commentary…, op. cit., p. 302. Cf. p. 384, ed. Friedlein.
See the edition and translation of this commentary in Archives Internationales d’Histoire des Sciences.
An interest in mathematics was not the prerogative of Oriental Aristotelian philosophers such as al-Kindi, al-Farabi and Avicenna; it was also shared by Western philosophers who had a direct influence on Maimonides such as Ibn Bâjja or Avempace (who died in 1138–39, three years after Maimonides’ birth). A study of Ibn Bâjja’s writings and, in particular, his summary of the mathematical works of Ibn Sayyed, are proof of his acquaintance with contemporary mathematicians and Apollonius’ Conic Sections. (Cf. Sharaf al-Din al-TGsT, Oeuvres mathématiques, op. cit., t. I, notes p. 129.) Maimonides was also acquainted with Apollonius’ Conic Sections, as his notes on some propositions show. See Hawashi ‘alit ha ’ Ashkal Kited) al-Makhrûtat [Commentary on some propositions in Conic Sections]. Ms Manisa, Genel 1706/6, ff. 26“-33”.
Dalalat al-Ha’ irin (Guide for the Perplexed), ed. Huseyin Atay, Ankara University Publication, no. 93, 1974, p. 215. See also the French translation by S. Munk, Paris, 1856, pp. 407–410, and the English translation by M. Friedländer, 2nd ed., 1904 (Dover, 1956 ), pp. 130–131.
Ibid., p. 214.
Ibid., p. 215.
Ibid., pp. 213–214.
Ibid., p. 214.
Averroes, Kited, al-nafs ( The Book of the Soul ), Hayderabad, 1947, pp. 55–56.
On the influence of De duabus lineis and the Guide for the Perplexed, particularly Book I, ch. 73, see M. Clagett, op. cit., p. 335 sqq.
This is what he wrote: “… en la Géométrie (qui pense avoir gagné le haut point de certitude parmy les sciences) il se trouve des démonstrations inévitables subvertissans la vérité de l’expérience: comme Jacques Peletier me disoit chez moy qu’il avoit trouvé deux lignes s’acheminant l’une vers l’autre pour se joindre, qu’il vérifioit toutefois ne pouvoir jamais, jusqu’à l’infinité, arriver à se toucher.” (Les Essais, Book II, ch. 12).
See Dialogues philosophiques, VII, I: “… N’êtes-vous pas forcé d’admettre les asymptotes en géométrie, sans comprendre comment ces lignes peuvent s’approcher toujours, et ne se toucher jamais? N’y a-t-il pas des choses aussi incompréhensibles que démontrées dans les propriétés du cercle? Concevoir donc qu’on doit admettre l’incompréhensible, quand l’existence de cet incompréhensible est prouvée.”
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Rashed, R. (2000). Al-Sijzī and Maimonides: A Mathematical and Philosophical Commentary on Proposition II—14 in Apollonius’ Conic Sections . In: Cohen, R.S., Levine, H. (eds) Maimonides and the Sciences. Boston Studies in the Philosophy of Science, vol 211. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2128-8_9
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