Medieval Hebrew Texts on the Quadrature of the Lune, 1996
By: Y. Tzvi Langermann
Title Medieval Hebrew Texts on the Quadrature of the Lune
Type Article
Language English
Date 1996
Journal Historia mathematica
Volume 23
Issue 1
Pages 31–53
Categories Cosmology, Jewish Averroism
Author(s) Y. Tzvi Langermann
Publisher(s)
Translator(s)
Hippocrates' successful quadrature of the lune was one of the earliest achievements of Greek geometry. Our only source for the nature of Hippocrates' work is Simplicius, who comments on Artistotle's remark that the inference from the quadrature of the lune to the quadrature of the circle is an example of faulty reasoning. In this article two groups of Hebrew texts are translated and analyzed. The first come from mathematical treatises, and their contents show that materials similar to those cited by Simplicius were translated and read in the later medieval period. The second group comprises constructions found as comments to the Averroean corpus, and they attest to the existence of a more limited tradition preserving simple constructions that were necessary to the understanding of Averroes' commentaries on Aristotle. Levi ben Gerson's reconstruction of the quadrature is wholly original. La quadrature de la lunule, par Hippocrate, fut une des premières réalisations de la géométrie grècque. Notre seule source concernant l'oeuvre d'Hippocrate est Simplicius, qui commente une remarque d'Aristote, selon laquelle il est fautif de se servir de la quadrature de la lunule pour connaı̂tre la quadrature du cercle. Dans cet article nous traduisons et analysons deux ensembles de textes hebraı̈ques portant sur ce sujet. Un premier ensemble renferme des textes qui proviennent de traités mathématiques et qui, par leur contenu, indiquent que des matériaux s'apparentant à ce que cite Simplicius étaient connus au Moyen Âge. Le second ensemble comprend des textes qui sont insérés dans des commentaires des écrits d'Averroès: ils attestent l'existence d'une tradition, d'une portée plus limitée, qui conserve des constructions simples qui étaient nécessaires à la compréhension de certains passages des commentaires d'Averroès. La reconstruction de la quadrature de la lunule qu'offre Lévi ben Gershon est entièrement originale. La quadratura della lunula, risolta da Ippocrate, fu uno dei primi successi della geometria greca. L'unica fonte relativa all'opera di Ippocrate e un'annotazione di Simplicio, a commento di un'osservazione di Aristotele, secondo cui servirsi della quadratura della lunula per risolvere la quadratura del cerchio e un esempio di inferenza indebita. Nel presente articolo sono tradotti e analizzati due gruppi di testi ebraici relativi all'argomento. Il primo e desunto da trattati matematici, che monstrano come materiali simili a quelli impiegati da Simplico fossero noti in età medievale. Il secondo gruppo e costituito da testi inseriti nei commenti agli scritti di Averroe, che attestano l'esistenza di una tradizione più limitata, ma che ha conservato alcune construzioni semplici, necessarie alla comprensione di passi dei commenti di Averroe. Del tutto originale risulta la ricostruzione della quadratura della lunula proposta da Levi ben Gershon.

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L'Abrégé de l'Almageste. Un inédit d'Averroès en version hébraïque, 1996
By: Juliane Lay, Juliane Lay
Title L'Abrégé de l'Almageste. Un inédit d'Averroès en version hébraïque
Type Article
Language French
Date 1996
Journal Arabic Sciences and Philosophy
Volume 6
Pages 23–61
Categories Cosmology
Author(s) Juliane Lay , Juliane Lay
Publisher(s)
Translator(s)
The Compendium of the Almagest of Averroes, extant only in Hebrew translation, remains unpublished and hardly studied. The present article aims to make it known. It provides a history of the Compendium: its date of writing, translation into Hebrew, and the transmission, reception, and audience of the Hebrew translation, as well as a preliminary study of the text. This includes an annotated outline of its contents, and a discussion of its sources and their critical use by Averroes. The article also contains a translation of significant extracts from the Prologue, with a brief analysis. The Compendium provides direct and relatively early evidence from a leading protagonist of the 12th-century movement by Andalusian thinkers - mostly Aristotelian philosophers - to criticize and reform Ptolemean astronomy.

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Averroes' De caelo. Ibn Rushd's Cosmology in his Commentaries on Aristotle's On the Heavens, 1995
By: Gerhard Endress
Title Averroes' De caelo. Ibn Rushd's Cosmology in his Commentaries on Aristotle's On the Heavens
Type Article
Language English
Date 1995
Journal Arabic Sciences and Philosophy
Volume 5
Pages 9–49
Categories Cosmology, Aristotle
Author(s) Gerhard Endress
Publisher(s)
Translator(s)
Averroes defended philosophy by returning to the true Aristotle. For this purpose, Aristotle's book “On the Heaven,” in which he explained the eternity, uniqueness and movement of the universe, occupied a place of special importance. But the Aristotelian philosopher had a hard time holding his own in the face of contradictions within the book and with respect to Aristotle's later works. In his early Compendium, later Paraphrase, and final Long Commentary of De Caelo, Ibn Rushd continued the efforts of the Hellenistic commentators in order to integrate all the elements of his doctrine into a unified system, to harmonize his early cosmology with his later Metaphysics - the early doctrine of natural movement of the elements, and of the self-moving star-souls (a Platonic element), with the doctrine of potency and actuality and the theory of the First Mover - and to uphold his models of homocentric planetary spheres against the mathematical paradigm of Ptolemaic astronomy. By insisting throughout on demonstrative arguments based on rational principles, he asserted the philosophers' claim to irrefutable truth.

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Aristotle's Theology and its Influence on the Philosophers of Islam, Judaism and Christianity, 1993
By: Constantine Georgiadis
Title Aristotle's Theology and its Influence on the Philosophers of Islam, Judaism and Christianity
Type Article
Language English
Date 1993
Journal Dialogue and Humanism
Volume 3
Pages 11–23
Categories Cosmology, Aristotle
Author(s) Constantine Georgiadis
Publisher(s)
Translator(s)

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Aristotle's Theology and its Influence on the Philosophers of Islam, Judaism and Christianity, 1993
By: Constantine Georgiadis
Title Aristotle's Theology and its Influence on the Philosophers of Islam, Judaism and Christianity
Type Article
Language English
Date 1993
Journal Dialogue and Humanism
Volume 3
Pages 11–23
Categories Cosmology, Aristotle
Author(s) Constantine Georgiadis
Publisher(s)
Translator(s)

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Averroes' De caelo. Ibn Rushd's Cosmology in his Commentaries on Aristotle's On the Heavens, 1995
By: Gerhard Endress
Title Averroes' De caelo. Ibn Rushd's Cosmology in his Commentaries on Aristotle's On the Heavens
Type Article
Language English
Date 1995
Journal Arabic Sciences and Philosophy
Volume 5
Pages 9–49
Categories Cosmology, Aristotle
Author(s) Gerhard Endress
Publisher(s)
Translator(s)
Averroes defended philosophy by returning to the true Aristotle. For this purpose, Aristotle's book “On the Heaven,” in which he explained the eternity, uniqueness and movement of the universe, occupied a place of special importance. But the Aristotelian philosopher had a hard time holding his own in the face of contradictions within the book and with respect to Aristotle's later works. In his early Compendium, later Paraphrase, and final Long Commentary of De Caelo, Ibn Rushd continued the efforts of the Hellenistic commentators in order to integrate all the elements of his doctrine into a unified system, to harmonize his early cosmology with his later Metaphysics - the early doctrine of natural movement of the elements, and of the self-moving star-souls (a Platonic element), with the doctrine of potency and actuality and the theory of the First Mover - and to uphold his models of homocentric planetary spheres against the mathematical paradigm of Ptolemaic astronomy. By insisting throughout on demonstrative arguments based on rational principles, he asserted the philosophers' claim to irrefutable truth.

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L'Abrégé de l'Almageste. Un inédit d'Averroès en version hébraïque, 1996
By: Juliane Lay, Juliane Lay
Title L'Abrégé de l'Almageste. Un inédit d'Averroès en version hébraïque
Type Article
Language French
Date 1996
Journal Arabic Sciences and Philosophy
Volume 6
Pages 23–61
Categories Cosmology
Author(s) Juliane Lay , Juliane Lay
Publisher(s)
Translator(s)
The Compendium of the Almagest of Averroes, extant only in Hebrew translation, remains unpublished and hardly studied. The present article aims to make it known. It provides a history of the Compendium: its date of writing, translation into Hebrew, and the transmission, reception, and audience of the Hebrew translation, as well as a preliminary study of the text. This includes an annotated outline of its contents, and a discussion of its sources and their critical use by Averroes. The article also contains a translation of significant extracts from the Prologue, with a brief analysis. The Compendium provides direct and relatively early evidence from a leading protagonist of the 12th-century movement by Andalusian thinkers - mostly Aristotelian philosophers - to criticize and reform Ptolemean astronomy.

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Medieval Hebrew Texts on the Quadrature of the Lune, 1996
By: Y. Tzvi Langermann
Title Medieval Hebrew Texts on the Quadrature of the Lune
Type Article
Language English
Date 1996
Journal Historia mathematica
Volume 23
Issue 1
Pages 31–53
Categories Cosmology, Jewish Averroism
Author(s) Y. Tzvi Langermann
Publisher(s)
Translator(s)
Hippocrates' successful quadrature of the lune was one of the earliest achievements of Greek geometry. Our only source for the nature of Hippocrates' work is Simplicius, who comments on Artistotle's remark that the inference from the quadrature of the lune to the quadrature of the circle is an example of faulty reasoning. In this article two groups of Hebrew texts are translated and analyzed. The first come from mathematical treatises, and their contents show that materials similar to those cited by Simplicius were translated and read in the later medieval period. The second group comprises constructions found as comments to the Averroean corpus, and they attest to the existence of a more limited tradition preserving simple constructions that were necessary to the understanding of Averroes' commentaries on Aristotle. Levi ben Gerson's reconstruction of the quadrature is wholly original. La quadrature de la lunule, par Hippocrate, fut une des premières réalisations de la géométrie grècque. Notre seule source concernant l'oeuvre d'Hippocrate est Simplicius, qui commente une remarque d'Aristote, selon laquelle il est fautif de se servir de la quadrature de la lunule pour connaı̂tre la quadrature du cercle. Dans cet article nous traduisons et analysons deux ensembles de textes hebraı̈ques portant sur ce sujet. Un premier ensemble renferme des textes qui proviennent de traités mathématiques et qui, par leur contenu, indiquent que des matériaux s'apparentant à ce que cite Simplicius étaient connus au Moyen Âge. Le second ensemble comprend des textes qui sont insérés dans des commentaires des écrits d'Averroès: ils attestent l'existence d'une tradition, d'une portée plus limitée, qui conserve des constructions simples qui étaient nécessaires à la compréhension de certains passages des commentaires d'Averroès. La reconstruction de la quadrature de la lunule qu'offre Lévi ben Gershon est entièrement originale. La quadratura della lunula, risolta da Ippocrate, fu uno dei primi successi della geometria greca. L'unica fonte relativa all'opera di Ippocrate e un'annotazione di Simplicio, a commento di un'osservazione di Aristotele, secondo cui servirsi della quadratura della lunula per risolvere la quadratura del cerchio e un esempio di inferenza indebita. Nel presente articolo sono tradotti e analizzati due gruppi di testi ebraici relativi all'argomento. Il primo e desunto da trattati matematici, che monstrano come materiali simili a quelli impiegati da Simplico fossero noti in età medievale. Il secondo gruppo e costituito da testi inseriti nei commenti agli scritti di Averroe, che attestano l'esistenza di una tradizione più limitata, ma che ha conservato alcune construzioni semplici, necessarie alla comprensione di passi dei commenti di Averroe. Del tutto originale risulta la ricostruzione della quadratura della lunula proposta da Levi ben Gershon.

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