Analisi critica d'opera, incentrata sulla recezione dell'opera di Tolomeo durante il Medioevo e sul pensiero scientifico-filosofico dell' Età Medievale e Rinascimentale.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Before Science: The Invention of the Friars’ Natural Philosophy by Roger French, Andrew CunninghamIrven M. ResnickRoger French and Andrew Cunningham. Before Science: The Invention of the Friars’ Natural Philosophy. Hants, UK: Scolar Press, 1996. Pp. x + 298. Cloth, $68.95.This is a peculiar book that depicts thirteenth-century natural philosophy as wholly dependent on the theological interests of the mendicant orders. For the Friars, “Natural (...) class='Hi'>philosophy was a study in which the central concerns were the detection, admiration and appreciation of God’s existence, goodness, providence, munificence, forethought and provision for His creation” (4). Although conceived as “a positive contribution to the discipline of the history of science” (3), the work begins and ends with the claim that medieval natural philosophers were not engaged in science.One difficulty is that the authors never make clear what they mean by science, although they evidently understand that it entails a repudiation of metaphysics and a doctrine of nature’s radical autonomy. Consequently, for French and Cunningham medieval “science” is a mythic construct of modern historians, since “[t]here was no scientific tradition (in the modern sense of the term ‘scientific’) of looking at nature in the thirteenth century, only a religio-political way of doing so” (273).Thus, when summarizing the accomplishments of Roger Bacon, they note that “[Bacon] has been credited, along with Grosseteste, with creating early ‘experimental science’. Bacon could not of course have been a ‘scientist’ because he lived in the wrong [End Page 623] age for this” (238). This seemingly casual conclusion is rather stunning not only in its own right, but also as a revelation of the authors’ own effort to disenfranchise medieval ‘scientists’ for having had the misfortune of living too soon.French and Cunningham propose that polemical or apologetical interests urged the Friars to study nature as a response to various heretics and especially the Cathars who, seemingly like moderns, sought to disengage the natural world from the Christian God, while using the vocabulary of Aristotle’s libri naturales. However this central argument demands better support. Since the authors can cite only one surviving Cathar text—De duobus principiis (ca. 1230)—almost everything known of this group is derived from anti-Cathar polemics. Based on this single text the authors can say no more than that it used “what looks very much like a commentary on Aristotle’s Physics or Metaphysics,” (134) but fail to identify more precisely its sources. It is clear that thirteenth-century orthodox polemics increasingly relied on Aristotelian materials, but the conclusion that natural philosophers did so only in response to heretics who beat them to the Aristotelian punch seems tendentious. The historian will likely remain unconvinced that the unparalleled translating activity of the late eleventh and twelfth centuries—the rendering into Latin of Arabic scientific knowledge (as in Constantine the African’s Pantegni or Adelard of Bath’s Quaestiones naturales), Greek medical literature (e.g. Galen’s Methodus medendi translated by Gerard of Cremona and Burgundio of Pisa) and mathematics (e.g. Euclid’s Optics, Theodosius’s Spherics, Archimedes’ On the Quadrature of the Circle, and Ptolemy’s Tetrabiblos and Almagest) culminating with thirteenth-century translations of Aristotle’s biological works—should all have stemmed from a preoccupation with heresy.A further shortcoming of this book is the limited attention given to works on natural philosophy by the Friars themselves. The book’s first seven of eleven chapters explore the educational establishments in which natural philosophy arose: first monastic and cathedral schools, and then the universities. The works of individual Friars receive only the briefest summary. Among the Dominican natural philosophers Albertus Magnus—the patron saint of scientists and one of a very few scholastics to have commented on all of Aristotle’s biological works—is awarded only five pages. For his mastery of Aristotle’s libri naturales Albertus has been called “the dominant figure in Latin learning and natural science of the thirteenth century.” (Cf. Lynn Thorndike, History of Magic and Experimental Science [New York: Macmillan, 1929], 2:521) Albertus described not only the natural world but also explored the philosophical foundations for scientific knowledge. Yet curiously French and Cunningham give much more attention... (shrink)

RésuméLe savant Ibn al-Ṣalāḥ est connu pour ses petits traités portant sur des questions particulières d'ouvrages mathématiques et philosophiques grecs. Il consacre plusieurs de ses travaux aux erreurs, plus ou moins importantes, qu'il trouve dans les travaux d'Euclide, de Ptolémée et d'Aristote. Le but de cet article, qui se concentre sur trois traités de Ptolémée et d'Aristote, est de décrire la méthode d'Ibn al-Ṣalāḥ et les objectifs qu'il poursuit dans les traités en question. Je suggère que ses traités sur l’Almageste, (...) le Traité du ciel et les Seconds analytiques suivent une structure semblable et qu'ils sont d'une grande valeur pour la recherche moderne en raison des éléments bibliographiques fournis par Ibn al-Ṣalāḥ. Pour ne citer qu'un exemple, Ibn al-Ṣalāḥ atteste de l'existence d'une traduction arabe des Seconds analytiques d'Aristote inconnue jusqu'ici. Cet article établit ainsi pour la première fois le profil de savant d'Ibn al-Ṣalāḥ : ses travaux nous disent quelles sources étaient disponibles aux savants actifs à Bagdad et Damas au XIIe siècle et comment il a tenté de résoudre les contradictions entre les différentes versions des textes faisant autorité. Cet article offre donc une contribution à notre connaissance de la transmission gréco-arabe des textes scientifiques et philosophiques. (shrink)

In the first part of chapter 2 of book II of the Physics Aristotle addresses the issue of the difference between mathematics and physics. In the course of his discussion he says some things about astronomy and the ‘ ‘ more physical branches of mathematics”. In this paper I discuss historical issues concerning the text, translation, and interpretation of the passage, focusing on two cruxes, the first reference to astronomy at 193b25–26 and the reference to the more physical branches at 194a7–8. In (...) section I, I criticize Ross’s interpretation of the passage and point out that his alteration of has no warrant in the Greek manuscripts. In the next three sections I treat three other interpretations, all of which depart from Ross's: in section II that of Simplicius, which I commend; in section III that of Thomas Aquinas, which is importantly influenced by a mistranslation of, and in section IV that of Ibn Rushd, which is based on an Arabic text corresponding to that printed by Ross. In the concluding section of the paper I describe the modern history of the Greek text of our passage and translations of it from the early twelfth century until the appearance of Ross's text in 1936. (shrink)

In this article, I analyze the coincidence of the prediction of the Earth–Sun distance carried out by Ptolemy in his Almagest and the one he carried out, with another method, in the Planetary Hypotheses. In both cases, the values obtained for the Earth–Sun distance are very similar, so that the great majority of historians have suspected that Ptolemy altered or at least selected the data in order to obtain this agreement. In this article, I will provide a reconstruction of some (...) way in which Ptolemy could have altered or selected the data and subsequently will try to argue in favor of its historical plausibility. (shrink)

The assumption that Ptolemy adopted star coordinates from a star catalog by Hipparchus is investigated based on Hipparchus’ equatorial star coordinates in his Commentary on the phenomena of Aratus and Eudoxus. Since Hipparchus’ catalog was presumably based on an equatorial coordinate system, his star positions must have been converted into the ecliptical system of Ptolemy’s catalog in his Almagest. By means of a statistical analysis method, data groups consistent with this conversion of coordinates are identified. The found groups show a (...) high degree of agreement between Hipparchus’ and Ptolemy’s data. The value of the obliquity of the ecliptic underlying the conversion is estimated by adjustment and statistically agrees with Ptolemy’s value of this parameter. The results allow the assumption that Ptolemy’s coordinates were determined from Hipparchus’ coordinates by an accurate star globe or even by calculation. For a calculative derivation of ecliptical coordinates from equatorial ones, possible calculation methods are discussed considering the mathematics of the Almagest. (shrink)

: To honor Bernard Goldstein, this article highlights in the "Defense of Theon against George of Trebizond" by Regiomontanus (1436-1476) themes that resonate with leading strands of Goldstein's scholarship. I argue that, in this poorly-known work, Regiomontanus's mastery of Ptolemy's mathematical astronomy, his interest in making astronomy physical, and his homocentric ideals stand in unresolved tension. Each of these themes resonates with Gold- stein's fundamental work on the Almagest, the Planetary Hypotheses, and al-Bitruji's Principles of Astronomy. I flesh out these (...) tensions with an intriguing interpretation of the history of astronomy, in which Regiomontanus contrasts the two-dimensional "eccentric astronomy" attributed to the Almagest and the Arabs with the three-dimensional spheres of the "later" astronomers. A similar contrast reappears when Regiomontanus portrays as a "fictitious art" an astronomy that does not go beyond the accommodation of computations to the appearances. To conclude, I use Regiomontanus's expression to reinstate (pace Goldstein and Barker in this journal, 1998) fictionalism as an actor's category in Osiander and sixteenth-century astronomy. (shrink)

A characteristic hallmark of medieval astronomy is the replacement of Ptolemy’s linear precession with so-called models of trepidation, which were deemed necessary to account for divergences between parameters and data transmitted by Ptolemy and those found by later astronomers. Trepidation is commonly thought to have dominated European astronomy from the twelfth century to the Copernican Revolution, meeting its demise only in the last quarter of the sixteenth century thanks to the observational work of Tycho Brahe. The present article seeks to (...) challenge this picture by surveying the extent to which Latin astronomers of the late Middle Ages expressed criticisms of trepidation models or rejected their validity in favour of linear precession. It argues that a readiness to abandon trepidation was more widespread prior to Brahe than hitherto realized and that it frequently came as the result of empirical considerations. This critical attitude towards trepidation reached an early culmination point with the work of Agostino Ricci, who demonstrated the theory’s redundancy with a penetrating analysis of the role of observational error in Ptolemy’s Almagest. (shrink)

Ptolemy presents only one argument for the eccentricity in his models of the superior planets, while each one of them has two eccentricities: one for center of the uniform motion, the other for the center of the constant distance. To take into account the first eccentricity, he introduces the equant point, but he provides no argument for the eccentricity of the center of the deferent. Why is the second eccentricity different from the first one? The 13 th century astronomer Quṭb (...) al-Dīn al-Shīrāzī, a member of the famous school of Marāgha, who was interested in this problem, suggests the “retrograde arcs” as the empirical origin of the second eccentricity and develops an argument to justify this conjecture. Although his argument is not without difficulty, his suggestion is in line with the suggestions made by some historians of astronomy in recent decades. Résumé Ptolémée ne donne qu'un seul argument pour expliquer dans son système l'excentricité des planètes supérieures, alors que chacune d'elles a deux excentricités: l'une par rapport au centre du mouvement uniforme, l'autre par rapport au centre de la distance constante. Pour rendre compte de la première excentricité, il introduit le point équant, mais il ne donne en revanche aucun argument pour l'excentricité par rapport au centre du cercle déférent. Or, pourquoi la seconde excentricité est-elle différente de la première? Quṭb al-Dīn al-Shīrāzī, astronome du xiii e siècle membre de l'école de Marāgha, qui s'est intéressé à cette question, a fait l'hypothèse que les “arcs de rétrogradation” constituent l'origine empirique de cette seconde excentricité. Bien que l'argument sur lequel il appuie cette hypothèse ne soit pas exempt de difficultés, sa suggestion rejoint celles faites par des historiens de l'astronomie durant les dernières décennies. (shrink)

In order to get rid of the contradictions he had identified in Ptolemy’s Astronomy, Ibn al-Haytham abandons cosmology and develops a purely kinematic description of the movement of the wandering stars. This description culminates with the proof that such a star, during its daily movement, reaches exactly one time a maximum height above the horizon and that any inferior height is reached exactly twice. The proofs of these facts necessitates new mathematical tools and Ibn al-Haytham is led to establish very (...) sophisticated statements concerning the variation of certain ratios of arcs of circles on the sphere. He also introduces the fruitful idea of assimilating a very small spherical triangle to a plane triangle. (shrink)

Review of Liba Taub, Ptolemy's universe; The natural philosophical and ethical foundations of Ptolemy's astronomy. Chicago: Open Court 1993. xiv, 188 p.

The reception of the rational sciences, scientific practice, discourse and methodology into Arabic Islamic society proceeded in several stages of exchange with the transmitters of Iranian, Christian-Aramaic and Byzantine-Greek learning. Translation and the acquisition of knowledge from the Hellenistic heritage went hand in hand with a continuous refinement of the methods of linguistic transposition and the creation of a standardized technical language in Arabic: terminology, rhetoric, and the genres of instruction. Demonstration more geometrico, first introduced by the paradigmatic (...) sciences-mathematics, astronomy, mechanics-and adopted by philosophers embracing the cosmology of Neoplatonism, was complemented and superseded by the methods of syllogistic demonstration. Faced with the establishment of philosophy as a demonstrative science, which claimed absolute and universal knowledge, even the hermeneuti. (shrink)

bit b. Qurra is especially known as a mathematician, but his work in astronomy is also important. This article reviews his eight surviving astronomical treatises, as well as relevant fragments of his lost works cited by later authors in Arabic and Latin. We conclude that, as an active participant in the scientific movement of 9th-century Baghdad, bit played a crucial role in the establishment of astronomy as an exact science. The argument is based on an assessment of his contribution (...) in three areas: the relationship between observation and theory, the of astronomy, and the relationship between astronomy and astronomy. (shrink)

Until recently, only two Arabic translations of Ptolemy’s Almagest were thought to have survived, one by al-Ḥajjāj made under the caliph al-Maʾmūn and one by Isḥāq b. Ḥunayn, later revised by Thābit b. Qurra, prepared in the second half of the third/ninth century. In the 2010s, a third Arabic version of the Almagest, authored by Thābit b. Qurra alone, was first shown by Dirk Grupe to be extant in a partial Latin translation in a Dresden manuscript, and then (...) in an Arabic manuscript in Jaipur that breaks off after chapter VI.2. We introduce here a second manuscript of this Thābit version, extant in the Khuda Bakhsh Library in Patna, which is around four centuries older than the Jaipur manuscript, was copied from a manuscript by the hand of al-Bīrūnī, and extends the text till the middle of Book VIII. After a general introduction, we provide a detailed description of this manuscript. (shrink)

The Greco-Roman mathematician Claudius Ptolemy is one of the most significant figures in the history of science. He is remembered today for his astronomy, but his philosophy is almost entirely lost to history. This groundbreaking book is the first to reconstruct Ptolemy’s general philosophical system—including his metaphysics, epistemology, and ethics—and to explore its relationship to astronomy, harmonics, element theory, astrology, cosmology, psychology, and theology. -/- In this stimulating intellectual history, Jacqueline Feke uncovers references to a complex and sophisticated philosophical (...) agenda scattered among Ptolemy’s technical studies in the physical and mathematical sciences. She shows how he developed a philosophy that was radical and even subversive, appropriating ideas and turning them against the very philosophers from whom he drew influence. Feke reveals how Ptolemy’s unique system is at once a critique of prevailing philosophical trends and a conception of the world in which mathematics reigns supreme. -/- A compelling work of scholarship, Ptolemy’s Philosophy demonstrates how Ptolemy situated mathematics at the very foundation of all philosophy—theoretical and practical—and advanced the mathematical way of life as the true path to human perfection. (shrink)

Johannes Kepler belonged to a long tradition of inquiring into nature with reference to God. This applies to Ptolemy, N. Copernicus, Chr. Clavius. Kepler's „new kind of poem” is analyzed in five sections which are based on Keplerian key words: Innovation, Hypothesis, Cause, Soul, Picture. Kepler consciously adhered to new questions, new answers, new methods. He relied on a new notion of hypothesis. His celestial dynamics included a celestial psychology whereby he used a visual conception of astronomy.

The model of scientific revolution genesis and structure, extracted from Einstein’s revolution and described in author’s previous publications, is applied to the Copernican one . In the case of Einstein’s revolution I had argued that its cause consisted in the clash between the main classical physics scientific programmes: newtonian mechanics, maxwellian electrodynamics, classical thermodynamics and statistical mechanics. Analogously in the present paper it is argued that the Copernican revolution took place due to realization of the dualism between mathematical astronomy and (...) Aristotelian qualitative physics in Ptolemy’s cosmology and the corresponding efforts to eliminate it. The works of Copernicus, Galileo, Kepler and Newton were all the stages of the mathematics descendance from skies to earth and reciprocal extrapolation of earth physics on divine phenomena. (shrink)

Ptolemy's Almagest, a brilliant treatise on theoretical astronomy combined with a practical handbook for computation, includes many compromises to reconcile discordant observations. This defense of Ptolemy examines in some detail a critical case concerning the model for Venus, which has sometimes been used as evidence for Ptolemy's perfidy. There the Alexandrian astronomer demonstrated his ingenuity when orbital constraints made it impossible to obtain directly the observed configurations he might have preferred.

The eighth-century Latin manuscript Milan, Veneranda Biblioteca Ambrosiana, L 99 Sup. contains fifteen palimpsest leaves previously used for three Greek scientific texts: a text of unknown authorship on mathematical mechanics and catoptrics, known as the Fragmentum Mathematicum Bobiense (three leaves), Ptolemy's Analemma (six leaves), and an astronomical text that has hitherto remained unidentified and almost entirely unread (six leaves). We report here on the current state of our research on this last text, based on multispectral images. The text, incompletely preserved, (...) is a treatise on the construction and uses of a nine-ringed armillary instrument, identifiable as the “meteoroscope” invented by Ptolemy and known to us from passages in Ptolemy's Geography and in writings of Pappus and Proclus. We further argue that the author of our text was Ptolemy himself. (shrink)

In an influential article, A. I. Sabra identified an intellectual trend from twelfth and thirteenth-century Andalusia which he described as the ‘‘Andalusian revolt against Ptolemaic astronomy.” Philosophers such as Ibn Rushd, Ibn Tufayl, and Maimonides objected to Ptolemy’s theories on philosophic grounds, not because of shortcomings in the theories' predictive accuracy. Sabra showed how al-Bitrūjī's Kitāb al-Hay'a attempted to account for observed planetary motions in a way that met the philosophic standards of those philosophers and others. In Nūr al-‘ālam, the (...) subject of this article, Joseph ibn Joseph ibn Nahmias endeavoured to improve upon al-Bitrūjī’s models. Levi Ben Gerson's Hebrew writings on astronomy criticized al-Bitrūjī, but Ibn Nahmias did not mention them. Nūr al-‘ālam deserves attention, too, because it is the first Arabic text on theoretical astronomy by a Jewish author to come to light. In the body of this article, I will describe and analyze Ibn Nahmias’ theory, from Nūr al-‘ālam, for the motion of the sun. (shrink)

The undoubted truth is that there exist for the planetary motions true and constant configurations from which no impossibilities or contradictions follow; they are not the same as the configurations asserted by Ptolemy; and Ptolemy neither grasped them nor did his understanding get to imagine what they truly are.

Na[sdotu]īr al-Dīn al-[Tdotu]ūsī, Memoir on Astronomy . [Sdotu]adr al-Sharī‘a. An Islamic Response to Greek Astronomy: Kitāb Ta‘dīl Hay’at al-Aflāk of [sdotu]adr al-Sharīa , Edited with Translation and Commentary by Ahmad S. Dallal, X + 461 pp., figs., index. Leiden - New York - Köln, E.J. Brill, 1995.

Arabic contributions to medicine, mathematics, astronomy, and other fields have been extensively studied, yet Arabic logic has never been systematically investigated. In this book, Nicholas Rescher sheds new light on the major philosophical contribution of Arab logicians. He provides a historical account of the evolution of Arabic logic, from its inception in the early ninth century through the sixteenth century, when these tenets gained wide acceptance. The book also includes a bio-bibliography of 170 Arabic logicians, and (...) a discussion of the place of each within the overall scheme of developments. (shrink)

The Epistles of the Brethren of Purity' is an encyclopedic compendium, probably composed in tenth-century Iraq by a society of adepts with Platonic, Pythagorean, and Shi'i tendencies. Its 52 sections ('epistles') are divided into four parts (Mathematics, Natural Philosophy, Sciences of the Soul and Intellect, and Theology). The current volume provides an edition, translation, and notes to Epistle 3 ('On Astronomia'), which forms one of the 14 sections on Mathematics. The content is a mixture of elementary astronomy and astrology, (...) but it is not a beginner's textbook. Rather, the purpose is to use examples from those disciplines to provide spiritual, moral, and soteriological guidance. Thus the Epistle uses the argument from design to show the necessity for a Creator who made the harmonious universe; this wondrous design is then employed by the authors as a model, providing humans with a paradigm for proper ethical, political, and even economic conduct; and the study of Astronomia helps the soul achieve ultimate happiness as it seeks to throw off the shackles of this mundane world and oppressive body in favour of the purity of the celestial realm.0Although by no means typical of Islamic astronomical literature, Epistle 3 of the Brethren of Purity gives a window into a fascinating and intriguing group operating during the early period of Islam who sought to continue and adopt one of the esoteric strands of Hellenistic philosophy within an Islamic context, meshing astronomy, astrology, Platonic-Pythagorean philosophy, Quranic and Biblical quotations, and anecdotes from the lives of the Abrahamic prophets. (shrink)

Mathematical Astronomy as the most developed branch of ancient exact sciences has been widely discussed - especially epistemological issues e.g. concerning astronomy as a prime example of the distinction between instrumentalist and realist understanding of theories. In contrast to these the very methodology of ancient astronomy has received little attention. Following the work of Jaakko Hintikka and Unto Remes Aristarchus' method of determining the distance of the Sun is sketched and Ptolemy's solar model is discussed in detail.

Abraham ibn Ezra d'Espagne (m. 1167) fut l'un des plus importants savants ayant contribué à la transmission de la science arabe à l'Occident. Ses ouvrages en astrologie et en astronomie, rédigés en hébreu puis traduits en latin, étaient considéréd comme faisant autorité par de nombreux savants juifs et Chrétiens. Parmi les ouvrages qu'il a traduits de l'arabe en hébreu, certains sont perdus dans leur langue originale et ses propres ouvrages renferment certaines informations concernant des sources anciennes mal ou pas du (...) tout connues par ailleurs. Ibn Ezra semble être le premier a avoir consigne l'une des sept méthodes pour dresser les maisons astrologiques. Cette méthode avait par la suite été utilisée par Lévi ben Gershom (m. 1344) dans le Midi de la France. (shrink)

In a somewhat polemical article on ‘Solstices, Equinoxes, and the Presocratics’ D. R. Dicks has recently challenged the usual view that the Presocratics in general, and the Milesians in particular, made significant contributions to the development of scientific astronomy in Greece. According to Dicks, mathematical astronomy begins with the work of Meton and Euctemon about 430 B.C. What passes for astronomy in the earlier period ‘was still in the pre-scientific stage’ of ‘rough-and-ready observations, unsystematically recorded and imperfectly understood, of practical (...) men’ whose chief concern was to fix the seasons for ploughing, seed-time, sailing voyages and religious festivals. Ionian speculation, says Dicks, took very little note of such observation: ‘some of its wilder flights of fancy might have been avoided, if it had taken more’. In this account of the rise of Greek astronomy, the natural philosophers have no part to play. Their theories represent a speculative enterprise without a scientific future, a philosophic sideline with no impact on the development of observational science from Hesiod to Meton or the development of mathematical astronomy from Meton to Ptolemy.I believe that such a dichotomy between early philosophy and early science in Greece is misguided in principle, and that it seriously distorts our picture of the initial phases of each discipline. It also imposes a considerable strain upon our credulity. Take the case of Anaxagoras who, according to Plato and Theophrastus, had given a causal explanation of eclipses of the moon a generation before Meton. (shrink)

Levi ben Gerson (1288–1344) was a medieval astronomer who responded in an unusual way to the Ptolemaic tradition. He significantly modified Ptolemy’s lunar and planetary theories, in part by appealing to physical reasoning. Moreover, he depended on his own observations, with instruments he invented, rather than on observations he found in literary sources. As a result of his close attention to the variation in apparent planetary sizes, a subject entirely absent from the Almagest, he discovered a new phenomenon of Mars (...) and noticed a serious flaw in Ptolemy’s treatment of the Moon. (shrink)

“Although up to now the [visual] image has been [understood as] a construct of reason,” Kepler observes in the fifth chapter of his Ad Vitellionem Paralipomena, “henceforth the [visible] representations of objects should be considered as paintings [ picturae ] that are actual[ly projected] on paper or some other screen.” While not intended as a historical generalization, this claim nonetheless reflects historical reality. Virtually all visual theorists before Kepler did, in fact, conceive of optical images as subjective, not objective constructs (...) – or, to put it in modern terms, as virtual rather than real entities. By current lights, of course, the distinction between virtual and real images is both obvious and common-place: whereas the latter can be physically projected upon a screen, the former cannot. (shrink)

This paper deals with the exact constructions of the regular heptagon in Greek and Arabic geometry, which are preserved in a number of mainly unpublished Arabic manuscripts. Appended are editions of the Arabic texts and English translations of Propositions 17 and 18 of the “Book of the Construction of the Circle, Divided into Seven Equal Parts”, attributed to Archimedes, and of the “Book on the Construction of the Heptagon in the Circle and the Division of the Rectilineal (...) Angle into Three Equal Parts” by the 10th century geometer Al-Sijzi. (shrink)

According to selective, retentive, scientific realism, past empirical success may be explained only by the parts of past theories that are responsible of their successful predictions being approximately true, and thus theoretically retained, or approximated, by the parts of posterior theories responsible of the same successful predictions. In this article, we present as case study the transit from Ptolemy’s to Kepler’s astronomy, and their successful predictions for Mars’ orbit. We present an account of Ptolemy’s successful prediction of Mars’ orbit from (...) Kepler’s perspective, and scrutinize whether the theoretical elements responsible for Ptolemy’s empirical success are approximately retained in Kepler. In order to give to the realist the best chances, we try different strategies. We conclude that all fail and thereby this case constitutes a prima facie strong anomaly for selective retentive realism. Structural realists may call preservation of structure to the rescue, but the existing notions of structure do not work. In absence of a new notion that works, the burden of the proof lies on the realist side. (shrink)

Al-Kindi was influenced by two Greek traditions in his attempts to explain vision, light and color. Most obviously, his works on optics are indebted to Euclid and, perhaps indirectly, to Ptolemy. But he also knew some works from the Aristotelian tradition that touch on the nature of color and vision. Al-Kindi explicitly rejects the Aristotelian account of vision in his De Aspectibus, and adopts a theory according to which we see by means of a visual ray emitted from the eye. (...) But in the same work, al-Kindi draws on Philoponus. (shrink)

The article deals with the Arabic sources of Chr. Clavius in Rome and the six different ways they were used by him in mathematics and astronomy. It inquires especially into his attitude towards al-Farghani, Thabit ibn Qurra, al-Bi[tdotu]ruji, Ibn Rushd, Mu[hdotu]ammad al-Baghdadi, Pseudo-Ibn al-Haytham, Jabir ibn Afla[hdotu], and Pseudo-al-[Tuotu]usi.

This article focuses on the role of statistical concepts in both experiment and theory in various scientific disciplines, especially physics, including astronomy, and psychology. In Sect. 1 the concept of uncertainty in astronomy is analyzed from Ptolemy to Laplace and Gauss. In Sect. 2 theoretical uses of probability and statistics in science are surveyed. Attention is focused on the historically important example of radioactive decay. In Sect. 3 the use of statistics in biology and the social sciences is examined, with (...) detailed consideration of various Chi-square statistical tests. Such tests are essential for proper evaluation of many different kinds of scientific hypotheses. (shrink)

This article takes up the adventure of the Arabic version of the Elements published in Rome at the Typographia Medicea in 1594 at the point where the first installment (Cassinet, Revue française d’histoire du livre 78–79:5–51, 1993) ended. In this new installment of the adventure, we situate the Rome edition within a stemma of connected Arabic copies spanning some four centuries. We show that the text of the Rome edition was typeset from Biblioteca Medicea Laurenziana, Or. 20 and (...) that Or. 20 in turn was copied from Or. 50. We show that a manuscript (Tehran, Sipahsalar 540) was later copied from the printed edition and that still later the text of the Rome edition was reissued in lithograph form in Fez. The story is important because the Rome edition influenced the development of non-Euclidean geometry in European mathematics and because the mistaken identity of its author has led to persistent errors in the history of mathematics. (shrink)

Proclus, head of the Philosophy School at Athens for fifty years, was one of the leading philosophical figures in Late Antiquity. Lucas Siorvanes here introduces Proclus to English-language readers, discussing his metaphysics and theory of knowledge and focusing in particular on his Neo-Platonism. Proclus lived in the turbulent fifth century A.D., a time of struggles among Christians, Jews, and pagans, the invasion of Attila the Hun, the fall of the Western Roman Empire, and the rise of the Eastern Roman (...) Empire in Byzantium. While Late Antiquity has been regarded as a time of superstition and forbiddingly complex philosophies, recent scholarship has shown it to be full of cultural and intellectual vigor. During Proclus's tenure as head of the Philosophy School, he systematized Neo-Platonism as the summit of ancient Greek thought, brought it to its peak of influence, and became responsible for the form in which it was transmitted to the Byzantine, Western European, and Islamic civilizations. Siorvanes's extensive original research presents Proclus as much more than just a metaphysician. He surveys all of Proclus's philosophical interests—including religion, physics, astronomy, mathematics, and poetry—revealing the philosopher's central concern with the problems of being and knowledge and relating the ideas of Proclus to those of such other major thinkers as Plato, Aristotle, and Ptolemy. To help the newcomer, Siorvanes supplies more than 200 quotations from Proclus's works. He also traces the impact of Proclus's Neo-Platonism across cultures, religions, and centuries, in such diverse areas as Christian and Islamic theologies, Renaissance art, Kepler's astronomy, Romantic poetry, Emerson's thought, modern philosophy and science, and current popular phrases. (shrink)

Suscités par la reprise massive de la recherche en astronomie au IXe siècle dans le monde islamique et essentiellement à Bagdad, laquelle nécessite des outils mathématiques nouveaux, une floraison de traités, tant astronomiques que mathématiques, voit le jour à cette époque. D'entre les traités mathématiques, un certain nombre est consacré à la ‘‘figure secteur”, c’est-à-dire au théorème dit ‘‘de Ménélaüs” sur la sphère, lequel généralise le théorème dit ‘‘de Ménélaüs” dans le plan. Ce théorème de Ménélaüs sur la sphère, ou (...) règle des six quantités, est, en l’absence du théorème des sinus sur la sphère, lequel ne date que de la deuxième moitié du Xe siècle, le principal outil de l'astronomie sphérique. Le traité de Thābit ibn Qurra sur La figure secteur est le premier de ces traités consacrés au théorème de Ménélaüs, tant dans le plan que sur la sphère, à nous être parvenu; point de départ de tout un courant, il influencera profondément le développement ultérieur de la géométrie sphérique. Ce traité, qui est en fait une épître adressée à un correspondant malheureusement anonyme, présente en outre l'intérêt de montrer que, dans le milieu scientifique de cette époque à Bagdad, beaucoup s'intéressaient à ce théorème, essayaient d'en énoncer d'autres cas de figure et de compléter la démonstration qu'en donne Ptolémée dans l'Almageste. (shrink)

The latest in the series based on the popular History of Philosophy podcast, this volume presents the first full history of philosophy in the Islamic world for a broad readership. It takes an approach unprecedented among introductions to this subject, by providing full coverage of Jewish and Christian thinkers as well as Muslims, and by taking the story of philosophy from its beginnings in the world of early Islam all the way through to the twentieth century. Major (...) figures like Avicenna, Averroes, and Maimonides are covered in great detail, but the book also looks at less familiar thinkers, including women philosophers. Attention is also given to the philosophical relevance of Islamic theology (kalam) and mysticism--the Sufi tradition within Islam, and Kabbalah among Jews--and to science, with chapters on disciplines like optics and astronomy. The book is divided into three sections, with the first looking at the first blossoming of Islamic theology and responses to the Greek philosophical tradition in the world of Arabic learning. This 'formative period' culminates with the work of Avicenna, the pivotal figure to whom most later thinkers feel they must respond. The second part of the book discusses philosophy in Muslim Spain (Andalusia), where Jewish philosophers come to the fore, though this is also the setting for such thinkers as Averroes and Ibn Arabi. Finally, a third section looks in unusual detail at later developments, touching on philosophy in the Ottoman, Mughal, and Safavid empires and showing how thinkers in the nineteenth to the twentieth century were still concerned to respond to the ideas that had animated philosophy in the Islamic world for centuries, while also responding to political and intellectual challenges from the European colonial powers. (shrink)

Among the phenomena examined in the Meteorologica, some, although they are sublunar, are too distant to be accessible to direct study. To remedy this situation, it was necessary to develop procedures and methods which could allow observation, and above all the geometrical control of observations. The eventual result of this research was to detach the phenomenon under consideration from meteorology, and to insert it within optics or astronomy. Abū Sahl al-Qūhī, composed a treatise on shooting stars in which he carries (...) out such an insertion. In a second treatise, he deals with another type of observation, intended to measure maritime, terrestrial, and celestial surfaces. Here, the author studies al-Qūhī's contribution and gives the editio princeps of these two treatises, as well as their translation. (shrink)

RésuméLe problème de la détermination de la Qibla est l'une des questions cruciales qui se posent à la culture scientifique de l'Islam médiéval; le résoudre correctement nécessite tant des théories mathématiques que des observations. Les mathématiques relèvent de deux chapitres: la trigonométrie plane et la trigonométrie sphérique. L'observation et les instruments d'observation sont indispensables à la détermination des coordonnées géographiques de La Mecque et du lieu donné; ces coordonnées sont en effet les données que l'on entre dans les formules donnant (...) la Qibla. Dans son Almageste, Abū al-Wafāʾ résout brillamment ce problème. Son travail porte tant sur les mathématiques que sur l'observation; il obtient des solutions modernes, adéquates et faciles. En trigonométrie plane, il donne de nouvelles définitions des fonctions trigonométriques, démontre les formules des sinus, donne une approximation de sin 1° grâce à laquelle il construit des tables de sinus et de tangentes d'une grande précision. En trigonométrie sphérique, il démontre quatre nouveaux théorèmes dont la règle des tangentes ; cette règle lui permet de trouver, comme nous le montrerons, des solutions simples au problème de la détermination de la Qibla. En ce qui concerne les observations, il décrit trois instruments utilisés par lui plusieurs années de suite à Bagdad. Cet article, nourri de nombreux textes arabes originaux traduits et commentés, donne une description détaillée, technique et analytique, des méthodes mathématiques d'Abū al-Wafāʾ pour la détermination de la Qibla. (shrink)

Peter Adamson presents the first full history of philosophy in the Islamic world for a broad readership. He traces its development from early Islam to the 20th century, ranging from Spain to South Asia, featuring Jewish and Christian thinkers as well as Muslim. Major figures like Avicenna, Averroes, and Maimonides are covered in great detail, but the book also looks at less familiar thinkers, including women philosophers. Attention is also given to the philosophical relevance of Islamic theology and mysticism--the (...) Sufi tradition within Islam, and Kabbalah among Jews--and to science, with chapters on disciplines like optics and astronomy. The first part of the book looks at the blossoming of Islamic theology and responses to the Greek philosophical tradition in the world of Arabic learning, the second discusses philosophy in Muslim Spain, and a third section looks in unusual detail at later developments, touching on philosophy in the Ottoman, Mughal, and Safavid empires. (shrink)

The Philosophy and logic in Islamic thought, unlike Christian culture, developed uncensored and as a result of great demand. After the biggest translation movement in history, important components of Ancient Greek, Syriac, Persian, Jewish and Hindu cultures were transferred to Arabic. Kalam, which developed earlier in Islamic culture, has also been effective in understanding and accepting the philosophical content. In the beginning, translations were made in fields such as medicine, chemistry, astronomy and mathematics. Philosophy literature was also (...) translated into Arabic due to its close relationship with other sciences and the need to fill the "gaps" in Islamic culture. The philosophy of logic was also transferred to Arab culture in its Aristotelian form. Especially the great influence of Aristotle helped strengthen the thought of logic among Arab philosophers and some theologians. As with other translation content, the logic has been translated into Arabic without any censorship. Contrary to the thinkers of Christian culture, Islamic philosophers learned all the subtleties of logic in a free intellectual environment, and as a result, this fact created a way for them to make a unique contribution to the discipline of logic. Logic, as it has been transformed into Arabic elements in Islamic culture, has been influential in basic areas such as theology, language, fiqh and kalam. In this process, logic, which was handled intertwined with traditional philosophy, has progressed to become a refined thought, especially with the influence of the first great philosopher Fârâbî. Fârâbî is not only a great philosopher but also a great Islamic scholar, and these qualities enabled him to adapt logic to Arab culture and Islamic sciences from his Aristotelian roots. Fârâbî, just like Aristotle, wanted to use logic as a criterion of truth for philosophical fields. Fârâbî, who designed logic under two main headings such as concepts and judgments, adapted logic to Arab culture for Muslims in the reasoning process. This solid construction of logic not only strengthened philosophical thought, but also contributed to the later establishment of a solid structure in Islamic sciences. In this context, the understanding of Islamic philosophy and its transformation with the effect of logic require a close examination of Fârâbî's thought. In our article, we will briefly discuss the pre-Islamic origins of philosophy and logic, and on this plane, we will examine Fârâbî's contribution to philosophy of some basic issues such as God, the classification of sciences, and the philosophical dimension of logic and try to reveal his effects on Islamic culture from a general point of view. (shrink)

Among the phenomena examined in the Meteorologica , some, although they are sublunar, are too distant to be accessible to direct study. To remedy this situation, it was necessary to develop procedures and methods which could allow observation, and above all the geometrical control of observations. The eventual result of this research was to detach the phenomenon under consideration from meteorology, and to insert it within optics or astronomy. Abū Sahl al-Qūhī , composed a treatise on shooting stars in which (...) he carries out such an insertion. In a second treatise, he deals with another type of observation, intended to measure maritime, terrestrial, and celestial surfaces. Here, the author studies al-Qūhī's contribution and gives the editio princeps of these two treatises, as well as their translation. (shrink)

Ptolemy´s astronomy and the Galileo case: two historical and epistemological considerations The Galileo case is the most famous example of the encounter betwen science and Faith. The debate was centered, among others, in the field of epistemology and the history of science. The paper shows that the Galilean pretentions of interpreting the heliocentric hypothesis in a realistic way did not constituted a novelty, but rather it was a continuation of the most important Ptolemaic astronomical tradition. It also argues that the (...) Copernican hypothesis did not inaugurate, because of the introduction of the Earth´s motion, a new phase of conflict between astronomy and physics. This conflict already existed, at least, since the times of Ptolemy. (shrink)