In this paper, I explore general features of the “architecture” (relations of white space, diagram, and text on the page) of medieval manuscripts and early printed editions of Euclidean geometry. My focus is primarily on diagrams in the Arabic transmission, although I use some examples from both Byzantine Greek and medieval Latin manuscripts as a foil to throw light on distinctive features of the Arabic transmission. My investigations suggest that the “architecture” often takes shape against the backdrop of an educational (...) landscape. The constraints of the economic marketplace and cultural aesthetic ideals also appear to play a role in determining the “architecture” of both manuscripts and early printed editions. (shrink)

During the Middle Ages many Greek mathematical and astronomical texts were translated from Greek into Arabic and from Arabic into Latin. There were many factors complicating the study of them, such as translation from or into other languages, redactions, multiple translations, and independently transmitted scholia. A literal translation risks less in loss of meaning, but can be clumsy. This article includes lists of translations and a large bibliography, divided into sections.

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.

Medieval Arabic algebra is a good example of an artificial language.Yet despite its abstract, formal structure, its utility was restricted to problem solving. Geometry was the branch of mathematics used for expressing theories. While algebra was an art concerned with finding specific unknown numbers, geometry dealtwith generalmagnitudes.Algebra did possess the generosity needed to raise it to a more theoretical level—in the ninth century Abū Kāmil reinterpreted the algebraic unknown “thing” to prove a general result. But mathematicians had no motive to (...) rework their theories in algebraic form. Because it offered no advantage over geometry, algebra remained a practical art in both the Islamic world and in Europe until the scientific uphevals of the 17th–18th centuries. (shrink)

The government of the State of Ohio determined to design several mandatory programs in regular classes to help NRC’s female in mates to prepare themselves upon their release back to the community; one of the programs is Islamic teaching. It is a chance to insert and implement the innovated peaceful Islamic propagation beside the conventional one, especially in western countries like the United States of America. The chance for an innovated dakwah is open upon observing that a lot of non- (...) Muslimah in mates were curious about Islam in an inter-religious meeting. The Arabic script classis not a part of mandatory NRC programs, it is voluntary for non- Muslimin mates designed and implemented by the author. They learn to write and pronounce the Arabic alphabet from “alif’ to ‘ya’ within six weeks. This free class is to support the government programs in order to reduce recidivism among in mates, and upon completing this class they are encouraged to attending the Islamic teaching class. This paper is qualitative research using a sociology approach. The data collection for this research is using participative observation, voluntary interview, and documentation; the collected data were analyzed in the descriptive-qualitative method. The effectiveness and efficacy of the research should be measured in a quantity of non- Muslimah in mates who gradually and peacefully convert to become Muslimah after attending the Arabic script class. The benchmark of effectiveness should be affirmed in mathematic formula i.e. the effectiveness is equal to the number of Muslimah converts divided by the total participant time 100; it is x 100 = 33.33%. Among 9 non- Muslimah participants of free Arabic script class,3 of them converted to be Muslimah. (shrink)

This is the first critical edition of the first and second Epistles of the Brethren Purity--the Rasa 'il--in Arabic with a fully annotated English translation. It presents technical and epistemic analyses of mathematical concepts and their metaphysical bases, and an overview of the mathematical sciences within Islamic intellectual milieu.

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)

This study analyzes the content of 12th-grade mathematics textbooks and workbooks, based on their inclusion of mathematical discourse components. The mathematics textbooks and workbooks were used in a Saudi Arabian school, where students are transitioning from secondary education to university. The results revealed that Saudi Arabian school textbooks and workbooks did not appropriately include discourse components or discourse skills to help facilitate mathematical learning among students. Furthermore, these textbooks did not exceed level two of the four levels of inclusion. As (...) a result, the inclusion was insufficient in helping students meaningfully understand mathematical concepts, become active students, and develop successful community leadership. This implies that mathematics textbooks and workbooks should be revised to include mathematical discourse so that this inclusion is more student directed than teacher directed. (shrink)

RésuméDans les Sphériques, Ménélaüs ne démontre pas l'importante proposition III.5, mais propose seulement une esquisse de démonstration. Une fois le livre des Sphériques traduit en arabe, les mathématiciens, à partir de la fin du IXe siècle, ont voulu en donner une démonstration complète. Le développement de la géométrie sphérique a permis à Ibn ʿIrāq de parvenir au but. Un premier article a été consacré à sa contribution. Deux mathématiciens du XIIIe siècle – Naṣīr al-Dīn al-Ṭūsī et Ibn Abī Jarrāda – (...) ont repris la démonstration de cette même proposition, à partir de Ménélaüs et des acquis d'Ibn ʿIrāq. C'est le sujet du présent article. (shrink)

It has long been considered that Arabic algebra scarcely left any traces in mathematical literature of Hebrew expression. Thanks to the unpublished sources we have discovered, and to an attentive examination of already-known texts, one can no longer subscribe to such a judgement. The evidence we examine in this first article sheds light on the circulation, in erudite Jewish circles, of Arabic algebraic knowledge in Spain, Italy, Provence, and Sicily, between the 12th and the 14th centuries. The Epistle on number (...) by the Castillian astronomer Isaac ben Salomon al-A[hudot]dab was written in Sicily at the end of the 14th century, and based on the Talkhi[sudot] a'mal al-[hudot]isab of Ibn al-Banna' (1256-1321). That part of the Epistle that is devoted to algebra follows the tradition of al-Karaji. It offers, for the first time in Hebrew, a rational presentation of arithmetical operations extended to algebraic expressions. (shrink)

This article shows how Arab students at an Arab college in Israel, majoring in teaching of mathematics, English, and science, rely on metaphor as an important rhetorical tool for the advancement of their ideological positions and for criticism of the policies of the Israeli government, which discriminates against and disenfranchises Arab Israelis. The underlying hypothesis of the article is that the way Arab students in Israel use metaphor in their writing has unique rhetorical aspects that help to sharpen their message (...) in pursuit of the broader goal of emphasizing Arab Israelis’ suffering and changing for the better the Israeli government’s discriminatory patterns of action against them. (shrink)

Representations of the heavens in various levels of detail can be found in a number of branches of Arabic literature. One particular genre, the hay'a texts, has as its purpose a full though non-mathematical discussion of the arrangement of the celestial orbs; hay'a writers are particularly sensitive to the philosophical requirements which all systems must meet. The pivotal work in this genre, On the Configuration, was written by Ibn al-Haytham. Later writers continued to produce works in the spirit of On (...) the Configuration. In the east, al-Tusi and his followers developed new models; in the west, a group of thinkers tried to rediscover the models which, so they thought, were the ones endorsed by Aristotle himself. (shrink)

Philosophy; mathematics; Avicenna, 980-1037; Fārisī, Kamāl al-Dīn Abū al-Ḥasan, active 1300.

The Arabic-Islamic tradition is founded on the following new epistemic attitude that reinvents knowledge: to learn from the contributions of previous civilisations through the systematic survey of all extant scientific works; to contribute to the further development of knowledge by linking it, through usefulness, to practice and the practical need of society; to facilitate its learning for younger generations and its transmission to future civilizations since it is conceived not as a finished product but as an ongoing process. The worldwide (...) development of the reinvented knowledge has led to its universalisation and the rapid expansion of mathematics has particularly and led to the complete de-hellinisation of the Greek conception of science and philosophy. (shrink)

Ever since its publication by Heiberg in the 19th century, we have known that the surviving Greek text of The Measurement of the Circle by Archimedes is faulty, altered by the intervention of a compiler. At least some parts of it are therefore of dubious authenticity. More recently, an examination of the ninth-century Latin translation of the Arabic translation of this text has led to the conclusion that the translated Greek manuscript belongs to a better and older textual tradition than (...) the text edited by Heiberg. This study contains the editio princeps of the Arabic translation of The Measurement of the Circle, its first translation and a historical and mathematical analysis. The many readings of this translation over the centuries have inspired several “redactions.” Three of these will be edited, translated and examined in a forthcoming study. (shrink)

In terms of control of composition, the fabrication of money was arguably the most demanding of all pre-Industrial Revolution metallurgical practices. The calculations involved in such control needed arithmetical computations involving repeated multiplications and divisions, not only of integers but also of mixed numbers. Such computations were possible using Roman numerals, but with some difficulties. The advantages gained by employing arithmetic using Indo-arabic numerals for alloying calculations would have been the same as for other types of commercial calculations. A method (...) of calculating the proportions of two coinage alloys of different compositions that were needed to produce a third alloy of specified intermediate composition, eventually known as the rule of alternate alligation, was however, a specific requirement in the minting of money. This requirement made a particular demand on medieval mathematics, as a solution was not possible using arithmetic alone. Furthermore, the problem became indeterminate when more than two components were available for mixing. All the necessary methods of calculation were described by Fibonacci in his Liber abbaci. These methods are to be found in a sequence of practical arithmetics that stretch through the trattati d'abbaco of the Italian city states during the fourteenth and fifteenth centuries, to the first printed books of Continental authors such as Pacioli. Of the earliest sixteenth-century printed English books on practical arithmetic, The Grounde of Artes by Robert Recorde contained the first advance in the methodology of alternate alligation since Fibonacci. In the seventeenth century, formal proof of the rule of alternate alligation was given by Kersey in his practical arithmetics and his treatise on algebra. The topic was also addressed by several authors of academic algebras. It was in this century that the problem of indeterminacy in the solution of alternate alligation involving the mixture of more than two components, was finally resolved. English mint accounts provide little direct information on the alloying calculations carried out, and nothing on the methods used. However, the continued description of such calculations in other mint documents, merchants notebooks, and in goldsmiths' handbooks spanning four centuries imply that the calculations described in practical arithmetics were used in practice. Monetary matters had high economic and political profiles during the whole of the time span covered in this study. The influence of such considerations pervades the history of the technology of minting and the mathematics on which it called, and is discussed in context. (shrink)

This volume is a collection of essays in honour of Professor Mohammad Ardeshir. It examines topics which, in one way or another, are connected to the various aspects of his multidisciplinary research interests. Based on this criterion, the book is divided into three general categories. The first category includes papers on non-classical logics, including intuitionistic logic, constructive logic, basic logic, and substructural logic. The second category is made up of papers discussing issues in the contemporary philosophy of mathematics and logic. (...) The third category contains papers on Avicenna’s logic and philosophy. Mohammad Ardeshir is a full professor of mathematical logic at the Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran, where he has taught generations of students for around a quarter century. Mohammad Ardeshir is known in the first place for his prominent works in basic logic and constructive mathematics. His areas of interest are however much broader and include topics in intuitionistic philosophy of mathematics and Arabic philosophy of logic and mathematics. In addition to numerous research articles in leading international journals, Ardeshir is the author of a highly praised Persian textbook in mathematical logic. Partly through his writings and translations, the school of mathematical intuitionism was introduced to the Iranian academic community. (shrink)

This book highlights the emergence of a new mathematical rationality and the beginning of the mathematisation of physics in Classical Islam. Exchanges between mathematics, physics, linguistics, arts and music were a factor of creativity and progress in the mathematical, the physical and the social sciences. Goods and ideas travelled on a world-scale, mainly through the trade routes connecting East and Southern Asia with the Near East, allowing the transmission of Greek-Arabic medicine to Yuan Muslim China. The development of science, first (...) centred in the Near East, would gradually move to the Western side of the Mediterranean, as a result of Europe's appropriation of the Arab and Hellenistic heritage. Contributors are Paul Buell, Anas Ghrab, Hossein Masoumi Hamedani, Zeinab Karimian, Giovanna Lelli, Marouane ben Miled, Patricia Radelet-de Grave, and Roshdi Rashed. (shrink)

RésuméC'est le premier d'une série d'articles comportant quatre textes composés entre le XIeet le XIIIesiècle, qui traitent de la proposition 5 du livre III desSphériquesde Ménélaüs. Le premier article comprend des commentaires historiques et mathématiques de l'œuvre d'Ibn ʿIrāq en géométrie sphérique et une édition critique des deux textes qu'il a consacrés à la rectification de la proposition III.5, ainsi que la traduction de ces deux textes. Le second article propose une édition critique des textes de Naṣīr al-Dīn al-Ṭūsī et (...) d'Ibn Abī Jarrāda sur le même sujet, cette fois aussi avec une traduction et des commentaires historiques et mathématiques. (shrink)

The Ikhwan al-Safa (Brethren of Purity), the anonymous adepts of a tenth-century esoteric fraternity based in Basra and Baghdad, hold an eminent position in the history of science and philosophy in Islam due to the wide reception and assimilation of their monumental encyclopaedia, the Rasa'il Ikhwan al-Safa (Epistles of the Brethren of Purity). This compendium contains fifty-two epistles offering synoptic accounts of the classical sciences and philosophies of the age; divided into four classificatory parts, it treats themes in mathematics, logic, (...) natural philosophy, psychology, metaphysics, and theology, in addition to didactic fables. The Rasa'il constitutes a paradigmatic legacy in the canonization of philosophy and the sciences in mediaeval Islamic civilization, as well as having shown a permeating influence in Western culture. This is the fifth volume in a series presenting the very first critical edition of the Rasa'il in its original Arabic, complete with the first fully annotated English translation. Epistle 52: On Magic is the last in the corpus, and presents the short version of the 'Epistle on Magic, Incantations, and the Evil Eye'. Within its pages the authors of the epistle argue for the legitimacy of magic and the other occult sciences, and seek confirmation of their views in authorities as diverse as Plato, the Qur'ân, the Torah, the astrologer Abû Ma'shâr, and the mysterious sect of pagan star-worshippers known as the Sabians of Harrân. As in all other volumes of the series, this volume provides the first critical edition of the Arabic text, together with an English translation and a substantial range of notes. An extensive introduction highlights the unique relevance of this treatise within the framework of the Brethren's encyclopaedia itself, and to the history of science in general. (shrink)

This paper investigates the objections that were raised by the philosopher ‘Abd al-La&tdotu;īf al-Baghdādī against al-&Hdotu;asan ibn al-Haytham’s geometrisation of place. In this line of enquiry, I contrast the philosophical propositions that were advanced by al-Baghdādī in his tract: Fī al-Radd ‘alā Ibn al-Haytham fī al-makān, with the geometrical demonstrations that Ibn al-Haytham presented in his groundbreaking treatise: Qawl fī al-Makān. In examining the particulars of al-Baghdādī’s fragile defence of Aristotle’s definition of topos as delineated in Book IV of the (...) Physics, which was rejected on mathematical grounds by Ibn al-Haytham, a special attention is also given to highlighting the systemic distinctions between the entities that are studied within the speculative physical doctrines of common sense and immediate experience, and the postulated ‘objects’ of scientific and mathematical research. (shrink)

The perfect compass, used by al-Qūhī, al-Sijzī and his successors for the continuous drawing of conic sections, reappeared after a long eclipse in the works of Renaissance mathematicians like Francesco Barozzi in Venice. The resurgence of this instrument seems to have depended on its interest to solve new optico-perspective problems. Having reviewed the various instruments designed for the drawing of conic sections, the article is focused on the sole conic compass. Theoretical and empirical applications are detailed. Contrarily to the common (...) thesis of an independant discovery, various elements suggest a direct descent between the birkār al-tāmm of the Arabic mathematical tradition and the Italian conic compass. Then we present the most probable transmission hypothesis involving: 1° Ibn Yūnus and his disciples of Mosul, 2° Sultan Malik al-Kāmil in Damas, 3° Master Theodore and Frederick II at the court of Sicily, 4° Andalò di Negro and Robert of Anjou in Naples, 5° Lorenzo della Volpaia, Vinci, Sangallo and Michelangelo in Florence, 6° Ausonio, Contarini, Thiene and Francesco Barozzi in Venice. (shrink)

Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th–16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. This brought about the crucial change in the concept of number that made possible modern science — in which the symbolic "form" of a mathematical statement is completely inseparable from its "content" of physical meaning. Includes a translation of Vieta's Introduction to the Analytical Art. 1968 edition. Bibliography.

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)

Duhem has generally been understood to have maintained that the major Greek astronomers were instrumentalists. This view has emerged mainly from a reading of his 1908 publication To Save the Phenomena. In it he sharply contrasted a sophisticated Greek interpretation of astronomical models (for Duhem this was that they were mathematical contrivances) with a naive insistence of the Arabs on their concrete reality. But in Le Système du monde, which began to appear in 1913, Duhem modified his views on Greek (...) astronomy considerably; his more subtle understanding included the recognition that many Greeks subordinated mathematical astronomy to physical theory. But he could not completely repudiate his earlier views about Greek astronomy in part because his extreme nineteenth century prejudices led him to continue to insist on a clear-cut demarcation between Greek and Arabic astronomy. The inevitable result is a certain unevenness in the Système and some glaring inconsistencies. (shrink)

Summary Syriac translations and Syriac scholars played an important role in the transmission of the sciences, including the mathematical sciences, from the Greek to the Arabic world. Relatively little, unfortunately, remains of the translations and original mathematical works of earlier Syriac scholars, but some materials have survived, and further glimpses of what once existed may be gained from works of later authors. The paper will provide an overview of the earlier materials that have survived or are known to have existed. (...) This will be followed by an account of some of the later materials, which will include an example illustrating how further earlier materials can be recovered from the writings of later authors, and a mention, by way of an epilogue, of an instance where a Syriac scholar was involved in a major historical and scientific event in the West, namely the reform of the calendar by Gregory XIII. (shrink)

Summary In terms of control of composition, the fabrication of money was arguably the most demanding of all pre-Industrial Revolution metallurgical practices. The calculations involved in such control needed arithmetical computations involving repeated multiplications and divisions, not only of integers but also of mixed numbers. Such computations were possible using Roman numerals, but with some difficulties. The advantages gained by employing arithmetic using Indo-arabic numerals for alloying calculations would have been the same as for other types of commercial calculations. A (...) method of calculating the proportions of two coinage alloys of different compositions that were needed to produce a third alloy of specified intermediate composition, eventually known as the rule of alternate alligation, was however a specific requirement in the minting of money. This requirement made a particular demand on medieval mathematics, as a solution was not possible using arithmetic alone. Furthermore, the problem became indeterminate when more than two components were available for mixing. All the necessary methods of calculation were described by Fibonacci in his Liber abbaci. These methods are to be found in a sequence of practical arithmetics that stretch through the trattati d'abbaco of the Italian city states during the fourteenth and fifteenth centuries, to the first printed books of Continental authors such as Pacioli. Of the earliest sixteenth-century printed English books on practical arithmetic, The Grounde of Artes by Robert Recorde contained the first advance in the methodology of alternate alligation since Fibonacci. In the seventeenth century, formal proof of the rule of alternate alligation was given by Kersey in his practical arithmetics and in his treatise on algebra. The topic was also addressed by several authors of academic algebras. It was in this century that the problem of indeterminacy in the solution of alternate alligation involving the mixture of more than two components, was finally resolved. English mint accounts provide little direct information on the alloying calculation carried out, and nothing on the methods used. However, the continued description of such calculations in other mint documents, merchants notebooks, and in goldsmiths' handbooks spanning four centuries imply that the calculations described in practical arithmetics were used in practice. Monetary matters had high economic and political profiles during the whole of the time span covered in this study. The influence of such considerations pervades the history of the technology of minting and the mathematics on which it called, and is discussed in context. (shrink)

It was a strange posthumous fate that awaited the Englishman Robert of Ketton : he was to be both best known and most strenuously criticized for a work that he surely viewed as a sideline to his own interests and career. By trade Robert was a Latin translator of Arabic scientific and mathematical works, one of those remarkable twelfth-century men who, as his contemporary Petrus Alfonsi put it, were willing “to traverse distant provinces and withdraw into remote regions so as (...) to be able to attain fuller knowledge of the astronomical art.” Like other contemporary translators, such as the Italian Gerard of Cremona , Robert had left his birthplace—in his case Rutlandshire—and traveled to Spain in order to have access to the great works of Arabic astronomy and mathematics that could be found in the still very Arab Iberian Peninsula. By 1141 we find him and his close friend Herman of Carinthia studying and translating scientific works together in northeastern Spain, and in later years his astronomical interests and ecclesiastical responsibilities led him to travel widely in Spain and England. As a scientific translator, he is perhaps best known for his Liber algebrae et Almucabola, a Latin version of al-Khwarazmī's great manual of algebra, Al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa-al-muqābalah. (shrink)

The thesis deals with a section of the major philosophical summa by Avicenna (Ibn Sīnā, d. 1037), namely the Book of the Healing (Kitāb al-Šifāʾ). The summa is structured into four parts, devoted to Logic, Natural Philosophy, Mathematics and Metaphysics; the section at stake is Avicenna’s reworking of Porphyry’s Isagoge (Kitāb al-Madḫal, i.e. “Book of the Introduction”) opening the section of Logic of the Šifāʾ. The thesis is articulated into three main parts, namely (i) an edition of the Arabic text (...) of Avicenna’s Madḫal, (ii) an English translation and (iii) a systematic commentary; these three main parts are preceded by an Introduction (0) divided into two halves: (0a) a General Introduction focused on the doctrinal major innovations of the work and (0b) an Introduction to the Edition of the text, which offers a first comprehensive study of its direct and early indirect tradition and explains the criteria of the edition. (i) The only previous edition of Avicenna’s Madḫal was the one printed in Cairo in 1952 (then reprinted in Tehran in 1983 and in Beirut in 1993), based on ten manuscripts. The huge manuscript tradition of Avicenna’s Madḫal – and, more in general, of Avicenna’s Book of the Healing – is still a matter of investigation. According to the provisional results of the bibliographical research conducted in the present work, it can be estimated that the manuscript tradition of the Madḫal amounts to at least 119 certain witnesses and 14 possible additional witnesses (as explained in the Introduction to the edition, 0b). The text of the Cairo edition, far from being representative of the whole textual tradition, was reconstructed on the basis of ten manuscripts that were not selected on the basis of philological criteria and whose reciprocal stemmatic relations were not clear. Although a critical edition based on all the 119 certain witnesses of the work exceeds the scope of the present work, the edition provided in the thesis takes into account a larger number of manuscripts than the Cairo edition did and, most importantly, selects them by means of a preliminary collation made on portions of the text. The purpose of this preliminary collation is making the selection of the manuscripts employed less arbitrary and providing a reconstruction of their stemmatic relations (in the Introduction, 0b). Overall, 32 manuscripts among the 68 inspected were employed in the edition here proposed, 21 of which were systematically collated and 11 were eliminated as codices descripti. The present edition also assumes as a witness the twelfth-century Latin translation of the work, which is, at the present moment, among the earliest extant witnesses of the text. Hopefully, this editorial work allowed us to improve the text of the Cairo edition in a number of points that are crucial to the correct understanding of Avicenna’s argumentation. (ii) As this project started, complete translations of Avicenna’s Madḫal in modern languages were only available in Turkish and Russian. Chapters of the work had also been translated in other languages, but an English translation of the whole work was still a desideratum. A complete English translation is provided in the thesis, based on the newly-established Arabic text of the work and aiming at preserving the major possible consistency in rendering the relevant philosophical terms. As a complement to the translation, an apparatus of notes is offered to facilitate the immediate understanding of the text. (iii) The third section of the thesis consists in a systematic commentary on Avicenna’s Madḫal, which is meant to support a deeper understanding of the text in its entirety. The commentary deals with both historical and philosophical aspects; more in detail, it includes an analysis and an identification, when possible, of Avicenna’s sources, and underlines the points of major philosophical interest of the work, which are dealt in a more comprehensive manner in the General Introduction (0a). (shrink)

Do not believe that the philosophy that has reached us through the writings of Aristotle, Abû Nasr (al-Fârâbî), and the book of Healing (of Ibn Sinâ), will satisfy your longing; neither that any of the Andalusians has written anything adequate on this matter. For the men of superior understanding who lived in Andalusia before the spread of logic and philosophy in that country, devoted their lives to the mathematical sciences…; but could do nothing more…” Ibn Tufayl, Hayy ibn Yaqzân, p. (...) 12.Much remains to be done by way of determining exactly the ways in which Arab thought penetrated Western Islam-I refer both to its sociological extension and the depth of its psycho-cultural effect. The question thus posed is of considerable historical importance, above all if one wishes to cover the whole period from the beginning of the Eighth Century (i.e. the end of the First/beginning of the Second Century of the Hegira), up to the present day. In fact, the spread of Arab thought to the Maghreb, and its penetration in depth, was accelerated again after the reconquest of the politically autonomous areas. This situation lends our research a certain topicality, whence spring both advantages and disadvantages: there is the advantage of historical knowledge not being limited to an erudite accumulation of facts about a past that has no links with any extant community; yet there is the problem that it is hard not to evoke the past in order to justify present ideological ventures. (shrink)

This is a translation of Jacob Klein's study "Die Griechische Logistik und die Entstehung der Algebra" which appeared in 1934-1936. His principal thesis is that the Renaissance mathematicians of the sixteenth century did not simply continue the work of the Greek and Arab mathematicians but in the process of developing ancient mathematics introduced a radically new conception of number which has since guided modern mathematical thought. The central figure in this revolution is Vieta. Klein traces the influence of Vieta's ideas (...) upon Stevin, Descartes, Wallis, and other figures of the scientific revolution, after discussing the conception of number and arithmetic in Plato, Aristotle, and other Greek sources. Persons reading this book with a primary interest in the philosophical ideas involved will be frustrated by the mass of historical detail which often obscures rather than illuminates the philosophical issues. But the book deserves its reputation as an important historical study.--R. H. K. (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)

…sit necessaria sciencia mathematice ad bona anime procuranda.Scientific humanism in the 15th and 16th century witnessed the spread of Greek and Arabic mathematics, whose reading was disciplined by philological research, enriched by the practical sense of abacus masters and diffused by the press. This doesn't mean that before this time many of these works were totally unknown. Around the 13th century mathematics scholars were already familiar with the work of Theodosius, Archimedes, Vitruvius, the Banū Mūsā brothers and so on; however, (...) these works were confined to small intellectual circles, and turned into an object for philosophical speculation.This was the case of... (shrink)

The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical (...) practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of “geometric judgments” from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) “space” should be revisited for the purposes of life sciences. (shrink)

The Ikhwan al-Safa (Brethren of Purity), the anonymous adepts of a tenth-century esoteric fraternity based in Basra and Baghdad, hold an eminent position in the history of science and philosophy in Islam due to the wide reception and assimilation of their monumental encyclopaedia, the Rasa'il Ikhwan al-Safa ( Epistles of the Brethren of Purity ). This compendium contains fifty-two epistles offering synoptic accounts of the classical sciences and philosophies of the age; divided into four classificatory parts, it treats themes in (...) mathematics, logic, natural philosophy, psychology, metaphysics, and theology, in addition to didactic fables. The Rasa'il constitutes a paradigmatic legacy in the canonization of philosophy and the sciences in mediaeval Islamic civilization, as well as having shown a permeating influence in Western culture. The present volume is the second of this definitive series, consisting of the very first critical edition of the Rasa'il in its original Arabic, complete with the first fully annotated English translation. Prepared by Professor Carmela Baffioni, Epistles 10-14 comprise the foundations of logic, which remained a fundamental component in pedagogy until the twentieth century. The Ikhwan treat the Isagoge and the larger part of the Organon , both of which were circulating through the Islamic world at that time, as they set about detailing the ten categories of existents, the five predicables, and other such commonplaces of Aristotelian logic, including his seminal method of syllogistic inference. With the claim that logic is the noblest of man's arts, and man the noblest of creatures, the Ikhwan cast Aristotelian tropes in a spiritual light. (shrink)

The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic ; analytical philosophy, philosophy of science, philosophy of mathematics and decision theory and foundations of economics. (...) Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic. (shrink)

Qurʾān was revealed to the Prophet Muḥammad (pbuh) not as a written document, but by word of mouth over a period of approximately 23 years. He dictated the verses to the scribes of revelation. After this, Abū Bakr compiled the written verses; i.e. gathered between two covers. Thus when the Qurʾān was compiled as a text, a number of addresses lost their characteristics. This situation, which is a result of the shortcomings in inscription, suggested the necessity of separating the verses, (...) preserving the recitation method (waqf places) learned from Prophet and transmitting the Qurʾān towards new learners. As a result, the science of al-Waqf and al-Ibtidāʾ has emerged. The systematics of al-Sajāwandī was chosen among the people who systematized the waqfs marks and the mushafs that we have today are arranged according to the systematics of al-Sajāwandī. At this point, the issue of showing other addressing features of the Qurʾān, such as the emphasis, in text appeared as an area that to be considered. The aim of this study is to analyze this issue and to focus on the possibility and method of realizing the subject. If punctuation marks are to be added to the Qurʾānic text, this should be done by taking into account the characteristics of punctuation marks in Arabic. According to comparison between punctuation and wakf marks, it was seen that they have different characteristics. First difference is the systematic difference. Punctuation marks in modern Arabic script are divided into four groups: end marks, tone marks, quotation marks, and the signs used in mathematics. However, al-sajawānds consists of only end/stop marks. In this case, al-sajawānds do not function as punctuation marks indicating tone of voice/emphasis and quotations. The second difference is that punctuation marks are more about the meaning than waqf marks. Because waqf marks do not oblige reader to understand only one of the possible meanings. However, punctuation marks limit or even determine the meanings. In addition, waqf marks are also based on the recitation(s) of the Prophet/al-qirāʾat al-manqulah. Correct comprehension depends on correct reading. For correct reading, addressable features must be able to be incorporated into the text as much as possible. Today’s muṣḥaf, cannot show emotions, emphasis to the reader. Beside, each of the characteristics of waqf marks (al-waqf al-muʿānaqah ext.) cannot meet the end marks found in today’s punctuation marks. In this case, we can add emphasis marks to text in order to reflect the emphasis that are missing from them by keeping al-sajāwands. Likewise, the question of to where/whom the word belongs to, which may cause confusion in text, can be resolved with quotation marks. Hereby, it has been concluded that a pseudonym system that can reflect the emphasis features of the Qurʾān and show quotations, should be developed in addition to al-sajāwands. So, our proposal includes the following steps: keeping al-sajāwands existing in the muṣḥaf; placing the emphasis marks in today's punctuation marks, which will serve this function in places where the emphasis and tone of prayer’s voice cannot be reflected in writing; putting quotation marks. Thus, it will be possible to develop a system that can show the linguistic, grammatical, semantic, phonetic, emotional and reciprocity dimensions of address in the writing/text. In this context, the punctuation marks that we find useful to be added to the muṣḥaf are emphasis marks (:!؟) and some quotation marks («»: -). قَالَ فَمَنْ رَبُّكُمَا يَا مُوسٰى؟ قَالَ رَبُّنَا الَّذ۪ٓي اَعْطٰى كُلَّ شَيْءٍ خَلْقَهُ ثُمَّ هَدٰى. Tāhā 20/49-50 As an example, in this verse, there is a real question that is expected to be answered. Then a question mark can be put at the end of this sentence. In addition, a dot mark can be placed at the end of the answer sentence to indicate that the answer is concluded. (shrink)

This is the first critical edition of a fascinating medieval work on music, written in Iraq in the tenth century. It is accompanied by an English translation and full annotation. The Epistle examines not just the technical, scientific, and mathematical aspects of music, but its cosmic, psychological, and spiritual dimensions.

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)

The Ikhwan al-Safa' (Brethren of Purity), the anonymous adepts of a tenth-century esoteric fraternity based in Basra and Baghdad, hold an eminent position in the history of science and philosophy in Islam due to the wide reception and assimilation of their monumental encyclopaedia, the Rasa 'il Ikhwan al-Safa' (Epistles of the Brethren of Purity). This compendium contains fifty-two epistles offering synoptic accounts of the classical sciences and philosophies of the age; divided into four classificatory parts, it treats themes in mathematics, (...) logic, natural philosophy, psychology, metaphysics, and theology, in addition to didactic fables. Epistles 6 to 8 are from the first division of the Epistles, on the propaedeutical and mathematical sciences. Epistle 6 develops ideas concerning natural numbers and their arithmetic, geometric, and harmonic ratios, marked by the influence of Nicomachus of Gerasa and of Euclid. The Brethren here emphasize practical applications of proportionality in music, medicine, and alchemy. Epistle 7 addresses theoretical scientific knowledge as directed towards the spiritual realities of souls, the goal of which is to actualize human potential; this epistle also presents a remarkable classification of sciences. Epistle 8 surveys material cultures in the Islamic mediaeval milieu, embellished by a consideration of the effects of the heavenly bodies on the predisposition of individuals to follow specific trades. These three epistles are, of course, underpinned by the Brethren's perennial tropes of the microcosm/macrocosm analogy and the emanative hierarchy of existents. (shrink)