The Introduction to Geometry by Qustā ibn Lūqā: Translation and Commentary

The paper contains an English translation with commentary of the Introduction to Geometry by the Christian mathematician, astronomer and physician Qustā ibn Lūqā. This elementary work was written in Baghdad in the ninth century A.D. It consisted of circa 191 questions and answers, of which 186 are extant today. The Arabic text has been published in a previous volume of Suhayl by Youcef Guergour, on the basis of the two extant Arabic manuscripts. The Introduction to Geometry consists mainly of material which QusÐā collected from Greek sources, some of which are now lost. Most of chapter 2 of the Jumal al-Falsafa by Abu Abdallah al-Hindi (12th century) was directly copied from QusÐā’s Introduction

Progressions, Rays and Houses in Medieval Islamic Astrology: A Mathematical Classification

Medieval Islamic mathematicians and astronomers developed a variety of mathematical definitions and computations of the three astrological concepts of houses, rays (or aspects) and progressions. The medieval systems for the astrological houses have been classified by J.D. North and E.S. Kennedy, and the purpose of our paper is to attempt a similar classification for rays and progressions, on the basis of medieval Islamic astronomical handbooks and instruments. It turns out that there were at least six different systems for progressions, and no less than nine different systems for rays. We will investigate the historical relationships between these systems and we will also discuss the authors to whom the systems are attributed in the medieval Islamic sources

Progressions, Rays and Houses in Medieval Islamic Astrology: A Mathematical Classification

Medieval Islamic mathematicians and astronomers developed a variety of mathematical definitions and computations of the three astrological concepts of houses, rays (or aspects) and progressions. The medieval systems for the astrological houses have been classified by J.D. North and E.S. Kennedy, and the purpose of our paper is to attempt a similar classification for rays and progressions, on the basis of medieval Islamic astronomical handbooks and instruments. It turns out that there were at least six different systems for progressions, and no less than nine different systems for rays. We will investigate the historical relationships between these systems and we will also discuss the authors to whom the systems are attributed in the medieval Islamic sources

Парсическая роль интеллигенции в истории

In 1661, Borelli and Ecchellensis published a Latin translation of a text which they called the Ltmmas of Archimedes. The first fifteen propositions of this translation correspond to the contents of the Arabic Book of Assumptions, which the Arabic tradition attributes to Archimedes. The work is not found in Greek and the attribution is uncertain at best. Nevertheless, the Latin translation of the fifteen propositions was adopted as a work of Archimedes in the standard editions and translations by Heiberg, Heath, Ver Eecke and others. Our paper concerns the remaining two propositions, 16 and 17, in the Latin translation by Borelli and Ecchellensis, which are not found in the Arabic Book of Assumptions. Borelli and Ecchellensis believed that the Arabic Book of Assumptions is a mutilated version of a lost "old book" by Archimedes which is mentioned by Eutodus (ca. A.D. 500) in his commentary to Proposition 4 of Book 2 of Archimedes' On the Sphere and Cylinder. This proposition is about cutting a sphere by a plane in such a way that the volumes of the segments have a given ratio. Because the fifteen propositions in the Arabic Book of Assumptions have no connection whatsoever to this problem, Borelli and Ecchellensis "restored" two more propositions, their 16 and 17. Propositions 16 and 17 concern the problem of cutting a given line segment AG at a point X in such a way that the product AX· XG2 is equal to a given volume K. This problem is mentioned by Archimedes, and although he promised a solution, the solution is not found in On the Sphere and Cylinder. In his commentary, Eutodus presents a solution which he adapted from the "old book" of Archimedes which he had found. Proposition 17 is the synthesis of the problem by means of two conic sections, as adapted by Eutodus. Proposition 16 presents the diorismos: the problem can be solved only if K::::;;; AB · BG2, where point B is defined on AG such that AB = 1/zBG. We will show that Borelli and Ecchellensis adapted their Proposition 16 not from the commentary by Eutocius but from the Arabic text On Filling the Gaps in Archimedes' Sphere and Cylinder which was written by Abu Sahl al-Kuru in the tenth century, and which was published by Len Berggren. Borelli preferred al-Kiihi's diorismos (by elementary means) to the diorismos by means of conic sections in the commentary of Eutocius, even though Eutocius says that he had adapted it from the "old book." Just as some geometers in later Greek antiquity, Borelli and Ecchellensis bdieved that it is a "sin" to use conic sections in the solution of geometrical problems if elementary Euclidean means are possible. They (incorrectly) assumed that Archimedes also subscribed to this opinion, and thus they included their adaptation of al-Kuru's proposition in their restoration of the "old book" of Archimedes. Our paper includes the Latin text and an English translation of Propositions 16 and 17 of Borelli and Ecchellensis

Middeleeuwse islamitische geometrische ornamentiek

Overal in de islamitische wereld zijn prachtige geometrische patronen te zien in middeleeuwse moskeeën en paleizen. Wat zijn de methoden van de middeleeuwse ontwerpers? Welke wiskundige kennis gebruiken ze? En heeft de islamitische geometrische ornamentiek een diepere betekenis? Tijdens de CWI-vakantiecursus ’Symmetrie’ in augustus 2011 gaat Jan Hogendijk op deze vragen in

Mathematics and geometric ornamentation in the medieval Islamic world

We discuss medieval Arabic and Persian sources on the design and construction of geometric ornaments in Islamic civilization

Arabische astrologie en Westeuropese wiskunde

Wiskunde, dat is toch iets met stellingen en bewijzen? Zelfs de minst wiskundig-onderlegden zijn het daar nog wel over eens. Maar waar komt het werken met stelling en bewijs vandaan? En hoe en wanneer is men dit in West-Europa gaan doen? Jan Hogendijk, hoogleraar geschiedenis van de wiskunde, is specialist in de wis- en sterrenkunde in het middeleeuws islamitisch cultuurgebied. Dit artikel is een verkorte versie van zijn Bernoulli-lezing in Groningen, uitgesproken op 14 april van dit jaar