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

Vedic mathematics and the calculations of Guru Tirthaji

This article was written as a reaction to several publications in the Netherlands on methods of mental calculation, which have been presented as “Vedic mathematics.” The adjective “Vedic” suggests that these methods date back to the ancient Vedic period before 500 BCE.1 In this article I will first give two examples of genuine Vedic mathematics. After a brief intermezzo on the decimal position system and decimal fractions, the so-called “Vedic” methods of mental calculation will be identified as the inventions of a twentieth-century Guru. More information on the subject can be found in [3]

The scholar and the fencing master: The exchanges between Joseph Justus Scaliger and Ludolph van Ceulen on the circle quadrature (1594-1596)

In Chapter 21 of Vanden Circkel (On the Circle) [Van Ceulen, 1596], the arithmetic teacher and fencing master Ludolph van Ceulen published his analysis of 16 propositions which had been submitted to him by an anonymous “highly learned man”. In this paper, the author of the propositions will be identified as the classicist and humanist Joseph Justus Scaliger (1540-1609), who lived in the city of Leiden, just like Van Ceulen. The whole Chapter 21 of Van Ceulen’s Vanden Circkel turns out to be a criticism of Scaliger’s Cyclometrica (1594), a work which includes a false circle quadrature and many other incorrect theorems. The exchanges between Van Ceulen and Scaliger are analyzed in this paper and related to difference in social status and to different approaches to mathematics