جستجوی مقالات مرتبط با کلیدواژه « اصول اقلیدس » در نشریات گروه « تاریخ »

The first proposition of the tenth book of Euclid's Elements is the basis of Archimedes’ “method of exhaustion”, which is used by Euclid himself in book XII. Euclid proves this proposition for variable proportion. Ibn al-Haytham (4th AH) claims that in his ḥall-i shukūk he has proved this proposition for a fixed proportion as the general solution, whereas Euclid had done it just for particular cases. Ṭūsī (597-672 AH) in his recension of Euclid’s Elements, in which seems has been used fī ḥall-i shukūk a lot, repeats the same idea as Ibn al-Haytham’s. Ibn al-Ṣalāḥ al-Ḥamadanī (d. 548 AH) has a treatise in which he criticizes Ibn al-Haytham’s idea and brings three main objections. Muḥammad Bāqir Yazdī (alive in 1047 AH) in his commentary on tenth book of Euclid’s Elements criticizes Ṭūsī’s idea and explains that the general condition which Ṭūsī applies disrupts the proof of second proposition of the tenth book.

Menelaus’ Sphaerica can be considered as the most important classical text in the tradition of spherics books، written with the aim of the solution of problems arising in spherical astonomy. Euclid’s Elements is the the most important book on plane geometry. This article aims at a comparative study of Menelaus’s Sphaerica and Euclid’s Elements، to show that Book I of Sphaerica is an attempt to reconstruct Book I of the Elements for the case of spherical figures. We mention Menelaus’ achievements as well as the limits of his project. The topic of the congruent triangles is treated with special reference to the differences which exist between the plane and the spherical cases. We also show that the spherical counterpart of Euclid’s important theorm on the sum of the interior angles of a triangle (Euclid، I/32) has been put forward، for the first part، by Naṣīr al-Dīn al-Ṭūsī in his Recension of Menelaus’s Sphaerica.

The Elements of Euclid، sometimes knows as the “The Book of Euclid”، and in the mathematical texts of the Islamic period often referred to as “The Book of the Elements”، is one of the main sources of Islamic mathematics. This paper addresses the history of the translation of this book and its recension by Naṣīr al-Dīn Ṭūsī. Then، through a comparison of the first chapter of the fourth part of Quṭb al-Dīn Shīrāzī’s Durrat al-Tāj with the Arabic translation of Isḥāq ibn Ḥunayn and the recension of Ṭūsī، it is shown that the text of Shīrāzī is in fact a Persian translation of Ṭūsī’s Recension of the Elements، despite the existence of some differences between the two texts. One of these differences، which is analyzed in the last part of this paper، is a single figure produced by Shīrāzī and containing all the 48 propositions of the first book of the Elements.

“Euclid’s Elements” begins by an introduction into definitions، Postulates and Common Notions; the Postulates are presented in the science of geometry by Euclid without any or explanations. However، regarding the significance of Postulates which is the fundamental to geometrical proving and solving geometrical theorems، some translators and interpreters of Euclid’s Elements provide explanation for some of the Postulates and try to prove them. Qutb al-Din Shirazi and Faḍl ibn Hātam Neyrīzī are among the translators who believe that it is essential that some of the Postulates be explained and some others be proved. This article compares the methodologies of Qutb al-Din Shirazi and Faḍl ibn Hātam Neyrīzī، an older interpreter of Euclid’s Elements.