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Despite its importance in the history of Ancient science, Menelaus’ Spherics is still by and large unknown. This treatise, which lies at the foundation of spherical geometry, is lost in Greek but has been preserved in its Arabic versions. The reader will find here, for the first time edited and translated into English, the essentials of this tradition, namely: a fragment of an early Arabic translation and the first Arabic redaction of the Spherics composed by al-Māhānī /al-Harawī, together with a historical and mathematical study of Menelaus’ treatise. With this book, a new and important part of the Greek and Arabic legacy to the history of mathematics comes to light. This book will be an indispensable acquisition for any reader interested in the history of Ancient geometry and science and, more generally, in Greek and Arabic science and culture.
Geodesics (Mathematics) --- Sphere. --- Geometry, Differential. --- Curves on surfaces --- Surfaces --- Curved surfaces --- Geometry --- Shapes --- Surfaces, Curves on --- Differential geometry --- Geometry, Solid --- Orbs --- Geometry, Differential --- Global analysis (Mathematics) --- Mathematics --- Mathematical models. --- Menelaus, --- مانالاوس --- Mānālāwus --- Ménélaos, --- Menélaus, --- Millaeus, --- Ménélas, --- Ménélaüs, --- Menelao, --- Menelaos, --- Arabic mathematics. --- Greek geometry. --- History of non-Euclidean geometry. --- Spherics.
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Medieval Europe was a meeting place for the Christian, Jewish, and Islamic civilizations, and the fertile intellectual exchange of these cultures can be seen in the mathematical developments of the time. This sourcebook presents original Latin, Hebrew, and Arabic sources of medieval mathematics, and shows their cross-cultural influences. Most of the Hebrew and Arabic sources appear here in translation for the first time.Readers will discover key mathematical revelations, foundational texts, and sophisticated writings by Latin, Hebrew, and Arabic-speaking mathematicians, including Abner of Burgos's elegant arguments proving results on the conchoid-a curve previously unknown in medieval Europe; Levi ben Gershon's use of mathematical induction in combinatorial proofs; Al-Mu'taman Ibn Hūd's extensive survey of mathematics, which included proofs of Heron's Theorem and Ceva's Theorem; and Muhyī al-Dīn al-Maghribī's interesting proof of Euclid's parallel postulate. The book includes a general introduction, section introductions, footnotes, and references.The Sourcebook in the Mathematics of Medieval Europe and North Africa will be indispensable to anyone seeking out the important historical sources of premodern mathematics.
Mathematics, Medieval --- History. --- Medieval mathematics --- Arabic civilization. --- Arabic mathematics. --- Christian civilization. --- Hebrew civilization. --- Hebrew mathematics. --- Islamic civilization. --- Islamic mathematics. --- Islamic world. --- Jewish civilization. --- Latin Catholic Europe. --- Latin civilization. --- Latin mathematics. --- Latin schools. --- Medieval Europe. --- North Africa. --- Spain. --- abbacist schools. --- combinatorics. --- conchoids. --- curricula. --- decimals. --- geometric knowledge. --- intellectual exchange. --- mathematical induction. --- mathematical revelations. --- mathematics. --- medieval Europe. --- medieval Islam. --- medieval mathematics. --- medieval period. --- quadrivium. --- religion. --- universities.
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