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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.