## Menelaus' ›Spherics‹: Early Translation and al-Māhānī / al-Harawī's VersionDespite 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. |

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### Contents

3 | |

23 | |

73 | |

EDITION AND TRANSLATION OF MENELAUS PROPOSITIONS QUOTED IN IBN HŪDS ENCYCLOPEDIA | 91 |

MATHEMATICAL COMMENTARY | 125 |

THE PROPOSITIONS | 139 |

TEXTS AND TRANSLATIONS | 399 |

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### Common terms and phrases

Abū acute al-Harawī al-Māhānī Almagest angle ABD angle G angulus Arabic arc BA base BC is equal BC is greater BD is smaller chord circle cº-º Comments on Proposition compounded contain crd crd equal angles equal to DG Euclid’s Euclidean geometry Gerard of Cremona halves homologue hyperbolic geometry Ibn Abī Jarrāda Ibn al-Haytham Ibn Irāq intersection Jº 9 Jº Jº Jºe Jºus Latin translation lemma Let ABC Lºs Manisa Menelaus nadir arcus Naṣīr al-Dīn al-Ṭūsī º ºs obtuse ºut Pappus perpendicular point G pole Proposition 71 quadrant quarter ratio redaction remaining angles right angles Sector Figure semicircle sides sine rule sº tº sphere spherical geometry spherical triangle subtend Thābit ibn Qurra Theodosius theorem triangle ABC trigonometry trilateral figure wanted to prove