Sphaerica

work by Menelaus of Alexandria

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July 14, 2026

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Sphaerica is a significant work by Menelaus of Alexandria, a Greek mathematician and astronomer who lived in the 1st century AD. This treatise, which survives only in an Arabic translation, is foundational to the study of spherical geometry and spherical trigonometry.12

In Sphaerica, Menelaus established the principles for mathematically treating spherical triangles—triangles formed by arcs of great circles on a sphere's surface. He introduced the use of great circle arcs, a crucial development for spherical trigonometry, and explored theorems with applications in spherical astronomy. The work also contains Menelaus's theorem, which is fundamental to spherical trigonometry and astronomy.1

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trigonometry
Passage to Europe
…in Book 1 of the Sphaerica, a three-book treatise by Menelaus of Alexandria (c. 100 ce) in which Menelaus developed the spherical equivalents of Euclid’s propositions for planar triangles. A spherical triangle was understood to mean a figure formed on the surface of a sphere by three arcs of great…
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…in Book 1 of the Sphaerica, a three-book treatise by Menelaus of Alexandria (c. 100 ce) in which Menelaus developed the spherical equivalents of Euclid’s propositions for planar triangles. A spherical triangle was understood to mean a figure formed on the surface of a sphere by three arcs of great…
Read More

Menelaus of Alexandria
Menelaus’s most important work is Sphaerica, on the geometry of the sphere, extant only in an Arabic translation. In Book I he established the basis for a mathematical treatment of spherical triangles analogous to Euclid’s treatment of plane triangles. Furthermore, he originated the use of arcs of great circles instead…
Read More
Menelaus’s most important work is Sphaerica, on the geometry of the sphere, extant only in an Arabic translation. In Book I he established the basis for a mathematical treatment of spherical triangles analogous to Euclid’s treatment of plane triangles. Furthermore, he originated the use of arcs of great circles instead…
Read More