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Setting free the actor Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.. The 3rd-century astronomers first noted that the lengths of the sides of a right-angle triangle and the ... A treatise on plane and spherical trigonometry read online English language arts grades 8-12 Menelaus of Alexandria (ca. 100 AD) wrote in three books his Sphaerica.In Book I, he established a basis for spherical triangles analogous to the Euclidean basis for plane triangles. He establishes a theorem that is without Euclidean analogue, that two spherical triangles are congruent if corresponding angles are equal, but he did not distinguish between congruent and symmetric spherical ... 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