The Ancient Approach
The Ancient Approach
This chapter discusses the ancient approach to trigonometry, beginning with Hipparchus of Rhodes, the founder of trigonometry. It reconstructs when and where Hipparchus must have lived by taking into account the observations that he made as an astronomer and the references his successors made to him. It then considers the theorems of Menelaus of Alexandria, whose book Sphaerica completely reinvented the mathematical study of the sphere. In particular, it describes Menelaus's Theorem, which became the standard tool of spherical astronomy for the next 900 years. It also examines Abū Sahl al-Kūhī's use of the Menelaus theorems to solve the problem of rising times of arcs of the ecliptic.
Keywords: trigonometry, Hipparchus of Rhodes, theorems, Menelaus of Alexandria, Sphaerica, sphere, Menelaus's Theorem, Abū Sahl al-Kūhī, rising time, ecliptic
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