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Heavenly MathematicsThe Forgotten Art of Spherical Trigonometry$
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Glen Van Brummelen

Print publication date: 2017

Print ISBN-13: 9780691175997

Published to Princeton Scholarship Online: May 2018

DOI: 10.23943/princeton/9780691175997.001.0001

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The Medieval Approach

The Medieval Approach

(p.59) 4 The Medieval Approach
Heavenly Mathematics

Glen Van Brummelen

Princeton University Press

This chapter discusses the medieval approach to trigonometry, beginning with Abū Mahmūd al-Khujandī's theorem and the theorems of Abū Nasr Mansūr ibn ʻAlī ibn ʻIrāq. It then considers the Rule of Four Quantities, the first example of the principle of locality, and its relation to the spherical Law of Sines. It also analyzes Abū 'l-Wafā's proof of the Law of Sines in his Almagest and how the law becomes the planar Law of Sines when reduced to the plane. Finally, it provides an overview of the Indian approach to spherical astronomy, including finding declinations of arcs of the ecliptic, and how to solve the qibla problem to determine the direction of Mecca.

Keywords:   trigonometry, Abū Mahmūd al-Khujandī, Abū Nasr Mansūr ibn ʻAlī ibn ʻIrāq, Rule of Four Quantities, spherical Law of Sines, Abū 'l-Wafā, spherical astronomy, qibla, Mecca, planar Law of Sines

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