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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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PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 27 June 2022

Navigating by the Stars

Navigating by the Stars

(p.151) 9 Navigating by the Stars
Heavenly Mathematics

Glen Van Brummelen

Princeton University Press

This chapter explains how the star is used to find one's position on the Earth while in a ship at sea. Trigonometry was first used for navigation by fourteenth-century Venetian merchant ships. Several navigational techniques can be identified from navigators' personal notebooks, including the table of marteloio. Essentially an application of plane trigonometry, marteloio was part of a group of methods known today as “dead” reckoning. Between 1730 and 1759, a clockmaker by the name of John Harrison constructed a series of four chronometers that could keep remarkably accurate time, even on a ship tossed by waves. The chapter considers the use of the method of Saint Hilaire (also called intercept, cosine-haversine, or Davis's method) to determine three quantities of a star in an astronomical triangle: latitude, declination, and local hour angle. It also discusses the use of the Law of Cosines to solve the star's altitude.

Keywords:   trigonometry, navigation, marteloio, dead reckoning, John Harrison, chronometer, method of Saint Hilaire, star, astronomical triangle, Law of Cosines

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