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Sines, Versines and Haversines in Nautical Astronomy

Published online by Cambridge University Press:  18 January 2010

Charles H. Cotter
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Of immense importance to nautical astronomers are tables of trigonometrical functions. The history of these begins with the table of chords first suggested by Hipparchus two centuries before the beginning of the Christian Era. The earliest table of chords extant is that computed by Ptolemy (fl. c. 150 a.d.) whose table, true to the sexagesimal tradition, is based on the division of the radius of a circle into sixty parts. The first table of half-chords, or sines, is supposed to be of Indian origin and to date from the sixth century; but credit for being first to use a table of half-chords for solving spherical triangles belongs to the Arab mathematician Albategnius who flourished during the tenth century. The first printed table of sines, according to De Morgan, is a small work giving sines to each minute of arc from 0° to 90°, undated and unsigned but evidently published before 1500.

Type
Forum
Information
The Journal of Navigation , Volume 27 , Issue 4 , October 1974 , pp. 536 - 541
Copyright
Copyright © The Royal Institute of Navigation 1974

References

REFERENCES

De Morgan, A. (1861). Tables, The English Cyclopaedia, London.Google Scholar
Blundevil, T. (1594). His Exercises, contayning Eight Treatises… London. Seventh Edition ‘corrected and somewhat enlarged’ by Hartwell, R., London, 1636.Google Scholar
Wright, E. (1599). Certain Errors in Navigation detected and corrected… London.Google Scholar
Wright, E. (1616 Posthumous). A Description of the Admirable Table of Logarithms, London.Google Scholar
Gunter, E. (1620). Canon Triangulorum sive Tabulae Sinuum et Tangentium Artificialum, London.Google Scholar
Moore, J. Sir. (1681). A New Systeme of the Mathematics, London.Google Scholar
De Mendoza Rios, J. (1805). A Complete Collection of Tables for Navigation and Nautical Astronomy, London.Google Scholar
Andrews, J. (1805). Astronomical and Nautical Tables, London.Google Scholar
Inman, J. (1821). Navigation and Nautical Astronomy for the Use of British Seamen, Portsmouth. (Second edition, 1826; Third edition, 1835; Seventh edition, 1849.)Google Scholar
Inman, J. (1830). Nautical Tables Designed for the Use of British Seamen, London.Google Scholar
Muller, J. (Regiomontanus) (1533). De triangulis omniodis. Translated by Barnabus, Hughes, o.f.m. (1967), London.Google Scholar
Goodwin, H. B. (1899). The Simplification of Formulae in Nautical Astronomy. The Nautical Magazine, Volume 68, Glasgow.Google Scholar
Sherwin, H. (1705). Mathematical Tables, London.Google Scholar
Davis, P. L. H. (1905). Requisite Tables, London.Google Scholar