Abstract
In Chapter 3 our exposition was unhistorical in so far as Ptolemy did not present his spherical trigonometry as an abstract mathematical theory. He developed it in close connection with spherical astronomy, and we dealt with the two subjects separately only in order to get a coherent survey of the complete mathematical apparatus implicit in the Almagest. Accordingly we must now consider the astronomical aspect of Ptolemy’s spherical trigonometry, examining a series of problems connected with the geometry of the celestial sphere and its diurnal revolution. Only the main problems are investigated while a number of minor corollaries, or theorems of secondary importance are left out.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
A description of Ptolemy’s instrument - a meridian quadrant or ‘plinth’ - together with a discussion of his method and result has been given by Britton (1969). At Ptolemy’s time the actual value was ɛ = 23°;40,50. The error could arise from the difficulty of determining noon, or observing the shadow at noon; Britton arrives at no definite conclusion, but refutes the accusation made by Delambre (1817, ii, 75 ff.) that Ptolemy faked or tampered with his observations. - Concerning a slightly later Chinese determination leading to almost the same result, see Hartner (1954).
- 2.
Eratosthenes based his system upon two standard lines. The first passed from the Pillars of Hercules, through Rhodes to the Gulf of Issus and was supposed to be a circle parallel to the equator. The second passed through Byzantium, Rhodes, Alexandria, and the Nile island of Meroe and was regarded as part of a meridian circle. Cf. Strabo, Geogr. II, 1,1 and 1,4, 1-2.
- 3.
There is every reason to consider the gnomon the earliest astronomical instrument. It was presumably known in prehistoric times. Herodotu> (II, 109) asserts that the Greeks learned of its use from the Babylonians, while Diogenes Laertius (11,1) wrongly named Anaximander as its inventor. - Cfr. Dicks 1954 p. 77.
- 4.
According to Strabo (Geogr. II, 2, 3) the terms amphiscian, heteroscian, and periscian were coined by Posidonius (about 100 B.C.).
- 5.
Peters and Knobel(1915, p. 14) ascribed the discovery of this error to Delambre (1817, II, p. 211 and 284). In fact, it was known to previous astronomers, such as Roger Long (1742, p. 279).
- 6.
See Honigman (1929) and the bibliography in Brown (1949). For Parmenides, see Strabo (Geogr. II, 2,2), and for Aristotle the Meteor. (11, 5, 362 a). Hipparchus* criticism of Eratosthenes is mentioned in Strabo (Geogr. I, 1, 12).
- 7.
Ptolemy’s Geography remained unknown to the Latin Middle ages until about A.D. 1410 when a Byzantine scholar Emanuel Chrysoloras and his Italian pupil Jacobus Angelus produced a translation. This became the basis of the first printed version (Vincenza, 1475). Since then the Geography has appeared in more editions and translations than any of Ptolemy’s other works (see Sarton, 1927, I, 273 ff.). For a brief survey of its contents, see Brown 1949, pp. 58-80.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Pedersen, O. (2011). Spherical Astronomy in the Almagest. In: Jones, A. (eds) A Survey of the Almagest. Sources and Studies in the History of Mathematics and Physical Sciences. Springer, New York, NY. https://doi.org/10.1007/978-0-387-84826-6_4
Download citation
DOI: https://doi.org/10.1007/978-0-387-84826-6_4
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-84825-9
Online ISBN: 978-0-387-84826-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)