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The Use of Analogy in Book VII of Apollonius’ Conica

Published online by Cambridge University Press:  01 September 2003

Michael Fried
Michael Fried
Affiliation:
Program for Science and Technology Education, Ben-Gurion University of the Negev
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Abstract

Argument

Apollonius of Perga’s Conica, like almost all Greek mathematical works, relies heavily on the use of proportion, of analogia. Analogy as the assertion of a resemblance, however, also plays a role in the Conica. The homologue, which Apollonius introduces in Book VII, is a striking example of analogia in both senses. On the one hand, the homologue is defined by means of a precise proportion relating the diameter and latus rectum of a conic section to fixed segments along the diameter. On the other hand, Apollonius’ use of the homologue in Book VII makes it clear that he meant it truly to evoke the latus rectum in the reader’s mind; in this way, Apollonius treats the homologue as an image of the latus rectum. The example of the homologue thus suggests the possibility that, in Greek mathematics, proportion was not only a vital manipulatory tool but also a means of making images.

Type
Articles
Information
Science in Context , Volume 16 , Issue 3 , September 2003 , pp. 349 - 365
Copyright
2003 Cambridge University Press

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References

Apollonius. 1710. Apollonii Pergaei Conicorum libri octo. Edited by Edmund Halley. Volume 2. Oxford.
Apollonius. 1891, 1893. Apollonii Pergaei quae Graece exstant cum commentariis antiquis. Edited by I. L. Heiberg. 2 volumes. Leipzig: Teubner.
Decorps-Foulquier, Micheline. 1999. “Sur les figures du traité des Coniques d’Apollonios de Pergé édité par Eutocius d’Ascalon.” Revue d’histoire des mathématiques. 5:61-82.Google Scholar
Fried, Michael N. and Sabetai Unguru. 2001. Apollonius of Perga’s Conica: Text, Context, Subtext. Leiden: Brill.
Held, Julius. 1969. Rembrandt’s Aristotle and Other Rembrandt Studies. Princeton, N.J.: Princeton University Press
Saito, Ken. 1985. “Book II of Euclid’s Elements in the Light of the Theory of Conic Sections.” Historia Scientiarum 28:31-60.Google Scholar
Toomer, G. J.1990. Apollonius Conics Books V to VII. New York: Springer-Verlag.