Astronomy and Ptolemy

Ptolemy(100- 178) also made numerous observations of the heavens and wrote several books, one being the Matematical Collections, which consisted of 13 books. The collection was the most influential astronomical work from its time. Islamic scientist bgan calling the book al-magisti or Almagist.

Ptolemy also gave a theorem, which helps derive sum and difference formulas of sine and cosine:


Ptolemy's Theorem:
Given any quadrilateral inscribed in a circle, the product of the diagonals equals the sum of the products of teh opposite sides: AC*BD = AB*DC + AD*BC

The proof of Ptolemy's theorem involves finding 2 pairs of similar triangles,in the diagram above, thus getting 2 different ratios. Then combining the 2 ratios yields the desired equation. With tables of trigonometric ratios the astronomers were able to solve right triangles easily and approach Apollonius' questions.

Unanswered Questions:

1. Did Ptolemy's Theorem have any other practical uses other than find trig identities?

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