Claudius Ptolemy
Exercises

We learned in the Introduction
to this chapter that the modern sine function is related to the ancient
chord function by the formula crd a
= 2 sin a/2.
Use this formula and your calculator's sine key to compute the following
chord values, and compare your answers with the values in Ptolemy's
Table. Don't forget to make sure that your calculator is in degree
(not radian) mode; you will also need to convert your calculator's decimal
values into Ptolemy's sexagesimal values for the comparisons.
(a) crd 2°
(b) crd 63°
(c) crd 93 ^{1}/_{2}°
(d) crd 127 ^{1}/_{2}°
(e) crd 171 ^{1}/_{2}°

Ptolemy computes
crd 72° from the geometry of the pentagon. Use the formula
that represents his method for dealing with supplementary angles to calculate
crd 108°. Compare your answer with the value in Ptolemy's
Table.

Ptolemy explains how the method he
derives for finding the chord of an angle which is the difference of angles
whose chords are known allows him to determine
crd 12° from the values of crd 72° and
crd 60° which he knows. See note
19. Carry out this computation and compare with the value of
crd 12° from his table.

Use the value of crd 12°
from Ptolemy's Table with the formula
that represents his method for find the chord
of the halfangle to calculate crd 6°, crd 3°,
crd 1 ^{1}/_{2}°, and crd ^{3}/_{4}°,
comparing your values with those in the table
(and in the last case, with the text).
See note 20.

Use the value
of crd 1° which Ptolemy finds in the text together
with the formula that represents his method for finding the chord
of the supplement of the sum of angles whose chords are given to calculate
the value of crd 2°. See note
26. Compare your value with that given in the table.
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last modified 10/9/00
Copyright (c) 2000. Daniel
E. Otero