"At the end of Book I, Chapter 11, of the ' of... Ptolemy... there is a table of the function \mathrm {crd} \theta ... calculated to three significant sexigesimal places for the domain \theta = 1/2^{\circ}, 1^{\circ}, 1\ 1/2^{\circ}, \ldots , 180^{\circ } and having a column of tabular differences for . In Book I, 9, Ptolemy explains how this table was computed. ...[I]n developing the theory frequent recourse is had to the geometry and geometrical algebra... in the Elements of Euclid. ...Ptolemy is giveing a systematic exposition of... a doctrine well known in his time. This would have included... the work of Hipparchus..."