ABSTRACT
As an auxiliary in the study of the movement of heavenly bodies, trigonometry, originally, goes back at least to Hipparchus, to whom the first table of chords is attributed. Around the sixth century the Indian scientists had already replaced the archaic chord of the double arc by its half, in other words R times our sine (labelled here Sin for R sin), giving the radius R of the circle or the sphere several values (150, 3438, 120 etc.). The contribution in this area of Indian science is not limited to the introduction of the sine. Nevertheless, in the eyes of the Arab astronomers of the ninth century, the Almagest will not take long to overtake the Indian siddhanta. The book seduces by the rigour of its exposure, by its demonstrations and by the observation programmes it suggests. As paradoxical as it might seem, the enormous building constructed by Claudius Ptolemy in his famous Almagest rests essentially on very elementary geometrical propositions. In the quite complex calculations relating to planetary models, we constantly arrive at Pythagoras’s theorem and the chord that would represent the side of the right angle of a right-angled triangle of which the hypotenuse would be equal to the diameter of the circle of reference (with R = 60, as common usage in sexagesimal numeration). Thus sides and angles of plane triangles are obtained from one another. The same geometric language is found in chapter 10 of the first book, applied to the construction of the table of chords, where he implicitly covers the addition formulae of the arcs. As for spherical astronomy, it is apparently reduced to a dozen simple applications of the theorem of Menelaus.
