Contextualizing Playfair and Colebrooke 233
said that the question that the geometry of the Hindus could have a diff er-
ent basis from the Greek ones is implied by the ‘professedly’ in the question.
Th at this is what Playfair meant might be inferred from his elaboration
upon the question he posed:
I am led to propose this question, by having observed, not only that the whole of the
Indian Astronomy is a system constructed with great geometrical skill, but that the
trigonometrical rules given in the translation from the Surya Siddhanta , with which
Mr. Davis 22 has obliged the world, point out some very curious theorems, which
must have been known to the author of that ancient book. 23
According to Playfair, as he engages with Davis’ translation of the Surya
Siddhanta the ‘trigonometrical canon’ of Indian astronomy is constructed
on the basis of a theorem. Th e theorem is stated as:
If there be three arches 24 of a circle in arithmetical progression, the sum of the sines
of the two extremes arches is to twice the sine of the middle arch as the cosine of
common diff erence of the arches to the radius of the circle. 25
Th ough the theorem was not known to Europe before Viete, Playfair
continues, the method was employed by the Indian astronomers for con-
structing trigonometrical tables, and was based on the simpler procedure
of calculating sines and arcs than through the use of methods that were
based on extracting square roots. 26 Th e immediate task for Playfair appears
to have been to identify those mathematical works where the theorem on
which the trigonometrical rule employed in astronomy is fi rst laid out.
Th is brings us back to Burrow’s concern with the origins of Indian math-
ematics.
Contrasting approaches: sift ing the mathematical from the
astronomical rexts
In the late eighteenth century it would have been possible to diff eren-
tiate between the eff orts of the British Indologists and those of their
French counterparts studying Indian astronomy and mathematics on two
counts. Methodologically speaking, while the British Indologists were busy
22 Samuel Davis (1760–1819) was a judge in Bengal and produced one of the fi rst translations of
the Surya Siddhanta.
23 Playfair 1792 : 151.
24 An ‘arc of a circle’ is what is meant here. I have kept the original spelling.
25 Playfair 1792 : 152.
26 Playfair 1792 : 152.