V.
19. We have, in the above notes, given in outline the historically important matters relating to Indian mathematics. For points of detail the works mentioned in the annexed bibliography should be consulted; but we here briefly indicate the other contents of the Indian works, and in the following sections we shall refer to certain topics that have achieved a somewhat fictitious importance, to the personalities of the Indian mathematicians and to the relations between the mathematics of the Chinese, the Arabs and the Indians.
20. Besides the subjects already mentioned Brahmagupta deals very briefly with the ordinary arithmetical operations, square and cube-root, rule of three, etc,; interest, mixtures of metals, arithmetical progressions, sums of the squares of natural numbers; geometry as already described but also including elementary notions of the circle; elementary mensuration of solids, shadow problems, negative and positive qualities, cipher, surds, simple algebraic identities; indeterminate equations of the first and second degree, which occupy the greater portion of the work, and simple equations of the first and second degrees which receive comparatively but little attention.
Mahāvīra's work is fuller but more elementary on the whole. The ordinary operations are treated with more completeness and geometrical progressions are introduced; many problems on indeterminates are given but no mention is made of the 'cyclic method' and it contains no formal algebra. It is the only Indian work that deals with ellipses (inaccurately).
