George Rusby Kaye

“ Brahmagupta gives a fairly complete set of rules dealing with the cyclic quadrilateral and either he or the mathematician from whom he obtained his material had a definite end in view—the construction of a cyclic quadrilateral with rational elements.—The commentators did not fully appreciate the theorems, some of which are given in the works of Mahāvīra and S'rīdhara; and by the time of Bhāskara they had ceased to be understood. Bhāskara indeed condemns them outright as unsound. "How can a person" he says "neither specifying one of the perpendiculars, nor either of the diagonals, ask the rest? ”

“ The Indian methods for the solution of may be summarised as follows:
If and then will where r is any suitable integer.
Also where n is any assumed number.
The complete integral solution is given by a combination (a) and (b) of which the former only is given by Brahmagupta, while both are given by Bhāskara (five centuries later) . The latter designates (a) the 'method by composition' and (b) the 'cyclic method.' These solutions are alone sufficient to give to the Indian works an important place in the history of mathematics. ”

“ Angles are not dealt with at all;
(3) There is no mention of parallels and no theory of proportion;
(4) Traditional inaccuracies are not uncommon;
(5) A gradual decline in geometrical knowledge is noticeable. On the other hand, we have the following noteworthy rules relating to cyclic quadrilaterals—where x and y are the diagonals of the cyclic quadrilateral (a, b, c, d) . This (ii) is sometimes designated as 'Brahmagupta's theorem'.
16. The absence of definitions and indifference to logical order sufficiently differentiate the Indian geometry from that of the early Greeks ”