Page:Indian mathematics, Kaye (1915).djvu/30

 Other problems connected with the rational right-angled triangle given by Bhāskara are of some historical interest: e.g., (1) The sum of the sides is 40 and the area 60, (2) The sum of the sides is 56 and their product $\scriptstyle{7 \times 600}$, (3) The area is numerically equal to the hypotenuse, (4) The area is numerically equal to the product of the sides. 15. The geometry of this period is characterised by: (1) Lack of definitions, etc.; (2) 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; but the absence of what may be termed a theory of geometry hardly accounts for the complete absence of any reference to parallels and angles. Whereas on the one hand the Indians have been credited with the invention of the sine function, on the other there is no evidence to show that they were acquainted with even the most elementary theorems (as such) relating to angles. The presence of a number of incorrect rules side by side with correct ones is significant. The one relating to the area of triangles and quadrilaterals, viz., the area is equal to the