Page:Indian mathematics, Kaye (1915).djvu/66

 L. 139. A side is put. From that multiplied by twice some assumed number and divided by one less than the square of the assumed number a perpendicular is obtained. This being set aside is multiplied by the arbitrary number and the side as put is subtracted—the remainder will be the hypotenuse. Such a triangle is termed 'genuine.'

L. 189. Thus, with the same sides, may be many diagonals in the quadrilateral. Yet, though indeterminate, diagonals have been sought as determinate by Brahmagupta and others.

L. 213. The circumference less the arc being multiplied by the arc the product is termed 'first.' From the quarter of the square of the circumference multiplied by five subtract that first product. By the remainder divide the first product multiplied by four times the diameter. The quotient will be the chord.

V. 170. In the like suppositions, when the operation, owing to restriction, disappoints the answer must by the intelligent be discovered by the exercise of ingenuity. Accordingly it said: 'The conditions—a clear intellect, assumption of unknown quantities, equation, and the rule of three—are means of operation in analysis.'

V. 224. The rule of three terms is arithmetic; spotless understanding is algebra. What is there unknown to the intelligent? Therefore for the dull alone it is set forth. V. 225. To augment wisdom and strengthen confidence, read, read, mathematician, this abridgement elegant in style, easily understood by youth, comprising the whole essence of calculation and containing the demonstration of its principles—full of excellence and free from defect.