Page:Indian mathematics, Kaye (1915).djvu/80

 66. What number is that which multiplied by nought and added to half itself and multiplied by three and divided by nought amounts to the given number sixty-three? Answer—14. This assumes that $$\scriptstyle{\frac{0}{0}=1}$$. 67. What four numbers are such that their product is equal to twenty times their sum, say, learned mathematician who art conversant with the topic of the product of unknown quantities? Answer—5, 4, 2, 11. Bhāskara puts arbitrary values for three of the quantities and gets 11 for the fourth. 68. If you are conversant with operations of algebra tell the number of which the fourth power less double the sum of the square and of two hundred times the simple number is ten thousand less one? Answer—11. This may be expressed by $\scriptstyle{x^4-2(x^2+200x)=9999}$. It is the only case in which the fourth power occurs. 69. The square of the sum of two numbers added to the cube of their sum is equal to twice the sum of their cubes? Answer—1, 20; 5, 76, etc. 70. Tell me, if you know, two numbers such that the sum of them multiplied respectively by four and three may when added to two be equal to the product of the same numbers? Answer—5, 10 and 11, 6. 71. Sav quickly, mathematician, what is the multiplier by which two hundred and twenty-one being multiplied and sixty-five added to the product, the sum divided by a hundred and ninety-five becomes cleared? Answer—5, 20, 35 &amp;c. L=the Līlāvatī, V=Vīja Gaņita, both by Bhāskara, M=Mahāvīra, S=SrīdharaŚrīdhara [sic], C=Chaturveda.