Page:Indian mathematics, Kaye (1915).djvu/65

 vi. 147. Divide by their rate prices. Diminish by the least among them and then multiply by the least the mixed price of all the things and subtract from the given number of things. Now split up (this) into as many (as there are left) and then divide. These separated from the total price give the price of the dearest article of purchase. [This is a solution of example 36 below.]

vi. 169. It has to be known that the products of gold as multiplied by their colours when divided by the mixed gold gives rise to the resulting colour (varņa). [See examples 24 and 25 below.]

vii. 2. Area has been taken to be of two kinds by Jina in accordance with the result—namely, that which is for practical purposes and that which is minutely accurate.

vii, 233. Thus ends the section of devilishly difficult problems. Śrīdhara's Triśatikā—(Circa A.D. 1030). 1. Of a series of numbers beginning with unity and increasing by one, the sum is equal to half the product of the number of terms and the number of terms together with unity.

32. In exchange of commodities the prices being transposed apply the previous rule (of three). With reference to the sale of living beings the price is inversely proportional to their age.

65. If the gnomon be divided by twice the sum of the gnomon and the shadow the fraction of the day elapsed or which remains will be obtained. Bhāskara—(Born A.D. 1114). L. 1. I propound this easy process of calculation, delightful by its elegance, perspicuous with concise terms, soft and correct and pleasing to the learned.