EARLY HINDOO MATHEMATICS. 337 



of 2, 5, 32, 193, 18, 10, and 100, added together; and the remainder 

 when their sum is subtracted from 10,000." 



He then rapidly plunges into multiplication as follows : " Exam- 

 ple. Beautiful and dear Lilivati, whose eyes are like a fawn's ! tell 

 me what are the numbers resulting from 135 taken into 12 ? . . . . Tell 

 me, auspicious woman, what is the quotient of the product divided by 

 the same multiplier?" 



The treatise continues rapidly through the usual rules, but pauses 

 at the reduction of fractions to hold up the avaricious man to scorn : 

 " The quarter of a sixteenth of the fifth of three-quarters of two-thirds 

 of a moiety of a dramma was given to a beggar by a person from 

 whom he asked alms ; tell me how many cowry-shells the miser gave 

 if thou be conversant in arithmetic with the reduction termed subdi- 

 vision of fractions." 



The " venerable preceptor," as Bhascara calls himself, illustrates 

 what he terms the rule of supposition by the following example : " Out 

 of a swarm of bees, one-fifth part settled on a blossom of Cadamba y 

 and one-third on a flower of SilincThri / three times the difference of 

 those numbers flew to the bloom of a Gutaja. One bee which re- 

 mained, hovered and flew about in the air, allured at the same moment 

 by the pleasing fragrance of a jasmin and pan dan us. Tell me, charm- 

 ing woman, the number of bees." 



This example is sufficiently poetical, but there is given a section on 

 interest, and one on purchase and sale for merchants. It is easily 

 seen that this arithmetic vai'ies but little from that taught in our com- 

 mon schools to-day. The processes are nearly the same, and the ad- 

 vance of the Hindoos in this science is due largely to their admirable 

 system of notation, viz., that called the Arabic, which, however, was 

 undoubtedly derived by the Arabs from Hindoo teachers, as is admitted 

 by the best authorities. 



The next section of the book is occupied with a kind of arithmetical 

 geometry, which has for its basis the relation between the squares of 

 the sides of a right-angled triangle. The demonstration of this cele- 

 brated theorem is given both geometrically and algebraically by one 

 of the commentators. This algebraic demonstration is so short and 

 so direct that it will be given : If C and D are the greater and less 

 sides of a right-angled triangle, and B the hypothenuse whose greater 

 and less segments are c and d, then 



B : C = C : c or c = W 



B 



Also, B:D = D:d or d = D_' 



B~ 



Therefore B = c + d = CJ + I) 2 and B a = C 2 + D \ 



B 



It is noteworthy that Wallis, in his " Treatise on Angular Sections," 

 vol. in. 22 



