158 A SHORT HISTORY OF SCIENCE 



straight line to the village. The distance traversed by each was the 

 same. Find x. 



Beautiful and dear Lilavati, whose eyes are like a fawn's ! tell me 

 what are the numbers resulting from one hundred and thirty-five, 

 taken into twelve ? if thou be skilled in multiplication by whole or by 

 parts, whether by subdivision or form or separation of digits. Tell 

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

 the same multiplier? 



The son of Pritha exasperated in combat, shot a quiver of arrows 

 to slay Carna. With half his arrows, he parried those of his an- 

 tagonist ; with four times the square-root of the quiver-full, he killed 

 his horse ; with six arrows, he slew Salya ; with three he demolished 

 the umbrella, standard and bow ; and with one, he cut off the head 

 of the foe. How many were the arrows, which Arjuna let fly ? 



For the volume contains a thousand lines including precept and 

 example. Sometimes exemplified to explain the sense and bearing 

 of a rule ; sometimes to illustrate its scope and adaptation ; one while 

 to show variety of inferences ; another while to manifest the principle. 

 For there is no end of instances ; and therefore a few only are exhibited. 

 Since the wide ocean of science is difficultly traversed by men of little 

 understanding ; and, on the other hand, the intelligent have no occa- 

 sion for copious instruction. A particle of tuition conveys science to a 

 comprehensive mind ; and having reached it, expands of its own im- 

 pulse. As oil poured upon water, as a secret entrusted to the vile, as 

 alms bestowed upon the worthy, however little, so does science infused 

 into a wise mind spread by intrinsic force. 



It is apparent to men of clear understanding, that the rule of three 

 terms constitutes arithmetic ; and sagacity, algebra. Accordingly I 

 have said in the chapter of Spherics : 



' 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.' 



Five centuries later Bhaskara also wrote an astronomy contain- 

 ing mathematical chapters, and the contents of this work soon 

 became known through the Arabs to western Europe. While the 

 preceding writers had no algebraic symbolism, but depended 

 laboriously on words and sentences, Bhaskara made considerable 

 progress in abbreviated notation. A partial list of subjects, treated 



