!48 Gesammtsitzung 



Bekanntlich ist in dem Werk Bhascara's (12. Jahrh. n. Chr.) 

 Lilawati genannt, eine Abhandlung über die Aritbmetik der Inder 

 enthalten. Ich entnehme daraus die Ausziehung der Quadratwur- 

 zel und zwar nach der Übersetzung Taylor's (Bombay 1816), 

 die'das Verfahren und die Erläuterungen des Commentators Ga- 

 nesa vollständiger giebt, als die Bearbeitung Colebrooke's Da 

 die genannte Übersetzung äufserst selten ist, so will ich die btelle 

 hier vollständig reproduciren. Bhascara's Vorschrift zur Aus- 

 ziehung der Quadratwurzel lautet: 

 Of the Square Root. 

 Subtract from the last uneven period the greatest Square which 

 it contains. Set down double the Square root in a separate line, 

 and after dividing by it the next even period, subtract the Square 

 of the quotient from the next uneven period, and also set down 

 double this quotient in the line: Then divide the next even period 

 by the number in the line, and on subtracting the Square of the 

 quotient from the next uneven period, set down double this quo- 

 tient in the line. Thus repeat the Operation thro' all the figures. 

 The half of the separate or quotient line is the root. — 



Dazu giebt Taylor folgende Expiration, zugleich mit der 

 Übersetzung des Commentars von Ganesa: 



The figures in the first, third, fifth etc. places, reckoning from the 

 rio-ht, are called visama or uneven, and are marked by a perpendi- 

 cular stroke. Those in the second, fourth, sixth etc. places, are cal- 

 led sama or even, and are marked by a horizontal stroke. In the 

 Operation the period receives its name from the denomination of the 

 first figure on the right hand. When the first figure on the right is une- 

 ven the periodis called uneven; whenthis first figure is even, thepenod 

 is called even. Thus in the subsequent example of extracting the Squa- 

 re root of 88209, the numbers 48, 122, 410, 49, are respectively na- 

 med even, uneven, even, uneven. The details of ^Operation are 

 thus given in the commentary, tacking for exemple 88209. „Make 

 the marks even and uneven. Here the last uneven figure is 8; 

 from this subtract 4 which is the Square of 2, and there remains 

 of the Square number 48209: Then multiply the root of 4 by 2, 

 the product is 4; set this down in a separate line, and by it di- 

 vide te next even period 48; the quotient is 9, and there remains 



