cJxvi Journal of the Asiatic Society of Bengal. [N.S., XIII, 



movement 

 names. The 



, both containing similar technical terms and astronomical 

 he Greek "kentron" is undoubtedly the origin of the Indian 

 kendra and the greek zodiacal names were known to the Indian writers, 

 also the Greek names of the planets. 



As to the question of priority as between the two systems, there is 

 every reason to consider that the Greek system was prior to the Indian 

 in time. This however is a less convinciing argument because of the 

 uncertainty which always attaches to such early chronology than the fact 

 that the Greek system was the result of a development which can be 

 traced in successive stages of thought during preceding eras, whereas 

 the Indian system stand out in complete isolation from all that preceded 

 it. There is an absolute gulf between the Siddhanta system in its earli- 

 est form and the Puranic doctrine already alluded to, which cannot be 

 bridged. A new influence must be assumed to account for a change so 

 abrupt, for which there was no preparation in the eras which went before. 



To my mind this is a consideration which ought to outweigh every 

 other form of argument in leading us to conclude that the Indian system 

 was an offshoot from that of the Greeks. 



The system thus formulated has undergone practically no develop- 

 ment since the time of its adoption. 



But if India has to renounce her claim to be the discoverer of this 

 system , she deserves a renown of really higher value because of the bril- 

 liant names which adorn this period. The names of Aryabhatta. Varaha. 

 Mihira, Brahmagupta and Bhaskaracharya, to mention only the best 

 known, add a great lustre to this age of Indian research. Greece had 

 developed a mathematical system of wonderful perfection in the domain 

 of geometry. On this was built up her astronomical theory. In India 

 mathematics played a different part. It did not serve as the foundation 

 of the theory but as the instrument of calculation in the practical appli- 

 cation of the system, in the solution of problems which were likelv to 

 arise Hence its methods are analytical, embracing a scheme of algebra 

 and trigonometry which marks a great advance in mathematical attain- 

 ment. Here India can make good her claim to originality. In respect of 

 both arithmetic and algebra India has been the world's teacher. Algebra, 

 although it bears an Arab name, was borrowed from the Indians by the 

 Arabians and our numeral system is not Arabic but Indian. 



The representation of the value of numbers according to their posi- 

 tion in a decimal scale the solution of quadratic and bi-quadratic equa- 

 ls a n d more part.cularly the solution of indeterminate equations of 

 n™U?h ♦■ r t S ^ C ° nd de| ? ree ' these a ™ a few of the characteristic 



deaW I SS^S d !f /° al 8 ebraic Progress. The kultaka method for 

 mTtWn «♦• i tw indetermin ate equations has been described by a great 

 the )tZ «f t r t0rian , as 'J the fir »est mathematical achievement before 

 wSpK«H f La ? mn ? , who > centuries later, re-discovered the method 



In f« £? JT" 1 T ha I t0 the Hindu mathematicians, 

 instead of Z ™ ? ed,t u of havi *g ^ased its trigonometry on the Sine 



^stf tLtranchtf matSlcf 1 *" *"* ^^ ^ *" ** 



sion A neveXeL'' Sed * l4 }t m the va,ue oi '• a ™™ accurate expres- 

 love" foJ7nrm,^f ^ ° f hi ? succe3s «^ with a characteristically Indian 

 moved /To L fh 8 y mme t"c a l or symbolical character frequently ero- 

 than < ^or Vu ^ V * "* ° f this ratio > a much less accurate expression 

 matherna?L fl ;l 5'' V&lueS em P lo y* d by earlier writers. These Hindu 

 Si -Sest TtST r y v ^ t0 the mhnitesimal calculus ; yet one of 

 p£™^ite£l£ nh]Bd mt ° err ° r in «*"*>** the volume of the 



ReometrV r Dr a ovi?o 1 fe^ here to mk these *™> questions :-Why did 

 theTndian P Ind Wh tra ^ ,V ^ fc ° the Greek mathematician and algebra to 

 d«ful dSee of r3S y i * d Gre6Ce pUrSUe its mathematics to such a won- 

 -reat devSonmL? ^ ,et6n r ' while India e ™" when on the threshold of 

 great dexelopments stopped short and never advanced anv further on 



