Vol. VII, No. 11.] References to Indian Mathematics. 807 
[V.S.] 
For the rectangle bk=gh and the rectangle az=az, whence 
by adding we have bamzki = rectangle ah 
or ab. bi + mz. kz=ad. dh 
or ab. gd +ag. bd=ad. bg 
{ va g apie 
( 
é : k 
| 
re 
. - . 
Zz. n 
By setting ag=a the first assumed number of the rule and 
gd =e, the first error, and further ab=£ and bd=e,, we have 
a, €, +a, @, 
é, +e, 
nd 
Led 
sd Dana 
This is more than sufficient warrant for rejecting Woepcke’ 8 
translation and discarding the theory of Indian origin that his 
incorrect rendering implied. 
Lys 
It will have been noticed that in the Algoritmi of Muham- 
mad | b. Miisi and the arithmetic of Planudes the ‘proof by 
nine’ is employed, but we find no trace of this method in an. 
early Hindu work. Avicenna (980-1037 a.p. be is, however, said 
to attribute a connected rule to the Hind After having 
mentioned that the unit figures br — num abees are alwa 
1, 4, 9, 6 or 5 he goes on to say—‘ As to the verification of the 
squares by the———— method it is aaa one, or four, or 
seven, or nine. Now unity corresponds to one or eight, to four, 
two or seven, to seven, four or five, and if it is nine there will 
be three, or six, or nine.’’ The blank to be filled is the trans- 
lation of the word hindasi. Woepcke gives ‘Indian’ but 
acknowledges that it should ordinarily be ‘geometrical.’ His 
reason for rejecting the term ‘ geometrical’ is that the rule in 
question appears to hae es no connection with any geometrical 
method, apr his reason for giving ‘Indian’ as the on mapa 
appears to be based on the assumption that the Arabs ow 
their BO pars scaridige to the Hindus. Now Wovrcke 
is wrong on both points for, as likely as not, the rule was based 
on a geometrical st asunabiation! and the Arabs owed very little 
1 I have already given one geometrical illustration of the rule 
(Journal Asiatic Socy., Bengal, 1907, p. 491) and it is easy enough to 
devise others. 
