806 Journal of the Asiatic Society of Bengal. {December, 1911. 
mi 72 os) x+ qgt= 16 + $16 or 
2=16 + 2:16 =28 + 
As stated above, the great majority of the problems are solved 
by the first of these methods, or regula duorum falsorwm. There 
are, however, two examples of the method of ‘ inversion’ as 
used by the Hindus.! Here is one of these examples *:— 
ee eh 9, 2 
w—5-2—} (e-5-2)-2-f{x—5—2 
eee. 9) 9) 9) 
2 
%=2 (2 (2 (1 + 2) + 2) + 2) =36. 
These two examples of the method of ‘ inversion’ of course 
do not constitute a connection with India while, on the other 
hand, the occurrence of 21 examples of the r 
us 
falsorum out of 33 problems does prove pretty conclusively — 
that the work was not of Hindu origin. 
tion of the balance, and goes on to say, ‘‘ As to the balance this 
procedure is a geometrical method (al-sina ’at al hindasiyyal). 
ndasiyya 
knowledges that ordinarily it should be ‘ geometrical.’’ Hesay8 — 
that there is absolutely nothing geometrical in the rule of the two 
ion, g on to : | 
geometrically by the help of a figure; and el-Sabi gives the 
following demonstration ° :— 
If the line ab is divided into three parts—ag, gd, db—then 
ab. gd + ag. bd=ad. bq. 
1 Lilavati, §$47-49, ete. 
2 Libri, vol. 1, 
» 1, p. 343, Us 
See Suter’s Die Mathematiker und Astronomen der Araber und Ihre 
5 
Werke, pp. 13, 43, 66, ete., etc. F 
‘ * The nearest the Hindus get to this method is in their pe 
supposition’ (ishta karman) or ‘single false position’ after the 
man fashion. See Cantor i, 618, and Colebrooke, p. 23. 
