AS PRACTISED BY THE ARABS. 



59 



For abbreviation, let p be put = 10 and let M be distinguished into 

 parts or periods of 6 figures each, counting from the units place, that 

 is, from 6 backwards. Then M will assume this appearance. 



a <pi> 4 b p 31 -f c p 3 ° 

 _|_ d <p Z9 + e <z> 18 + / J7 -f g f 6 4 # <P 35 4 ? 9 34 

 _j_ j pi + k p™ + I f -f m <p so 4- w <p 19 -f p p 18 



•f w f -f a; f -f y p 9 -\- z p s -f a p 7 -f (3 <p 5 



-j-yp s -f- a <p 4 4- g © 3 4 £ <p 2 + n p + Q 

 which is equal to 



(a p" -\- b p 4- c) X £ 3 ° 



-f (a <p s -f e p 4 



+ y <p 5 4 & p 4 



4- 0/ <P S 4 r p 4 



4- (m; <p s 4 a? p 4 



4 # pf -f. /* $ 4 x p 24 

 4 m p°- 4 « <p 4- jp) X f 18 



4- * p 2 + u p 4 v) x p 1 * 



4 a: p 2 + a p 4- |3) X p 6 



-f S £ 2 4 * P 4- & 

 Then for abbreviation let there be put 



4/P 3 

 -f lp z 

 4 * P 3 

 4- y f 



4 £ f 3 









a p z 



4 b p 



4 c 



= A 



d <p s 



4 e p* 



+ fp 5 



4- g f 



+ h p 



4 » 



= B 



i £ s 



4- Jc p* 



4 / £ 3 



4 m p" 



4- * <P 



4 /> 



= C 



q p* 



4- »• £ 4 



4- s p 3 



4- * P 2 



4 M @ 



4 V 



= D 



w p 5 



4 ^£ 4 



4- gf P 3 



4 z p" 



4- a P 



4 /3 



= E 



7 P* 



4- ^ £ 4 



+ % P % 



4 ^ 2 



4 9 P 



4- * 



= F 



Ap 3 



And then M becomes 

 -f B^ 24 + C p 18 4 D p x " 4 E p 6 



+ F. 



which a very little consideration will shew may be thus expressed — 











1 





A$%B 



f 6 4C p"+T> 



p«-f-E 



f+F 



in which expression A contains only 3 figures, and B, C, D, E and F 

 each contain 6, and hence by Lena. 4 each of these numbers Z. p 6 - 



R 



