AS PRACTISED BY THE ARABS. 167 



Maximum, and wherein consequently by Paras. 67 and 68,) the excess should 



100 r 



be as great as possible. Then the assumed Root will be a -j ■ 



200 a -f 1 



100 X 2 a 200 a 



zz a -\ ■■ = a -f and then 



200 a -j- 1 200 a -f 1, 



Let A — 3 and assumed Root zt lf-g- f • 



HTllAn 1200 I 2 -I i 4 O I 4 Q 3 9 5 9 8 



J.11CIJ. 1 „ 1 I J. -f- 2 ay -J- 40 4oi — "40401' 



Let A — 8 and assumed Root — 2 -f-g-f. 



TllPn 9*0 1 2 A I 1 fi_0_0 I 16 P 1 5 8 3 9 6 



J. 11C1X «i 40i | "* -f- 4 U - ~f 16 8 1 " 16 8 1' 



Let A ~ 15 and assumed Root r= 3|-g-|-. 



Tlipn Q 600 I 2 Q_|_ 3600 J 3 6 — 1 < 3 5 6 3 9 4 



X UCU O -g-grYl » -J - 6""tTT "T 361201 lU 361S01' 



In which it will easily be observed, that the excesses, though large, 

 are yet still Z_ 1, and that they increase with the increase of a. 



77). These speculations might easily be continued and diversified, 

 and pursued into higher powers ; but this, like all other Mathematical 

 subjects, leads to interminable results, and as an abrupt conclusion must 

 be made somewhere, so it is high time, considering the length of this 

 Paper, that it should be made here. Some apology is, perhaps, necessary 

 for the great length to which the Essay has already extended, and which 

 is, indeed, much greater than I had supposed would have been necessary ; 

 but it is not very easy to abridge such a detail without rendering it 



u 1 



