AS PRACTISED BY THE ARABS. 155 



Then If] 3 = 1 4- V + W + Hi = 6fH> and deficiency = f££. 



62). It also appears from hence that the deficiency in the form 

 a 3 -j- r, is always less than in the form (a -f I) 5 — r. For — 



When A = 2 — V -f 1, deficiency = -fj*, and when A — 7 = 2 s — 1, 

 there is a greater deficiency -§-§4. 



When A = 3 — l 3 -f 2, deficiency = ^||, and when A = 6 = 2 3 — 2, 

 there is a greater deficiency ■§-§-§-. 



When A -= 4 = I 3 + 3, deficiency — 1 -3^, and when A = 5 = 2 5 — 3, 

 there is a greater deficiency l-^V- 



This is also confirmed by the examples of Par. 44), for there the 

 deficiency in the first example, or 2 6 -f- 1, is less than that in the fourth 

 example, or 3 6 — 1 . And the deficiency in the second example, or 2 6 -j- 332, 

 is less than that in the third example, or 3 6 — 332. 



63). And we may also observe that the deficiencies produced by 

 assuming the Cube Root are greater than by assuming the Square Roots 

 of the same number. Thus — ■ 



By the assumed v 2 deficiency is -|. By the assumed 5/ 2 there is greater deficiency i?*. 



By the assumed %J 3 deficiency is |. By the assumed %J 3 there is greater deficiency ||g. 



By the assumed %J 5 deficiency is £%. By the assumed %i 5 there is greater deficiency IA3- 



By the assumed />/ 6 deficiency is £j. By the assumed *J 6 there is greater deficiency 3^&. 



By the assumed ZJ 7 deficiency is -fj. By the assumed />/ 7 there is greater deficiency |£i. 



Agreeable to what was conjectured in the latter part of Par. 54,) 

 and which was confirmed by the very great deficiencies in example 2d 

 and 3d of Par. 41.) 



R 1 



