201 



In like manner, to find a divisor of six dimensions, if tfie 

 substituted terms were begun with G, 3, 4,3, 2, &c. the cor- 

 responding results would give the series of divisors, 136745, 

 45182, 11495, 1870, Qo, &c. 



136745— (3x6 + 7)= —3240 11 —540 



' - S -; — 200 



45182— (3 x5 + 7)zr —1700 Jen —340 ~G0 ,^ 



* ?-^ . — 140 — '" rt 



11495— (3x4+ 7)r: — 800>.||— 200 —**_,., 



1870— (3x3 + 7) r: — 320|^|— 108 ~^^~36 "» 



95— (3x2 + 7)=: — 104^^=^ _59 —34 



" ' —22 



0+12 — 36 + 56 — 52= —20 



Ic + k^ + ko^ + k^ + k^=0+ 12— 34 + 22— 20=0 and p=0 



— 540— (0 + 0)rr — 540.i —90 



—340— (0 + 0)= —340 J;; —68 ~^^ —4 



—200— (0 + 0)= —200 ^1 —50 ~'5 _4 



_,08-(0 + 0)= -108 1^-36 -'* -4 



— 52- (0 + 0)= — 52|2— 2G ~7 —4 



— 20 



/+/,+/,=— 4 + 6— 20=— 18, «7=zi=— 2. 



^ 1.2 



The divisor is Sat — 2x — 18x + 7=0, 



Thus, from 13, 7, 1, —5, —11, we have derived the divisor 

 6.r— 5=0, and from the numbers 34, 19, 10, 7, 10, we have 

 the divisor 3^+7-0, But as these are binomial divisors, and 

 as the usual rules extend only to divisors of one, two, and 

 three dimensions, from them the equation does not appear to 

 admit a trinomial divisor. However, according to the rules 

 for finding a divisor of four dimensions, from the numbers 



5^, 



