i8e> A Treatise os Algebra.

400 — zim

must be greater than---Furthermore, since

O

aim— 400 -fr- 62; v

)t 18 (=-1 = 5»» —. 100 + 2 -}.

4

2 z-fm az + w»

--, it is plain that- must be a whole Num-

4 4

her, and consequently m an even Number (by Note a:p. 167.) Therefore let m be now expounded by 16, 18,ao and 22 successively, which are all the even Num-bers between the two Limits of ,m ; and then the fore-said Value of * will be expressed by — 16 -j- 2 -j- —,

2

% + 1 2 , * 4-1

— L -j- 2 -j-, 5 + -^lid 15+ 2-j-

2 ' 2 2

respectively. In the first of which Cases the Limits

( 400 — 17 m 400-

—- and

of 2 being iL?s and

10 .. , 6

io^, z, it is manifest, can, in that Cafe, have only oneValue in whole Numbers, which is 12, and which" be-ing substituted for 2, in the foresaid Equations, givesx 22 2, and y ■= 2, for the corresponding Values of xand y. Moreover, since the Limits of 2, in the secondCase, where m is — 18, are g,* c and 3s, it is plainthat z may be equal to any odd Number between theforesaid Limits; but z, here, cannot be an even Num-

2 + I \

her, because then x (——6 -j- z-\ - j would not

be a whole Number. Therefore in this Cafe we havethree different Answers, wherein the Values of z are 5,7 and 93 those of x, 2, 5 and 8, and those of y equal toxi, 6 and 1 respectively. And by proceeding aster thesame Manner all the Values in the other Cases will befound ; and then we shall have the nine following An-swers, in whole Numbers.