176 A 'Treatise of Algebra.

ber that was to be found. In the fame Manner the leastNumber may be found, which being successively divid-ed by 4, or more given Divisors, shall have given Re-mainders.

Q^U E-$ T I O N 10.

Jf 7 y -f- HZ = 224; ’tif required to find all thepossible Values of. x, y and z in whole Numbers.

In this, and other Questions of the fame kind, whereyou have three or more indeterminate Quantities andonly one Equation, it will be proper, first of all, tofind the Limits of those Quantities: Thus, in the pre-

224— 7y — 1 iz

sent Case, because x is =2-, and because

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the least Values of y and z cannot (by the Question) beJess than Unity, it is plain that x cannot be greater than

224— 7— 11 . , . , .

■-or 41 : And, in the fame manner it will

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appear that y cannot be greater than 29, nor z. greaterthan 19; which therefore are the required Limits in this

224— Jy —IIZ

> Case. Moreover, since x is =-=4?

i+2y + z

— V — zz-—

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zy -}- z -f- Imanifest that -

: a whole Number, it ismust also be a whole Num-

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her: Let z 1 be therefore considered as a knownQuantity, and let the fame be represented by a, and then

2y + a

the last Expression will become-; from which,

by proceeding according to the foregoing Lemma, weshall get y — za (— zz -f- 2) from whence the correspond-ing Value of * will come out — 42 — 52.

Let z be now taken == i, then will * = 37 and y = 4;from the former of which Values, let the Coefficient ofy be, continually, subtracted, and to the latter, let thatof x , be, continually, added (according to the foregoing

Note)

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