TIIE RESOLUTION Of 
190 
By making-■■■- -• zz y, we have x zz 28y I- e; which 
value being substituted in our second expression, it 
28?/ g ■f' ' 
becomes —; which, as well as y, is to be 
28?/ 4 e f 
a whole number: but^ 1 , bv making h zz e 
19 J ° 
—/, will bezz y 1- 
Qy 4- h m 
T9 ’ 
and therefore 
1 Qy and 
lSy 4- 2/? being both divisible by 19, their difference 
y — 26 must be also divisible by the same number; 
whence it is evident, that one value of y is 26 ; and 
that 26 + 192 (supposing z a whole number) will be a 
general value of y ; and consequently that x { =z 28y 
4- e) zz 532z 4- 566 4- c is a general value of t, an 
swering the two first conditions. Let this, therefore, 
be substituted in the remaining expression - ■ - which, 
. . % . 532z 4- 566 f e — g 
by that means, becomes — 352 
J 15 
7z -4- /3 
4 3b H—~ - (supposing B — \ \b e—* g zz I2e 
-7-11/ — g.) Here island I4z 4- 2/3 being both di-* 
visible by 15, their difference 2 — 2/3 must likewise be 
divisible by the same number ; and therefore one value 
of 2 will be 2/3, and the general value of 2 — 2/3 4- 
15w: from whence the general value of x ( zz 5322 4- 
566 4- e) is given — 7980?e 4- 1064/3 4- 566 4- e; 
which, by restoring the values of 6, and /3, becomes 
7980u? 4-*12625e — 11760/ — 1064g. 
Now T to have all the terms affirmative, and their co 
efficients the least possible, letia be taken zz — e 4- 2/ 
4- g; whence there results 4S45e 4- 4200/ 4- 69l6g, 
for a new value of x: from which, by expounding e, j\ 
and g, by their given values, and dividing the whole by 
7980, the least value of x, which is the remainder of 
the division, will be known.