86 A 'treatise of Algebra.

* 3 *

^ : -J, or as, 5 : 3 :: x : — — the Share of C ; also, asx

| : i, or as, 2 : 1 :: x : ~ = the Share of D.

2

Therefore, by the Question, * — -f- — -f- — — a i

4 5 2

whence 40*-}- 3 ox -j- 24* -j- 2 ox — 40s, that is H4X

40a 20a

— 40a; consequently x —-= — = 7, 4 , the Share

"4 57

of A ; therefore j that of B will be = 5 j that ofC — 4' *, and,that of D j z= 3^,.

P R O B L E M XV.

A Shepherd , i/i Time of War , fell in with a Party ofSoldiers, who plund. red him of half his Piock, and halfa Sheep over and above ; after he was parted from thema second Party met him, who took half what he hadleft , and likewise half a Sheep over ; and, soon afterthis, a third Party met him and used him in the sameManner , and then he found he had onh 5* (a.) Sheepleft: ’Tis required to find, from hence, the Number ofSheep he had at first. ■

Let x (as usual) be the Number sought ; then, ac-cording to the Question, the Number of Sheep left, afterbeing plundered the first time, will be expreiled byx x — 1 x— I

■-;, or-; half whereof is -; from which

2 2 4

1 /x — 1 x '— 3

subtract 7, and the Remainder (- J ) — : -

V 4 4

will, it is manifest, be the Number of Sheep left, afterbeing plundered the second time: In like Manner, ifx — 3 x — 3 \ '

from — (the half of - 1 you, again, take

8 4 '

there