The elements of Euclid, explained and demonstrated in a new and most easie method with the uses of each proposition in all the parts of the mathematicks / by Claude Francois Milliet D'Chales, a Jesuit ; done out of French, corrected and augmented, and illustrated with nine copper plates, and the effigies of Euclid, by Reeve Williams ...

PROPOSITION XXVIII. THEOREM.

IF there be a greater Reason of the first to the second, than of the third to the fourth; there shall be also a greater Reason of the first and second to the second, than of the third and fourth to the fourth.

9.	4.	6.	3.
A,	B,	C,	D,
E,
8.

If there be a greater Reason of A to B, than of C to D; there shall be also a greater Reason of AB to B, than of CD to D. Let us suppose there is the same Reason of E to B, as of C to D.

Demonstration. There is the same Reason of E to B, as of C to D: Thence (by the 18th.) there shall be the same Reason of EB to B, as of CD to D. and AB being greater than EB, there shall be a greater Reason of AB to B, than of EB to B; and by consequence than of CD to D.