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 XXVII. 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 to the third, than of the second to the fourth.

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

If there be a grea∣ter Reason of A to B, than of C to D; I demonstrate that there shall be a greater Rea∣son of A to C, than of B to D. Let there be the same Reason of E to B, as of C to D; A shall be greater than E.

Demonstration. There is the same Reason of E to B, as of C to D; thence (by the 16th.) there shall be the same Reason of E to C, as of B to D. And because A is greater than E, the Reason of A to C shall be greater than that of E to C. There is therefore a greater Reason of A to C, than of B to D.