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 XII. PROBLEM.

TO find a fourth Proportional to three Lines given.

Let there be proposed three Lines AB, BC, DE, to which must be found a fourth proportional, make an Angle as FAC, at discretion; take on AC the Lines AB, BC; and on AF, the Line AD equal to DE: then draw DB, and its parallel FC. I say that DF is the Line you seek for; that is to say, that there is the same Reason of AB to BC, as of DE, or AD to DF.

Demonstration. In the Triangle FAC, the Line DB is parallel to the Base FC; there is thence the same reason of AB to BC, as of AD to DF (by the 2d.)

USE.

THe use of the Compass of Proportion (or Sector) is established on these Propositions: for we divide a Line as we

please, by the Compass of Proportion: we do the Rule of Three without making use of Arithmetick: we extract the Square Root and Cube Root: we double the Cube: we measure all sorts of Triangles: we find the Content of Superficies, and the solidity of Bodies; we augment or diminish any figure whatever, according to what Proportion we please; and all those uses are Demonstrated by the foregoing Propositions.