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 XXX. PROBLEM.

TO cut a Line given into extream and mean Proportion.

It is proposed to cut the Line AB in extream, and mean Proportion; that is to say, in such a manner, that there may be the same Ratio of AB to AC, as of AC to CB. Divide the Line AB (by the 11th. of the second) in such a manner that the Rectangle comprehended under AB, CB, be equal to the Square of AC.

Demonstration. Seeing the Rectangle of AB, BC, is equal to the Square of AC; there will be the same Ratio of AB to AC, as of AC to BC (by the 17th.)

USE.

THis Proposition is necessary in the Thirteenth Book of Euclid, to find the length of the Sides of some of the five Regular Bodies. Father Lucas of St. Se∣pulchres

hath Composed a Book of the Pro∣prieties of a Line, which is cut into ex∣tream and mean Proportion.