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 II. THEOREM.

LInes which cut one another, are in the same Plane, as well as all the parts of a Triangle.

If the Two Lines BE, CD, cut one another in the Point A; and if there be made a Triangle by drawing the Base BC: I say that all the parts of the Tri∣angle ABC, are in the same plane, and that the Lines BE, CD, are likewise therein.

Demonstration. It cannot be said that any one part of the Triangle ABC, is in a Plane, and that the other part is without; without saying that one part of

a Line is in one Plane, and that the other part of the same Line is not therein; which is contrary to the first Proposition: and seeing that the sides of the Triangle are in th same Plane wherein the Tri∣angle is; the Lines BE, CD, shall be in the same Plane.

USE.

THis Proposition doth sufficiently de∣termine a Plane, by two streight Lines mutually intersecting each other, or by a Triangle; I have made use thereof in Opticks, to prove that the objective parallel Lines which fall on the Tablet, ought to be Represented by Lines which concur in a Point.