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 ...

EUCLID's Design in this Book is to give the first Principles of Geometry; and to do the same. Methodically, he begins with the Definitions, and Explication of the most ordinary Terms, then he exhibits certain Suppositions, and having proposed those Maxims which natural Reason teacheth, he pretends to put forward nothing without Demonstration, and to convince any one which will consent to

nothing but what he shall be obliged to acknowledge; in his first Propositions he treateth of Lines, and of the several Angles made by their intersecting each other, and having occasion to Demonstrate their Proprieties, and compare certain Triangles, he doth the same in the First Eight Propositions; then teacheth the Practical way of dividing an Angle and a Line into two equal parts, and to draw a Perpendicular he pursues to the propriety of a Triangle; and having shewn those of Parallel Lines, he makes an end of the Explication of this First Figure, and passeth forwards to Parallelograms; giving a way to reduce all sorts of Polygons into a more Regular Figure: He endeth this Book with that Celebrated Proposition of Pythagoras, and Demonstrates, that in a Rectangular Triangle, the Square of the Base is equal to the sum of the Squares of the Sides, including the Right Angle.