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 XXIII. PROBLEM.

TO make an Angle equal to an Angle given in any Point of a Line.

Let it be proposed to make an Angle equal to EDF, at the Point A, of the Line AB, at the Points A and D, as Centers, draw two Arches BC, EF, with the same extent of the Compasses; then take the Distance EF between your Compasses, put one Foot in B, and cut off BC, and draw AC. I say that the Angles BAC, EDF, are equal.

Demonstration. The Triangles ABC, DEF, have the Sides AB, AC equal to the Sides DE, DF; since that the Arches BC, EF, were described with the same extent of the Compass, they have also their Bases BC, EF, equal: Therefore the Angles BAC, DEF, are equal (by the 8^th.)

USE.

THis Problem is so necessary in Sur∣veying Fortifications, Prospective, Dialling, and in all other parts of the Mathematicks; so that the greatest part

of their Practice would be impossible, if one Angle could not be made equal to ano∣ther, or of any number of Degrees re∣quired.