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 IX. PROBLEM.

TO Bisect or Divide into two equal parts a Right-Lined Angle given, SAT.

Take AS equal to AT, and draw the Line ST, upon which make an equi∣lateral Triangle SVT; draw the Right Line VA, it shall Bisect the Angle.

Demonstration. AS is equal to AT, and the Side AV is common, and the Base SV equal to VT; therefore the Angle SAV is equal to TAV, which was to be done.

USE.

THis Proposition is very useful to Divide a Quadrant into Degrees, it being the same thing to Divide an Angle, or to Divide an Arch into two equal parts; for the Line AV Divideth as well the Arch ST at the Angle SAT, for if you put the Semi-Diameter on a Quadrant, you cut off an Arch of 60 Degrees, and Dividing that

Arch into Two Equal parts, you have 30 Degrees, which being again Divided into two equal parts, you have 15 Degrees. It is true, to make an end of this Division you must Divide an Arch in Three, which is not yet known to Geometricians. Our Sea Compasses are Divided into 32 Points by this Proposition.