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TO inscribe a Regular Pentagon in a Circle.
To inscribe a Regular Pentagon in a Circle; describe (by the 10th) an Iso∣sceles Triangle ABC, which shall have the Angles ABC, ACB, on the Base, each double to the Angle A. Inscribe in the Circle, a Triangle DEF, equi∣angled to the Triangle ABC; divide into Two equally the Angles DEF, DFE, draw the Lines EG, FH. Lastly, joyn the Lines DH, DG, GF,
EH: and you shall have made a Regu∣lar Pentagon, that is to say, which hath all its Sides equal, as well as all its Angles.
Demonstration. The Angles DEG, GEF, DFH, HFE, are the halfs of the Angles DEF, DFE, which are each double to the Angle A; and by consequence the five Arches, which serve to them for Bases, are equal (by the 26th. of the 3d.) and the Lines HD, HE, EF, FG, GD, are equal (by the 29th. of the 3d.) Secondly, the Angles DGF, GFE, having each for Base thereof, the equal Arks shall be likewise equal. Thence all the Sides, and Angles of the Pentagons are equal.