Elementary plane geometry : inductive and deductive / by Alfred Baker . 0. Producethe three sides of these angles both ways to the cir-cumference, and join the succeeding points of intersec-tion. The construction being accurately made, thebevel will show the equality of the angles ABC, BCD,. . , and the dividers will show the equality of thesides AB, BC, . . . Since, however, each of the triano^les in the fisrureis equilateral, ha\ing its sides equal to the radius,the sides of the hexagon are equal to the radius ofthe circle. Hence the easiest way to describe a hexa-gon in a circle is to measu
Elementary plane geometry : inductive and deductive / by Alfred Baker . 0. Producethe three sides of these angles both ways to the cir-cumference, and join the succeeding points of intersec-tion. The construction being accurately made, thebevel will show the equality of the angles ABC, BCD,. . , and the dividers will show the equality of thesides AB, BC, . . . Since, however, each of the triano^les in the fisrureis equilateral, ha\ing its sides equal to the radius,the sides of the hexagon are equal to the radius ofthe circle. Hence the easiest way to describe a hexa-gon in a circle is to measure off, with the di%iders,six chords in succession, each equal to the radius. Evidently the angle of a regular hexagon is 120®.* 121 122 Geometey. 2. If tangents to the circle be drawn atthe angular points of thehexagon ABCDEF, the tan- l^^—^^ gents form another hexa- l^ngon, which is said to beabout the circle. The equality dof the sides GH, HK, .... maybe tested with the dividers, and kthe equality of the angles GHK,HKL, . . with the 3. If we wish to construct a regular hexagon withsides of given length, we describe a circle with radiusof this length, and in it inscribe a regular hexagon asin § 1. 4. To inscribe a regular octagon in a circle We may construct at thecentre eight angles, each of45, and join the ends ofconsecutive radii boundingthese angles j or, perhapsmore conveniently, we mayproceed as follows : Draw twodiameters at right angles toone another and join theirextremities. VVe thus have asquare in the circle. Through the centre, usingparallel rulers, draw diameters parallel to the sides ofthe square. The quadrants are thus bisected, and weget eight equal angles at the centre. Joining ends ofthe successive radii which bound these angles, wehave an octagon inscribed in the circle. The accuracy
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