Elementary plane geometry : inductive and deductive / by Alfred Baker . 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, usingparall
Elementary plane geometry : inductive and deductive / by Alfred Baker . 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. Regulae Polygons. 123 of tlie construction may be tested by using the dividers to determine whether the sides are equal, and the bevel to determine whether the angles areequal. Each of the angles at the centre is 45. Henceeach of the angles at the base of any of the isoscelestriangles, OAB, OBC, ... is 67^, and the angle of aregular octagon is 135°. 5. If tangents be drawn at the angular pointsof the octagon ABCDEFGH, the tangents formanother regular octagon which is said to beabout the circle. 6. To describe a regular octagon with side,AB, of given length we may proceed as follows: Construct the angle ABC of 135\ and make BC = AB and BC in K and L, and draw KO, LO pei^pen-dicular to AB and BC. With 0 ascentre, and radius OA, OB or OCdescribe a circle. On this layoff with the dividers six chordsequal to AB or BC, beginningat the point C or A. That therest of the circle is exactlytaken up with six such chordsaffords a test of the accuracywith which the angle ABC (135°) is c
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