. Cottage, lodge, and villa architecture. each other ; bisect m k in a. Upon a,as a centre, with the distance a f, describe the arc f b. Upon f, as a centre, with the< distancep b describe the arc b g, cutting the circle at g. Join g a, and carry it round the circle fivetimes, and it will produce the required pentagon. The arcs contained between the extremitiesof any side of the pentagon, as h k, being bisected as at h k, will give the side of a decagon, orten-sided figure, inscribed in the same circle. Problem XVII. To construct a hexagon on a given line. 1. Let a b (fig. 26) be the given
. Cottage, lodge, and villa architecture. each other ; bisect m k in a. Upon a,as a centre, with the distance a f, describe the arc f b. Upon f, as a centre, with the< distancep b describe the arc b g, cutting the circle at g. Join g a, and carry it round the circle fivetimes, and it will produce the required pentagon. The arcs contained between the extremitiesof any side of the pentagon, as h k, being bisected as at h k, will give the side of a decagon, orten-sided figure, inscribed in the same circle. Problem XVII. To construct a hexagon on a given line. 1. Let a b (fig. 26) be the given line. On the extremities of thisline, with the extent of the line as a radius, describe arcs intersectingeach other at c. 2. On c, as a centre, with the same radius, describe a circle. Fromthe intersections at d and e, with the arcs before described, set off d fand e g on the circle. 3. Join a d, d f, f g, and e b, which will form the hexagon the circumscribing circle is given, the following method may be adopted. Fig. 12 PRACTICAL GEOMETRY. Fig. 27.
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