An Elementary Treatise On the Geometrical And Algebraical Investigation of Maxim
An Elementary Treatise On the Geometrical And Algebraical Investigation of Maxim
D Daniel Cresswell
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Let A and B be two equal regular polygons of which A has the greater number of sides ; the peri meter of A is less than that of B. Let a third polygon C be supposed to have the same number of sides as A, and the same perimeter as #; then C (Art. 37. ) is greater than B, and, therefore, greater than the equal polygon A\ its perimeter is, therefore, (Art. 23. ) greater than that of A\ i. E. The perimeter of B is greater than that of A. r i PROP. XXII. 40. Problem. A regular polygon being given, t...o describe about a given circle another polygon similar to the given polygon. Let ABC be the given polygon, and DEFthe given circle ; it is required to describe about the circle D EF a poly gon similar to the given polygon ABC. OF MAXIMA AND MINIMA. 59 Find (E. 1. 3. ) the center H of the given circle; join H and any assumed point Z), in the circum- JL> ference; find G (Art. 35. ) the center of the circle described about the polygon ABC\ join G, ^f and G, C and G, 7, &c. ; then (E. 28. And 27.
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