An Elementary Treatise On the Geometrical And Algebraical Investigation of Maxim

Cover 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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