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" The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their surfaces are to each other as the squares of those sides (Book IV. "
Elements of Geometry and Trigonometry Translated from the French of A.M ... - Page 105
by Charles Davies - 1849 - 359 pages
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...their homologous sides proportional ; 'consequently they are einrilai (Book IV. Def. 1.). • . _' J Cor. The perimeters of two regular polygons of the...surfaces are to each other as the squares of those sidei (Book IV. Prop. XXVII.). Scholium. The angle of a regular polygon, like the angle ot an equiangular...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 372 pages
...question have their angles equal, and their homologous sides proportional ; consequently they are similai (Book IV. Def. 1.). Cor. The perimeters of two regular...other as the squares of those sides (Book IV. Prop. XXVIL). Scholium. The angle of a regular polygon, like the angle ot an equiangular polygon, is determined...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...214, 215, 216, 217, 218, 219, 220, 221, and 228. , , 232. Theorem. The homologous sides of regular polygons of the same number of sides are to each other as the radii of their circumscribed circles, -and also as the radii of their inscribed circles. Demonstration....
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 386 pages
...are equal, and likewise the sides ab, be, cd, &c. (Def.) ; it is plain that AB : ab : : BC : be : : CD : cd, &c. ; hence the two figures in question have...the squares of those sides (Book IV. Prop. XXVII.). Scholium. The angle of a regular polygon, like the angle of an equiangular polygon, is determined by...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1839 - 372 pages
...the angles C and c, &c. are equal. Again, since the polygons are regular, the sides AB, BC, CD, &c. are equal, and likewise the sides ab, bc, cd, &c....the squares of those sides (Book IV. Prop. XXVII.). Scholium. The angle of a regular polygon, like the angle of an equiangular polygon, is detennined by...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 235 pages
...equal, and their homologous sides proportional ; therefore they are similar (162). 264. Corollary. The perimeters of two regular polygons of the same...as their homologous sides, and their surfaces are as the squares of these sides (221). 265. Scholium. The angle of a regular polygon is determined by...
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Elements of Geometry and Trigonometry

Geometry - 1843 - 404 pages
...the angles C and c, &c. are equal. Again, since the polygons are regular, the sides AB, BC, CD, &c. are equal, and likewise the sides ab, bc, cd, &c....XXVII.). PROPOSITION II. THEOREM. Any regular polygon may be inscribed in a circle, and circumscribed about one. Let ABCDE &c. be a regular polygon : describe...
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Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...area of a circle is equal to its circumference multiplied by half its radius.* PROP. VII. THEOREM. The perimeters of two regular polygons of the same number of sides, are to each other as the radii of the circumscribed circles : and their areas are to each other, as the squares of those...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 237 pages
...each other as the radii of the circumscribed circles, and also as the radii of the inscribed circles ; and their surfaces are to each other as the squares of those radii. Let AB he a side of one of the polygons, O the centre, and conse- a— quently OA the radius...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 pages
...; consequently they are similar (B. FV, Def. 3). Cor. The perimeters of two regular polygons having the same number of sides, are to each other as their homologous sides ; and their areas are to each other as the squares of those sides (B. IV, Prop. xvi). (84.) It has been shown (...
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