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" The areas of two regular polygons of the same number of sides are to each other as the squares of their radii, or as the squares of their apothems. "
The Elements of Plane Geometry - Side 200
av Charles Austin Hobbs - 1899 - 240 sider
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Elements of Geometry

Adrien Marie Legendre - 1819 - 208 sider
...their homologous sides proportional ; therefore they are similar (162). 264. Corollary. The perimeters of two regular polygons of the same number of sides are to each other as their homologous sides, and their surfaces are as the squares of these sides (221). 265. Scholium....
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 224 sider
...their homologous sides proportional ; therefore they are similar (162). 264. Corollary. The perimeters of two regular polygons of the same number of sides are to each other as their homologous sides, and their surfaces are as the squares of these sides (221). 265. Scholium....
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Elements of Geometry

Adrien Marie Legendre - 1825 - 224 sider
...their homologous sides proportional ; therefore they are similar (162). 264. Corollary. The perimeters of two regular polygons of the same number of sides are to each other as their homologous sides, and their surfaces are as the squares of these sides (221). 265. Scholium....
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - 1828 - 316 sider
...their homologous sides proportional ; consequently (102.) they -are similar. 264. Cor. The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their surfaces, as the squares of those sides (221.) 265. Scholium. The...
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ELEMENTS OF GEOMETRY UPON THE INDUCTIVE METHOD.

JAMES HAYWARD - 1829
...circumscribed circles; and ON, on, are radii of the inscribed circles. We therefore say—The areas of regular polygons of the same number of sides, are to each other as the squares of the radii of the circumscribed circles, and also of the inscribed circles. (on)* 0 (boc) (bo) 2...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - 1829 - 129 sider
...that it is made up of infinitely small straight lines. 95. THEOREM. — The pe.rime.le.rs of regular polygons of the. same number of sides are to each other as the radii of their circumscribed circles. By th^orimeter of a polygon we mean the sum of its sides;^Snen...
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First lessons in Plane Geometry. Together with an application of them to the ...

Francis Joseph Grund - 1830 - 12 sider
...the areas of the polygons and the areas of the circles themselves will be imperceptible ; and because the areas of two regular polygons of the same number of sides are in the same ratio, as the areas of the squares upon the radii of the circles in which they are inscribed,...
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An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Del 1

Francis Joseph Grund - 1834 - 190 sider
...the areas of the polygons and the areas of the circles themselves will be imperceptible ; and because the areas of two regular polygons of the same number of sides are in the same ratio as the areas of the squares upon the radii of the circles in which they are inscribed...
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An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Del 1

Francis Joseph Grund - 1834 - 190 sider
...are to each other in the proportion of the radii of the inscribed or circumscribed circles. 2. Tlie areas of two regular polygons of the same number of sides, are in the same ratio as the squares constructed upon the radii of the inscribed or circumscribed circles....
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1836 - 359 sider
...sides proportional ; 'consequently they are einrilai (Book IV. Def. 1.). • . _' J Cor. 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 sidei (Book IV....
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