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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 areas are to each other as the squares of those sides (Prop. "
An Elementary Treatise on Plane and Solid Geometry - Page 70
by Benjamin Peirce - 1837 - 159 pages
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 208 pages
...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 - Geometry - 1822 - 367 pages
...of the inscribed circle. PROPOSITION VIII. THEOREM. The perimeters of two regular polygons, Juming the same number of sides, are to each other as the radii of the circumscribed circles, and also as the radii of the inscribed circles ; their surfaces are to each...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...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 - Geometry - 1825 - 280 pages
...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 - Geometry - 1828 - 316 pages
...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: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 129 pages
...(10) namely, 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...other as the radii of their circumscribed circles. By th^orimeter of a polygon we mean the sum of its sides;^Snen we say that the perimeter ABCDEF (fig....
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 172 pages
...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)...
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First lessons in Plane Geometry. Together with an application of them to the ...

Francis Joseph Grund - Geometry, Plane - 1830 - 274 pages
...the same ratio, as the radii of the inscribed or circumscribed circles. 35. The areas of two regular polygons of the same number of sides, are to each other as the areas of the squares, constructed upon the radii of the inscribed or circumscribed circles. 36. The...
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An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Part 1

Francis Joseph Grund - Geometry, Plane - 1834 - 190 pages
...the same ratio, as the radii of the inscribed or circumscribed circles. 35. The areas of two regular polygons of the same number of sides, are to each other as the areas of the squares constructed upon the radii of the inscribed or circumscribed circles. 86. The...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...; '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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