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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. "
Elements of Geometry - Page 58
by Adrien Marie Legendre - 1825 - 224 pages
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 208 pages
...sides proportional ; therefore they are similar. THEOREM. 221. The paimeters of similar polygons are as their homologous sides, and their surfaces are as the squares of these sides. Demonstration. 1. By the nature of similar figures we have Fig. 129. AB '• FG : : BC : GH'• '•...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...sides proportional ; therefore they are similar. THEOREM. 221. The perimeters of similar polygons are as their homologous sides, and their surfaces are as the squares of these sides. ^ Demonstration. 1. By the nature of similar figures we have Fig. 129. AB : FG : : BC : GH : : CD :...
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Elements of Geometry

Adrien Marie Legendre - 1825 - 224 pages
...proportional ; therefore they are similar. THEOREM. 221. Thf perimeters of similar polygons are as tfieir homologous sides, and their surfaces are as the squares of these sides. Demons I rat ion, 1. By the nature of similar figures we have Fig. 129. AB : FG : : BC : GH : : CD...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 316 pages
...angles equal, and their homologous sides proportional ; consequently (102.) they -are similar. 264. Cor. The perimeters of two regular polygons of the same...other as their homologous sides, and their surfaces, as the squares of those sides (221.) 265. Scholium. The angle of a regular polygon, like the angle...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 129 pages
...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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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 - 12 pages
...perimeter of that figure. The above proportion may therefore be expressed in shorter terms; namely, the perimeters of two regular polygons of the same number of sides, are to each other in the proportion of the radii of the inscribed or circumscribed circles. 2. The areas of two regular...
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An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Part 1

Francis Joseph Grund - Geometry, Plane - 1834 - 190 pages
...perimeter of that figure. The above proportion may therefore be expressed in shorter terms ; namely, the perimeters of two regular polygons of the same number of sides, are to each other in the proportion of the radii of the inscribed or circumscribed circles. 2. Tlie areas of two regular...
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An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Part 1

Francis Joseph Grund - Geometry, Plane - 1834 - 190 pages
...each other in 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....
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An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Part 1

Francis Joseph Grund - Geometry, Plane - 1834 - 190 pages
...Two regular polygons of the same number of sides are similar figures. 34. The sums of all the sides of two regular polygons of the same number of sides, are to each other in the same ratio, as the radii of the inscribed or circumscribed circles. 35. The areas of two regular...
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