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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

Adrien Marie Legendre - Geometry - 1819 - 208 pages
...angles 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 deteruiined by...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 280 pages
...angles 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...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...angles 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: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 pages
...angles equal, and their homologous sides proportional ; consequently (102.) they -are similar. 264. Cor. The perimeters of two regular polygons of the...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 Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 228 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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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 158 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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First lessons in Plane Geometry. Together with an application of them to the ...

Francis Joseph Grund - Geometry, Plane - 1830 - 274 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 - 206 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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