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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. "
Plane Geometry - Page 255
by Fletcher Durell, Elmer Ellsworth Arnold - 1917 - 318 pages
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 574 pages
...circle is the same as the perpendicular let fall from the centre upon one of the sides. THEOREM. 282. The perimeters of regular polygons of the same number of sides are as the radii of the circumscribed circles, and also as the radii of Hie inscribed circles ; and their...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 394 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 other as the squares of...
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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
...circle is the same as the perpendicular let fall from the centre upon one of the sides. THEOREM. 282. The perimeters of regular polygons of the same number of sides are as the radii of the circumscribed circles, and also as the radii of the inscribed circles ; and their...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 276 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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The North American Review, Volume 27

Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - American fiction - 1828 - 598 pages
...Admitting our principle, this proposition is included in that of art. 282. It is there demonstrated, that ' the perimeters of regular polygons of the same number of sides, are as the radii of their inscribed circles ; and their surfaces are as the squares of these same radii.'...
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The North American Review, Volume 27

Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - American fiction - 1828 - 598 pages
...Admitting our principle, this proposition is included in that of art. 282. It is there demonstrated, that ' the perimeters of regular polygons of the same number of sides, are as the radii of their inscribed circles ; and their surfaces are as the squares of these same radii.'...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 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 - 138 pages
...given of a curved line (10) namely, that it is made up of infinitely small straight lines. 95. — The perimeters of regular polygons of the same number of sides are to each other as the radii of their circumscribed circles — . By the perimeter of a polygon we mean the sum of its sides. Then...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 156 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 to each other as the radii of their circumscribed circles. By th^orimeter of a polygon we mean the sum of its sides;^Snen we say...
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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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