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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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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...Therefore the polygons fulfill the two conditions of similarity. 10. Corollary. The perimeters of regular polygons of the same number of sides are to each other as the radii of the circumscribed circles, or as the radii of the inscribed circles ; and their areas...
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A Treatise on Special, Or Elementary Geometry

Edward Olney - Geometry - 1872 - 472 pages
...the corresponding diagonals (35O), p : P : : r : HQED , .g,370. COR. 1. — The perimeters of regular polygons of the same number of sides are to each other as the apothems of the polygons. For the apothems are to each other as the sides of the polygons (351)....
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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872 - 566 pages
...the corresponding diagonals (35O), p : P : : r : R q. ED 370. COR. 1. — 77(6 perimeters of regular polygons of the same number of sides are to each other as the apothems of the polygons. For the apothems are to each other as the sides of the polygons (351)....
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...Therefore the polygons fulfill the two conditions of similarity. 10. Corollary. The perimeters of regular polygons of the same number of sides are to each other as the radii of the circumscribed circles, or as the radii of the inscribed circles; and their areas are...
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New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 pages
...have their angles equal, and their homologous sides proportional; hence they are similar (172). 222. Cor. The perimeters of two regular polygons of the...to each other as their homologous sides, and their areas are to each other as the squares of those sides (Theo. XXI.). 223. Scholium. The angle of a regular...
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Catalogue - Harvard University

Harvard University - 1873 - 732 pages
...construct a polygon similar to a given polygon^ upon a given line. 6. The homologous sides of regular polygons of the same number of sides are to each other as the radii of their circumscribed circles, and also as the radii of their inscribed circles. Prove ;...
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New Elementary Geometry: With Practical Applications : a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1874 - 206 pages
...have their angles equal, and their homologous sides proportional; hence they are similar (176). 222. Cor. The perimeters of two regular polygons of the...to each other as their homologous sides, and their areas are to each other as the squares of those sides (Theo. XXI.). 223. Scholium. The angle of a regular...
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The elements of geometry, in eight books; or, First step in applied logic

L J V. Gerard - 1874 - 424 pages
...perimeter of the other, as any one side of the first is to any one side of the second, WWTBD COROLLARY I. The perimeters of two regular polygons of the same number of sides, are to each other as their radii. THEOREM 61. A regular polygon is symmetric to each radius produced lieyond the centre. Let there...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 264 pages
...XCII. Two circumferences are to one another as their radii. This proposition follows from the fact that the perimeters of two regular polygons of the same number of sides are as the radii of the circumscribed or the radii of the inscribed circles. Let GH be a circumference...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1877 - 458 pages
...of the inscribed circle. Therefore the a'rea of a regular polygon, etc. PROPOSITION VIII. THEOREM,. The perimeters of two regular polygons of the same number of sides are to each other as the radii of the inscribed or circumscribed circles, and their areas are as the squares of these radii....
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