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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 Geometry: Simplified for Beginners Not Versed in ... - Page 138
by Francis Joseph Grund - 1834 - 190 pages
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New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 pages
...equal, and their homologous sides proportional; hence they are similar (172). 222. Cor. 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 (Theo. XXI.)....
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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 ; and...
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The elements of geometry, in eight books; or, First step in applied logic

L J V. Gerard - 1874 - 428 pages
...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....
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New Elementary Geometry: With Practical Applications : a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1874 - 206 pages
...equal, and their homologous sides proportional; hence they are similar (176). 222. Cor. 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 (Theo. XXI.)....
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1877 - 458 pages
...they are consequently similar (B. IV., Def. 4). Therefore, regular polygons, etc. Cor. The perimeters of two regular polygons of the same number of sides are to each other as their homologous sides, and their areas are as the squares of those sides (B. IV., Pr. 27). Scholium....
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Harvard Examination Papers

Robert Fowler Leighton - 1877 - 372 pages
...angle be if the chord passes through the centre of the circle ? 5. Prove that the perimeters of regular polygons, of the same number of sides, are to each other as the radii of the circumscribed circles. State, without proving, what the ratio of the areas of the polygons...
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A Geometry for Beginners

George Anthony Hill - Geometry - 1881 - 332 pages
...similar polygons with their perimeters (see § 177, Corollary 2). 2. Prove that the areas of regular polygons of the same number of sides are to each other, (»'.) as the squares of their sides; (»'.) as the squares of their perimeters. 3. If in two hexagonal parks a side...
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Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - Geometry - 1883 - 352 pages
...are to each other as the corresponding diagonals (387), 416. COROLLARY 1.—The perimeters of regular polygons of the same number of sides are to each other as the apothems of the polygons 1382). 417. COROLLARY 2.—The circumferences of circles are to each other...
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The Eclectic School Geometry: A Revision of Evan's School Geometry

Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...perimeters of the two polygons (Def. 3, Sec. VII, Book I). Therefore, the perimeters, etc. THEOREM XVII. The areas of two regular polygons of the same number of sides are to each other as the squares of their sides. Let ABCDE, abcde, be two regular polygons of the same number of sides; for...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...III. Regular polygons of the same number of sides are similar. 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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