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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 82
by Adrien Marie Legendre - 1841 - 235 pages
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...angles equal, and their homologous sides proportional ; hence they are similar (Art. 210). 347. Cor. The perimeters of two regular polygons of the same...to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop. XXXI. Bk. IV.). 348. Scholium. The angle...
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Primary Elements of Plane and Solid Geometry: For Schools and Academies

Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...two polygons (Def. 3, Sec. VII, BI) Therefore, the perimeters, etc. BOOK II. 67 THEOREM XI. The areas of two regular polygons of the same number of sides are to each other as the squares of their sides. Let ABODE, abede, be two regular polygons of the same number of sides,...
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Treatise on Plane and Solid Geometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...corresponding side of the second. Therefore, the polygons are similar (433). 450. Corollary — The areas of two regular polygons of the same number of sides are to each other as the squares of their homologous lines (436). 451. Corollary. — The ratio of the radius to the side...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1868 - 340 pages
...angles equal, and their homologous sides proportional ; hence they are similar (Art. 210). 347. Cor. The perimeters of two regular polygons of the same...to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop. XXXI. Bk. IV.). 348. Scholium. The angle...
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 438 pages
...corresponding side of the second. Therefore, the polygons are similar (433). 450. Corollary. — The areas of two regular polygons • of the same number of sides are to each other as the squares of their homologous lines (436). 451. Corollary. — The ratio of the radius to the side...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 pages
...radius of the inscribed circle. Therefore *he area of a regular polygon, &c. PROPOSITION VIII. THEOREM. The perimeters of two regular polygons of the same number of sides, are as the radii of the inscribed or circumscribed cir cles, and their surfaces are as the squares of the...
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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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Treatise on Plane and Solid Geometry for Colleges, Schools, and Private Students

Eli Todd Tappan - Geometry - 1873 - 288 pages
...corresponding side of the second. Therefore, the polygons are similar (433). 450. Corollary. — The areas of two regular polygons of the same number of sides are to each other as the squares of their homologous lines (436). 451. Corollary — The ratio of the radius to the side...
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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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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872 - 562 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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