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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

## Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 468 pages
...right-angled triangle OGA, OG = VOA'-AG2; that is, r = We also have j> = na; consequently, "" - a THEOREM VI. The perimeters of two regular polygons of the same number of sides are proportional to the radii of their inscribed circles, or of their circumscribed circles ; and their...

## Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 520 pages
...their angles equal, and their homologous sides proportional ; hence they are similar (Art. 210). 347. 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 (Prop. XXXI. Bk. IV.). 348. Scholium. The angle...

## Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 628 pages
...their angles equal, and their homologous sides proportional ; hence they are similar (Art. 210). 347. 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 (Prop. XXXI. Bk. IV.). 348. Scholium. The angle...

## Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 506 pages
...their angles equal, and their homologous sides proportional ; hence they are similar (Art. 210). 347. 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 (Prop. XXXI. Bk. IV.). 348. Scholium. The angle...

## 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,...

## Treatise on Plane and Solid Geometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry, Modern - 1864 - 292 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...

## Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1868 - 338 pages
...their angles equal, and their homologous sides proportional ; hence they are similar (Art. 210). 347. 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 (Prop. XXXI. Bk. IV.). 348. Scholium. The angle...

## Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 436 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...