Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Books Books
" 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 109
by Charles Davies - 1849 - 359 pages
Full view - About this book

Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 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....
Full view - About this book

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...
Full view - About this book

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...
Full view - About this book

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...
Full view - About this book

The Eclectic School Geometry

Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...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;...
Full view - About this book

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...
Full view - About this book

A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 272 pages
...the two polygons are similar. § 319 QED REGULAR POLYGONS AND CIRCLES. PROPOSITION V. THEOREM. 413. The perimeters of two 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. D BA M....
Full view - About this book

A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 264 pages
...altitudes of similar A have the same ratio as their bases). .-.P:P'=OA:O'A'=OM:OM'. QED 414. COR. The areas of two regular polygons of the same number of sides are to each other as the squares of the radii of their circumscribed circles, and also as the squares of the radii of their...
Full view - About this book

Principles of Plane Geometry

James Wallace MacDonald - Geometry - 1889 - 80 pages
...a regular pentedecagon in a given circle. Proposition X. A Theorem. Proposition XI. A Theorem. 276. The perimeters of two regular polygons of the same number of sides are to each other : I. As their sides. II. As the radii of circumscribed circles. III. As the radii of inscribed circles....
Full view - About this book

Principles of Plane Geometry

James Wallace MacDonald - Geometry - 1894 - 76 pages
...275. Two regular polygons of the same number of sides are similar. Proposition XI. A Theorem. 276. The perimeters of two regular polygons of the same number of sides are to each other : I. As their sides. II. As the radii of circumscribed circles. III. As the radii of inscribed circles....
Full view - About this book




  1. My library
  2. Help
  3. Advanced Book Search
  4. Download EPUB
  5. Download PDF