The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems. Elements of Geometry - Page 170by Andrew Wheeler Phillips, Irving Fisher - 1897 - 354 pagesFull view - About this book
| Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...3. The area of a circle is - multiplied bv the square of the radius. Hence, any two circles are to each other as the squares of their radii, or as the squares of their diameters, or generally as the squares of any two homologous lines. 4. The area of a circle is less... | |
| Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...again subdivided into varieties, &c. For ' surface, , - 4;rr3 = The surfaces of two spheres are to each other as the squares of their radii, or as the squares as spherical angle, spherical triangle, spherical polygon, &c. SPHERICAL ANGLE. An angle included of... | |
| Charles Davies, William Guy Peck - Mathematics - 1859 - 622 pages
...spherical angle, spherical triangle, spheri- . The sur?jccs of two spheres are to each other ea' polygon, as the squares of their radii, or as the squares of their diamctcre ; or in general, as the squares of any two homologous lines that can be drawn in the sphere.... | |
| Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...the ratio of the circumference to the diameter. 9O1. Corollary. — The areas of two circles are to each other as the squares of their radii ; or, as the squares of their diameters. 502. Corollary — When the radius is unity, the area is expressed by a. 503. Theorem —... | |
| Eli Todd Tappan - Geometry - 1868 - 444 pages
...the ratio of the circumference to the diameter. 501. Corollary. — The areas of two circles are to each other as the squares of their radii ; or, as the squares of their diameters. 502. Corollary — When the radius is unity, the area is expressed by ;r. 503. Theorem —... | |
| Eli Todd Tappan - Geometry - 1873 - 288 pages
...the ratio of the circumference to the diameter. 501. Corollary — The areas of two circles are to each other as the squares of their radii ; or, as the squares of their diameters. 502. Corollary — When the radius is unity, the area is expressed by TT. <3©3. Theorem... | |
| David Munn - 1873 - 160 pages
...It follows, therefore, that the lateral surfaces, or the total surfaces of similar cylinders, are to each other as the squares of their radii, or as the squares of their heights. Cor. 2. — If h = r, that is, if the height be equal to the radius of the base, the lateral... | |
| William Guy Peck - Conic sections - 1876 - 376 pages
...circumferences of two circles are to each other as their radii, or as their diameters, and their areas are to each other as the squares of their radii, or as the squares of their diameters. Cor. 2. Because similar sectors and similar segments are like parts of the circles to which... | |
| William Frothingham Bradbury - Geometry - 1877 - 262 pages
...Circumferences of circles are to each other as their radii, or as their diameters ; and the circles as the squares of their radii, or as the squares of their diameters. For circles are regular polygons of an infinite number of sides (44) ; and if the circumferences... | |
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