 | Charles Davies - Geometry - 1850 - 238 pages
...of each is equal to 1 : it also shows the length of the radius of the inscribed circle. Now, since the areas of similar polygons are to each other as the squares described on their homologous sides (Bk. IV. Th. xx), we have 1 : tabular area : : any side squared... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...polygons whose sides are unity, or 1, be calculated and arranged in the following TABLE. Now, since the areas of similar polygons are to each other as the squares of their homologous sides (B. IV., P. 27), we have, n 1 : any side squared : : tabular area : area.... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...polygons whose sides are unity, or 1, be calculated and arranged in the following TABLE. Now, since the areas of similar polygons are to each other as the squares of their homologous sides (B. Iv., r. 27), we have, o 1" : any side squared : : tabular area : area.... | |
 | Dana Pond Colburn - Arithmetic - 1855 - 396 pages
...squares, and parallelograms are to each other as the product of their bases by their altitudes. (/.) The areas of similar polygons are to each other as the squares of their like dimensions. (u.) The circumference of a circle equals very nearly 3.1416 * times its... | |
 | Charles Davies - Geometry - 1855 - 340 pages
...side of each is equal to 1 : it also shows the length of the radius of the inscribed circleNow, since the areas of similar polygons are to each other as the squares described on their homologous sides (Bk- IV Th- xx), we have I2 : tabular area : : any side squared... | |
 | Dana Pond Colburn - Arithmetic - 1856 - 392 pages
...squares, and parallelograms are to each other as the product of their bases by their altitudes. (t.) The areas of similar polygons are to each other as the squares of their like dimensions. («.) The circumference of a circle equals very nearly 3.1416* times its... | |
 | Elias Loomis - Conic sections - 1857 - 242 pages
...circumscribed circles; and also as the radii GH, gh of the inscribed circles. The surfaces of these polygons are to each other as the squares of the homologous sides BC, bc (Prop. I., Cor.) ; they are, therefore, as the squares of BG, bg. the radii of the cir cumscribed... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...circumscribed circles; and also as the radii GH, gh of the inscribed circles. The surfaces of these polygons are to each other as the squares of the homologous sides BC, be (Prop. I., Cor.) ; they are, therefore, as the squares of BG, bg, the radii of the cir cumscribed... | |
 | Dana Pond Colburn - 1858 - 288 pages
...the triangle MRN, figure 1, is to the area of ACB, figure 2, as MN times RS is to AB times A C. (u.) The areas of similar polygons are to each other as the squares of their like dimensions. ILLUSTRATION. — If the two triangles ABC and EFG are similar, the area... | |
 | Dana Pond Colburn - Arithmetic - 1860 - 388 pages
...squares, and parallelograms are to each other as the product of their bases by their altitudes. (/.) The areas of similar polygons are to each other as the squares of thcir like dimensions. («.) The circumference of a circle equals very nearly 3.1416* times its... | |
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Now, since the areas of similar polygons are to each other as the squares of their homologous sides... 
