| J. M. Scribner - Mechanical engineering - 1849 - 264 pages
...showing the multipliers of the ten regular polygons, when the sides of each are eqflal to 1 : Now, since **the areas of similar polygons are to each other as the squares** of their homologous sides, if the square of a side of a polygon be multiplied by the multiplier of... | |
| Daniel Adams - Arithmetic - 1849 - 142 pages
...feet, and the altitude of one of its equal triangles is 8'660254 feet ? Ans. 259>80762 sq. ft. IT 54. **The areas of similar polygons are to each other as the squares** of one of their sides. H 52. Hence, the areas of regular polygons may be more readily found by the... | |
| Charles Davies - Geometry - 1850 - 218 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 I2 : tabular area : : any side squared... | |
| Daniel Adams - Measurement - 1850 - 144 pages
...and the altitude of one of its equal triangles is 8<660254 feet ? Ans. 259<80762 sq. ft. ^T «S4L« **The areas of similar polygons are to each other as the squares** of one of their sides. If 52. Hence, the areas of regular polygons may be more readily found by the... | |
| George Roberts Perkins - Geometry - 1850 - 332 pages
...GHKLM, as any one antecedent ABC, is to its corresponding consequent GHK, or as AB' is to GH' Hence **the areas of similar polygons are to each other as the squares** of their homologous sides. Cor. If three similar rectilineal figures are constructed on the three sides... | |
| Charles Davies - Geometry - 1850 - 236 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 - 336 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... | |
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