 | 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 of a right-angled triangle,... | |
 | 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... | |
 | 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. Hence, to find the area of... | |
 | 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. Hence, to find the area... | |
 | Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...which are equal each to each, anil the sides about these angles ' taken in the same order. Proportional similar polygons are to each other as the squares of their homologous sides ; or, as the squares of any of their homologous lines. All mutually equiangular triangles are similar.... | |
 | 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... | |
| |
Now, since the areas of similar polygons are to each other as the squares of their homologous sides... 
