 | 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... | |
 | 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,... | |
 | 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... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...the regular 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
...the regular 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.... | |
 | Charles Davies - Geometry - 1855 - 340 pages
...the 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 - 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... | |
 | 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... | |
 | 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... | |
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Now, since the areas of similar polygons are to each other as the squares of their homologous sides... 
