 | 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 - 290 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 - 1860 - 390 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... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 472 pages
...similar, (Dcf. 16, B. II). Hence the theorem; a plane passed through a pyramid, etc. Cor, 1. Since the areas of similar polygons are to each other as the squares of their homologous sides, (TU. 22, B. H), we have area abode : area ABCDE : ab 2 : AB3. But, ab :... | |
 | Benjamin Greenleaf - Geometry - 1862 - 514 pages
...one antecedent А В С is to its consequent FGH (Prop. XI. Bk. П.), or as A B2 is to F Ga ; hence the areas of similar polygons are to each other as the squares described on their homologous sides. 278. Cor. 1. The perimeters of similar polygons are also to each... | |
 | Henry Barnard - Military education - 1862 - 399 pages
...triangle and on the hypothenuse are to each other as the adjacent segments and entire hypothenuse. The areas of similar polygons are to each other as the squares of the homologous sides of the polygons. Notions on surveying for content (arpentage}.—Method of... | |
 | Benjamin Greenleaf - Geometry - 1862 - 520 pages
...any one antecedent ABC is to its consequent FGH (Prop. XI. Bk. II.), or as A Ba is to F Ga ; hence the areas of similar polygons are to each other as the squares described on their homologous sides. 278. Cor. 1. The perimeters of similar polygons are also to each... | |
 | Education - 1862 - 752 pages
...triangle and on the hypothenuse are to each other as the adjacent segments and entire hypothenuse. "The areas of similar polygons are to each other as the squares of the homologous sides of the polygons. Notions on surveying for content (arpentnye). — Method of... | |
 | Henry Barnard - Military education - 1862 - 412 pages
...triangle and on the hynothenuHe are to each other as the adjacent segments ana entire hypothenuse. The areas of similar polygons are to each other as the squares of the homologous sides of the polygons. Notions on surveying for content (arpeniage).—Method of... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...perimeters of similar polygons are also to each other as their corresponding diagonals. 279. Cor. 2. The areas of similar polygons are to each other as the squares described on their corresponding diagonals. PROPOSITION XXXII. — THEOREM . 280. A chord in a circle... | |
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Now, since the areas of similar polygons are to each other as the squares of their homologous sides... 
