| 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... | |
| 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... | |
| Horatio Nelson Robinson - Geometry - 1860 - 470 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 - 532 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 - 410 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 - 518 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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