 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...as one antecedent ABC is to its consequent FGH, or as . .'// is to FG (219). Therefore the surfaces of similar polygons are to each other, as the squares of their homologous sides. 222. Corollary. If three similar figures be constructed whose homologous sides are equal to the three... | |
 | James Mitchell - Mathematics - 1823 - 666 pages
...similar triangles, have their homologous sides proportional. AH similar triangles, rectangles, and polygons, are to each other as the squares of their homologous sides. HORARY Circles, hour lines or circles, marking the hours on globes, dials, &c. HORARY Motion, the motion... | |
 | Etienne Bézout - Calculus - 1824 - 222 pages
...kind of demonstration was called reductio ad absurdum. By this means, having first ascertained that the areas of similar polygons are to each other as the squares of their homologous lines, they inferred that circles of different radii are to each other as the square of their radii.... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 pages
...3 'as one antecedent ABC is to its consequent FGH, or as AB is to FG (219). Therefore the surfaces of similar polygons are to each other, as the squares of their homologous sides. --,'• 222. Corollary. If three si'.nilar figures be constructed whose homologous sides are equal... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...- 2 as one antecedent ABC is to its consequent FGH, or as AB is to FG (219). Therefore the surfaces of similar polygons are to each other, as the squares of their homologous sides. • 222. Corollary. If three similar figures be constructed whose homologous sides are equal to the... | |
 | Timothy Walker - Geometry - 1829 - 156 pages
...SOLIDS. 192. In articles 116, 117, 164, 167, 168, the following propositions were demonstrated. 1. Two similar polygons are to each other as the squares of their homologous sides. 2. Two circles are to each other as the squares of their radii or diameters. 3. The surfaces of two... | |
 | Francis Joseph Grund - Geometry, Plane - 1830 - 274 pages
...sides opposite to the equal angles, and also as the squares upon the heights of the triangles. 21. The areas of similar polygons are to each other, as the squares constructed upon the corresponding sides. SECTION IV. OF THE PROPERTIES OF THE CIRCLE.* QUERY I. hi... | |
 | Francis Joseph Grund - Geometry, Plane - 1834 - 202 pages
...similar triangles are to each other, as the areas of the squares upon the corresponding sides. 23. The areas of similar polygons are to each other, as the squares constructed upon the corresponding sides. »••„ SECTION IV. OF THE PROPERTIES OF THE CIRCLE .*... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...polygon FGHIK, as one antecedent ABC, is to its consequent FGH, or as ABS is to FG2 (Prop. XXV.)j hence the areas of similar polygons are to each other as the squares described on the homologous sides. Cor. If three similar figures were constructed, on the three sides... | |
 | Benjamin Peirce - Geometry - 1837 - 216 pages
...Polygons. homologous altitudes, and, by art. 200, as the squares of their perimeters. 268. Theorem. Similar polygons are to each other as the squares of their homologous sides. Demonstration. In the similar polygons ABCD, &c., A'BCD, &,c. (fig. 108), ,the triangles ABC, AB'C,... | |
| |
Now, since the areas of similar polygons are to each other as the squares of their homologous sides... 
