| Adrien Marie Legendre - Geometry - 1819 - 574 pages
...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... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...one antecedent ABC is to its consequent FGH, or as AB is to — 2 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... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...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... | |
| Etienne Bézout - Calculus - 1836 - 216 pages
...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 squares of their radii.... | |
| Adrien Marie Legendre - Geometry - 1838 - 382 pages
...... 7.6942088 Undecagon ... 11 ... 9.3656399 Dodecagon ... 12 .... 11.1961524 Now. since the areas of similar polygons are to each other as the squares of their homologous sides (Book IV. Prop. XXVII.), we shall have I- : tabular area : : any side squared : area. Or, to find the... | |
| Adrien Marie Legendre - Geometry - 1841 - 288 pages
...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 three... | |
| J. M. Scribner - Measurement - 1844 - 130 pages
...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 of their homologous sides, if the square of the side of a polygon be multiplied by the multiplier of the like figure, the product... | |
| Benjamin Peirce - Geometry - 1847 - 204 pages
...ratio HP : PI, : FG. Ratio of Similar and Regular Polygons. 266. Theorem. Similar triangles are to each other as the squares of their homologous sides. Proof. In the similar triangles ABC, A'B'C' (fig. 109), we have, by § 199, CE: CE' = AB: AB', which, multiplied by the proportion... | |
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