| Nicolas Pike - Algebra - 1808 - 468 pages
...multipliers for all regular figures from the triangle to the dodecagon, will be of use te the learner. **If the square of the side of a polygon be multiplied...multiplier of the like figure^ the product will be** die area of the figure sought. ' To measure a Circle and its Parts. In the annexed circle A BCD, die... | |
| 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 - 280 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 - 158 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... | |
| Nicolas Pike - Arithmetic - 1832 - 544 pages
...multipliers for all regular figures from the triangle to the dodecagon, will be of use to the learner. **If the square of the side of a polygon be multiplied...multiplier of the like figure, the product will be the area** of the figure sought. 3" 4 5 6 7 , equal sides and _ 8 angles is a 9 10 .12. Number of Bides. Number... | |
| 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 .*... | |
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