| 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... | |
| Francis Joseph Grund - Geometry, Plane - 1834 - 190 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...QUERY I. In how many points can a straight line, CD,** meet the circumference of a circle J A. In two points, M, N, only. For, (f For, letting fall, from... | |
| Francis Joseph Grund - Geometry, Plane - 1834 - 206 pages
...of similar polygons are to each other, as the squares constructed upon the corresponding sides. 9* **SECTION IV. OF THE PROPERTIES OF THE CIRCLE." QUERY I. In how many points can a straight line, CD,** meet the circumference of a circle f A. In two points, only. For, C *%^T^ J> M, N, only. For, letting... | |
| Francis Joseph Grund - Geometry, Plane - 1834 - 190 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...squares constructed upon the corresponding sides.** 9* SECTION IV. OF THE PROPERTIES OF THE CIRCLE.* QUERY I. In how many points can a straight line, CD,... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 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... | |
| Charles Davies - Geometrical drawing - 1840 - 252 pages
...Undecagon, 9,3656404 1,2028437 i 12 Dodecagon, 11,1961524 1,8660254 Mensuration of Surfaces. Now, since **the areas of similar polygons are to each other as the squares** described on their homologous side (see Part I. § VII. Art. 3). we have I2 : tabular area : : any... | |
| J. M. Scribner - Measurement - 1844 - 123 pages
...of each is 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... | |
| Charles Davies - Geometrical drawing - 1846 - 254 pages
...radius of the inscribed circle. 50. How do you find the area of any polygon from the above table ? Since **the areas of similar polygons are to each other as the squares** described on their homologous sides, we have 1* : tabular area : : any side squared : area. Hence,... | |
| George Roberts Perkins - Geometry - 1847 - 308 pages
...GHKLM, as any one antecedent ABC, is to its corresponding consequent GHK, or as AB' is to GH'. Hence **the areas of similar polygons are to each other as the squares** of their homologous sides. Cor. If three similar rectilineal. figures are constructed on the three... | |
| Charles Davies - Trigonometry - 1849 - 384 pages
...Decagon .... 10 ... 7.0942088 Dodecagon ... 12 ... 11.1901524 Undecagon ... 11 ... 9.3050399 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 Or, to find the area of any regular... | |
| |