 | Adrien Marie Legendre - Geometry - 1822 - 394 pages
...polygon FGHIK, as one antecedent ABC is to its consequent FGH, or as AB2 is to FG2 ; hence the surfaces of similar polygons are to each other as the squares of the homologous sides. BOOK III. Cor. If three similar figures were constructed, on the three sides of a right-angled tnangle,... | |
 | Adrien Marie Legendre - 1825 - 570 pages
...circumscribed circles, and also as the radii DO, do, of the inscribed circles. The surfaces of these same polygons are to each other as the squares of the homologous sides AB, ab (221); they are therefore also as the squares of the radii of the circumscribed circles A0,... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...circumscribed circles, and also as the radii DO, do, of the inscribed circles. The surfaces of these same polygons are to each other as the squares of the homologous sides AB, ab (221); they are therefore also as the squares of the radii of the circumscribed circles AO,... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...circumscribed circles, and also as the radii DO, do, of the inscribed circles. The surfaces of these same polygons are to each other as the squares of the homologous sides AB, ab (221); they are therefore also as the squares of the radii of the circumscribed circles AO,... | |
 | John Radford Young - Euclid's Elements - 1827 - 246 pages
...are to each other as the radii of the inscribed circles. But (Prop. XXI. B. VI.) the surfaces of the polygons are to each other as the squares of the homologous sides AB, ab ; or BC, be, and these are as the squares of the radii (Prop. IV. Cor. 1. B. VI.), consequently... | |
 | 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... | |
 | Charles Davies - Geometrical drawing - 1840 - 262 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... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...circumscribed circles, and also as the radii DO, do, of the inscribed circles. The surfaces of these same polygons are to each other as the squares of the homologous sides AH, ab (221) ; they are therefore also as the squares of the radii of the circumscribed circles AO,... | |
| |
Now, since the areas of similar polygons are to each other as the squares of their homologous sides... 
