...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...

...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...

...- 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...

...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...

...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...

...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 .*...

...were known figures, their continual approximation to the curve, so as finally to differ from it bj less than any given quantity, led to the knowledge...circles of different radii are to each other as the squares of their radii. This is the second proposition of the 12th book of Euclid, and the 287th article...

...would have them verified incontestibly ; this they effected by proving that any supposition contrary 10 the existence of these properties led necessarily...circles of different radii are to each other as the squares of their radii. This is the second proposition of the 12th book of Euclid, and the 287th article...

...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...

...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,...