| John Playfair - Euclid's Elements - 1806 - 311 pages
...Which was to be done. PROP. XIX. THEOR. SIMILAR triangles are to one another in the duplicate ratio of **their homologous sides. Let ABC, DEF be two similar triangles, having the angle** B equal to the angle E ; and let AB be to BC, as DE to EF, so that the side BC is homologous to EFa;... | |
| Adrien Marie Legendre - Geometry - 1822 - 367 pages
...corresponding terms of those proportions, omit C/ng the common term ABE ; we have ABC : ADE : : AB.AC : AD.AE. **Cor. Hence the two triangles would be equivalent,...similar triangles are to each other as the squares** of their homologous sides. Let the angle A be equal to D, and the A. angle B=E. Then, first, by reason... | |
| Adrien Marie Legendre - Geometry - 1828 - 316 pages
...terms of those proper tions, omitting the common term ABE ; we have ABC : ADE : : AB.AC : AD.AE. 217. **Cor. Hence the two triangles would be equivalent,...AC ; which would happen if DC were parallel to BE.** 12 THEOREM. 218. Two similar triangles are to each other as the squares of their homologous sides.... | |
| John Playfair - Geometry - 1829 - 186 pages
...angles. .• PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of **their homologous sides. Let ABC, DEF be two similar triangles, having the** angles at A and D equal; and let AC : AB : : DF : DE so that the side AB be homologous to DE (Proper.... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...DE.DF : : AC2 : DF. Consequently, " ABC : DEF : : AC2 : DF2. Therefore, two similar triangles ABC, DEF, **are to each other as the squares described on their homologous sides** AC, DF, or as die squares of any other two homologous sides. PROPOSITION XXVI. THEOREM. Two similar... | |
| Adrien Marie Legendre - Geometry - 1837 - 359 pages
...corresponding terms of these proportion*, omitting the common term ABE ; we have ABC : ADE : AB .AC : AD.AE. **Cor. Hence the two triangles would be equivalent,...having the angle A equal to D, and the angle B=E.** Then, first, by reason of the equal an- Q gles A and D, according to the last proposition, we shall... | |
| Adrien Marie Legendre - Geometry - 1839 - 372 pages
...corresponding terms of these proportions, omitting the common term ABE ; we have ABC : ADE : ABAC : AD.AE. **Cor. Hence the two triangles would be equivalent,...if .the rectangle AB.AC were equal to the rectangle** AD. AE, or if we had AB : AD : : AE : AC ; which would happen if DC were parallel to BE. PROPOSITION... | |
| Charles Davies - Geometrical drawing - 1840 - 252 pages
...lie opposite equal angles 1 Are thew sides proportional 1 Properties of Polygons. 13. The areas of **similar triangles are to each other as the squares described on their homologous sides.** The similar triangles ABC, and DEF, are to each other, as the squares G and H, described on the homologous... | |
| Nathan Scholfield - 1845 - 894 pages
...satisfactory manner possible, to show in tiie corollaries, that the areas of all similar rectilinear figures **are to each other as the squares described on their homologous sides.** These, in Euclid, Lcijendre, and other authors, are made the subjects of several propositions, but... | |
| Charles Davies - Geometrical drawing - 1846 - 254 pages
...sum of the three to 120° x 3 = 360°. 47. How are similar polygons to each other? Similar polygons **are to each other as the squares described on their homologous sides.** Thus, the two similar polygons ABCDE, FGHIK, are to each other as the squares described on the homologous... | |
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