 | John Playfair - 1806 - 320 σελίδες
...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 - 1822 - 394 σελίδες
...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 - 1828 - 346 σελίδες
...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 - 1829 - 210 σελίδες
...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 - 1836 - 394 σελίδες
...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 - 1837 - 376 σελίδες
...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 - 1839 - 372 σελίδες
...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 - 1840 - 262 σελίδες
...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 σελίδες
...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 - 1846 - 254 σελίδες
...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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Two similar triangles are to each other as the squares described on their homologous sides. Let ABC, DEF, be two similar triangles, having the angle A equal to D, and The angle B=E. 
