| Euclid - 1835 - 540 Seiten
...given straight line similar to one given, and so on. 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 similar triangles, having the angle B equal to the angle E, and let AB be to... | |
| John Playfair - 1836 - 488 Seiten
...triangles are to one another in the duplicate ratio of their homologous sides. . Let ABC, DEF -be similar **triangles, having the angle B equal to the angle E, and let AB be to BC, as** A DEtoEF,sothat the side BC is homologous to E Fa ; the triangle ABC has to the triangle DEF, the duplicate... | |
| John Playfair - 1836 - 148 Seiten
...given straight line similar to one given, and so on. 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 similar triangles having the angle B equal to the angle E, and let AB be to... | |
| 1836 - 488 Seiten
...extremes be equal to the square of the mean, the three straight lines are proportionals. XIX. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. Сок. From this it is manifest, that if three straight lines be proportionals, as the first... | |
| Andrew Bell - 1837 - 290 Seiten
...described upon a given straight line similar to one given ; and so on. PROPOSITION XIX. THEOREM. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. Let ABC, DEF, he similar triangles, having the angle B equal to the angle E, and let AB be to... | |
| Euclid, James Thomson - 1837 - 410 Seiten
...on a given straight line, similar to one given : 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 similar triangles, having the angles B and E equal, and AB : BC : : DE : EF,... | |
| Robert Simson - 1838 - 434 Seiten
...triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar **triangles, having the angle B equal to the angle E, and let AB be to** BD, as DE to EF, so that the side BC is homologous to EF (12. def. 5.) ; the triangle ABC has to the... | |
| Euclides - 1840 - 82 Seiten
...rectilineal figure similar to a given rectilineal figure, and similarly situated. PROP. XIX. THEOR. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. PROP. XX. THEOR. Similar polygons may be divided into the same number of similar triangles,... | |
| Euclides - 1840 - 194 Seiten
...but ABC : CAG : : AB : AG (vi. Prop. i) ; and therefore ABC : DEF : : AB : AG, that is to say, the **triangles are to one another in the duplicate ratio of their homologous** sides AB, DE (v. Def. ii). COR. — Hence it is manifest that if three straight lines be proportional,... | |
| Joseph Denison - 1840 - 96 Seiten
...is to the homologous side de ; or as the square of ac is to the homologous side ae. Because similar **triangles are to one another in the duplicate ratio of their homologous** sides (6 Euclid, 19), the triangle ate is to the triangle abe in the duplicate ratio of the side ab... | |
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