 | Euclid - 1835 - 540 pages
...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 - Euclid's Elements - 1836 - 488 pages
...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 - Geometry - 1836 - 148 pages
...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... | |
 | Mathematics - 1836 - 488 pages
...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 - Euclid's Elements - 1837 - 290 pages
...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 - Geometry - 1837 - 410 pages
...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 - Geometry - 1838 - 434 pages
...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 pages
...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 - 192 pages
...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 - Euclid's Elements - 1840 - 96 pages
...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... | |
| |
Similar triangles are to one another in the duplicate ratio of their homologous sides. 
