 | Euclides - 1845 - 546 sider
...ratio of that which BC has to EF: but the triangle ABG is equal to the triangle DEF; therefore also the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has to EF. Therefore similar triangles, &c. QED COR. From this it is manifest, that if three straight lines be... | |
 | Euclid, John Playfair - 1846 - 334 sider
...angle E, and let AB be to BC, as DE to EF, so that the side BC is homologous to EF (def. 13. 5.) : the triangle ABC has to the triangle DEF, the duplicate ratio of that which BC has to EF. Take BG a third proportional to BC and EF (11. 6.), or such that BC : EF : : EF : BG, and join GA.... | |
 | Royal Military Academy, Woolwich - 1853 - 400 sider
...the angle E, and let AB be to BC, as DE to EF, so that the side BC is homologous to EF (12 Def. v.) : the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has to EF. Then, because, as AB to EC, so DE to EF ; alternately (16. v.), AB is to DE, as BC to EF : but as BC... | |
 | Euclides - 1853 - 176 sider
...angle e, and let ab he to b c. as de to ef, so that the side bc, is homologous to ef (v. def. 1 2) : the triangle abc has to the triangle def, the duplicate ratio of that which bc has to e f. Take bga third proportional to bc, ef (vi. 11) so that bc is to ef as ef tobg, and join ga: then,... | |
 | Euclides - 1853 - 334 sider
...triangle DEF the duplicate ratio of the ratio which BC has to EF. And in like manner it may be shewn that the triangle ABC has to the triangle DEF the duplicate ratio of the ratio which CA has to FD, or of the ratio which AB has to DE. "Which was to be proved. COB.—... | |
 | Euclides - 1855 - 230 sider
...ratio of that which BC has to EF ; but the triangle ABG is equal to the triangle DEF ; wherefore also the triangle ABC has to the triangle DEF the duplicate ratio of that which. BC has to EF. COROLLARY. From this it is manifest, that if three straight lines be proportionals, as the first is... | |
 | Euclides - 1863 - 122 sider
...the angle DEF, and let AB be to BC as DE to EF, so that the side BC is homologous to EF (V. Def. 12). The triangle ABC has to the triangle DEF the duplicate ratio of that which the side BC has to the side EF. Take BG a third proportional to BC and EF (VI. 11), 60 that BC is to... | |
 | Euclides - 1864 - 448 sider
...ratio of that which BC has to EF: but the triangle ABG is equal to the triangle DEF; therefore also the triangle ABC has to the triangle DEF, the duplicate ratio of that which .BClias to EF. Therefore similar triangles, &c. QE D, COR. From this it is manifest, that if three... | |
 | Robert Potts - 1865 - 528 sider
...ratio of that which BC has to EF: but the triangle ABG is equal to the triangle DEF; therefore also the triangle ABC has to the triangle DEF, the duplicate ratio of that which BC has to EF. Therefore, similar triangles, &c. QED CoR. From this it is manifest, that if three straight lines be... | |
 | Euclides - 1865 - 402 sider
...ratio of that which BC has to EF ; but the triangle ABG is equal to the triangle DEF; therefore also the triangle ABC has to the triangle DEF, the duplicate ratio of that which BC has to EF. Therefore, similar triangles, &c. QED Cor. From this it is manifest, that if three straight lines be... | |
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ABG ; (vi. 1.) therefore the triangle ABC has to the triangle ABG the duplicate ratio of that which BC has to EF: but the triangle ABG is equal to the triangle DEF; therefore also the triangle ABC has to the triangle DEF the duplicate ratio of that which... 
