 | 1835 - 684 sider
...D !•:, and of В С to EF, is the duplicate of the ratio of В С to EF (37. Cor. 1.). Therefore the triangle ABC has to the triangle DEF the duplicate ratio of that which В С has to E F. в а Otherwise : Take В G a third proportional to В С and EF, and join A G. Then... | |
 | John Playfair - 1836 - 148 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. Therefore, similar triangles, &c. QED COR. From this it is manifest, that if three straight lines be... | |
 | Andrew Bell - 1837 - 290 sider
...ratio of that which BG 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. Con. — From this it is manifest, that if three straight lines be proportionals, as the first is to... | |
 | Euclid, James Thomson - 1837 - 410 sider
...angles B and E equal, and AB : BC : : DE : EF, so that (V. def. 13.) the side BC is homologous to EF. The triangle ABC has to the triangle DEF, the duplicate ratio of that which BC has to EF. Take (VI. 11.) BG a third proportional to BC, EF, so that BC : EF : : EF : BG, and join GA.f Then,... | |
 | Robert Simson - 1838 - 434 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. Therefore, similar triangles, &c. QED COR. From this it is manifest, that if three straight lines be... | |
 | Euclides - 1841 - 378 sider
...duplicate ratio of that which BC has to EF: but the triangle ABG is equal to the triangle DEF; therefore 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... | |
 | John Playfair - 1842 - 332 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.... | |
 | Euclides - 1842 - 316 sider
...XIX. THEOR. SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. ABC has to the triangle DEF the duplicate ratio of that which вc has to EF. Take BG a third proportional to BC, EF (11. 6.): so that BC is to EF, as EF to BG, and... | |
 | Euclides, James Thomson - 1845 - 382 sider
...angles B and E equal, and AB : BC : : DE : EF, so that (V. def. 13) the side BC is homologous to EF. The triangle ABC has to the triangle DEF, the duplicate ratio of that which BC has to EF. Take (VI. 11) BG a third proportional to BC, EF, so that BC : EF : : EF : BG, and join GA .» Then,... | |
 | Euclid - 1845 - 218 sider
...angle E, and let AB be to BC, as DE to EF, • 12 Def. :.. so that the side BC is homologous to EF*: the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has to EF. t 11. 6. Take BG a third proportional to BC, EFf, so that BC is to EF, as EF to BG, and join GA : i... | |
| |
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... 
