 | Robert Simson - Trigonometry - 1762 - 488 pages
...ratio of that which BC has to EF. but the triangle ABG is equal to the irhngle DEF ; wherefore alfq the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has to EF. therefore fimilar triangks, &c. Q^ED COR . From this it is manifeft, that if three ftraight lines be... | |
 | Robert Simson - Trigonometry - 1775 - 534 pages
...ratio of that which BC has to EF: But the triangle ABG is equal to the triangle DEF; wherefore alfo the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has to EF. Therefore umilar triangles, &c. CKE. D. CoR. From this it is manifeft, that if three ftraight lines... | |
 | Euclid - 1781 - 552 pages
...BC, as DE to EF, fo that the fide BC is homologous to EF* : The triangle ABC has to the na. def.5. triangle DEF, the duplicate ratio of that which BC has to EF. Take BG a third proportional to BC, EF", fo that BC is to b n. 6. EFi as EF to BG, and join GA : Then,... | |
 | John Playfair - Euclid's Elements - 1795 - 462 pages
...ratio of that which BC has to EF : but the triangle ABG is equal to the triangle DEF ; wherefore alfo the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has to EF. Therefore fimilar triangles, &.c. Q^ ED CoR. From this it is manifeft, that if three ftraight lines... | |
 | Alexander Ingram - Trigonometry - 1799 - 374 pages
...the angle E, and let AB be to BC, as DE to EF, fo ni.Def.5- that the fide BC is homologous to EF a : The triangle ABC has to the triangle DEF, the duplicate ratio of that which BG h?.s to EF. b n. 6. Take BG a third proportional to BC, EF b, fo that BC is to EF, as EF to BG,... | |
 | Robert Simson - Trigonometry - 1804 - 528 pages
...ratio of that which BC has tP EF. but the triangle ARG is equal to the triangle DEF ; wherefore alfo the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has to EF, therefore fimilar triangles, &c. C^._ ED CoR. From this it is mantfeft, that if three ftraight lines... | |
 | John Playfair, Euclid - Circle-squaring - 1804 - 468 pages
...to EF : and the triangle ABG is equal tc the triangle DEF; wherefore alfo the triangle ABC has t» the triangle DEF the duplicate ratio of that which BC has to EF. Therefore fimilar triangles, &c. CX ED CoR. From this it is manifeil, that if three ilraight line;... | |
 | John Playfair - Mathematics - 1806 - 320 pages
...and let AB be to BC, as DE to EF, so that the side BC is homologous to EFa; the triangle aDef.13.5. ABC has to the triangle DEF the duplicate ratio of that which BC has to EF. Take BG a third proportional to BC, EFb, and join GA. b H- SBecause AB : BC : : DE : EFC, " c 4. 6.... | |
 | Euclid - Geometry - 1810 - 554 pages
...be to BC, as DE to EF, so that the side BC is homologous to EFa; the triangle ABC has to theal2.def5 triangle DEF the duplicate ratio of that which BC has to EF. Take BG a third proportional to BC, EFb, so that BC is tob 11. 6. EF, as EF to BG, and join GA ; then,... | |
 | Euclides - 1814 - 556 pages
...let AB be to BC, as DE to EF, so that the side BC is homologous to EF a : the triangle • 12 Dei 5. ABC has to the triangle DEF, the duplicate ratio of that which BC has to EF. Take BG a third proportional to BC, EF b , so that BC * 1i.6. is to EF, as EF to BG, and join GA: Then,... | |
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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... 
