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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... "
The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... - Side 45
av Euclid, James Williamson - 1781 - 309 sider
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1762 - 466 sider
...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...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - 1775 - 520 sider
...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...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 520 sider
...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,...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

Euclid, John Playfair - 1795 - 400 sider
...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...
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - 1799 - 351 sider
...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,...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - 1804
...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...
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Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1804 - 440 sider
...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;...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 sider
...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....
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 518 sider
...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,...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...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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