Books Books
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 ... - Page 45
by Euclid, James Williamson - 1781 - 309 pages

## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

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...

## The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

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...

## The First Six Books: Together with the Eleventh and Twelfth

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,...

## Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

Euclid, 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...

## The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

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,...

## The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804 - 530 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...

## Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

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;...

## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 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....