 | Euclides - 1816 - 588 sider
...ratio of that which BC has to EF : But the triangle ABG is equal to the triangle DKF: 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... | |
 | John Playfair - 1819 - 350 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. triangles ABG, DEF, which are about the equal angles, are reciprocally proportional : but triangles,... | |
 | Peter Nicholson - 1825 - 1046 sider
...ratio of that which BC hat 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 bas to EF. Therefore similar triangles, &c. QED Con. From this it is manifest, that if three straight... | |
 | Robert Simson - 1827 - 546 sider
...be to BC, as DE to EF, so that the side BC may be * homologous to EF : the triangle ABC shall have to the triangle DEF the duplicate ratio of that which BC has to EF. Take * BG a third proportional to BC, EF, so that BC may be to EF, as EF to BG, and join GA : then,... | |
 | Euclid, Robert Simson - 1829 - 548 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 hastoEF. Therefore, similar triangles, &c. QED COR. From this it is manifest, that if three straight... | |
 | Pierce Morton - 1830 - 584 sider
...AB to DE, 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 toEF. GEOMETRY. fi? Otherwise : Take Boa third proportional to В С and EF, and join A G.... | |
 | John Playfair - 1832 - 358 sider
...the 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 toEF. Take BG a third proportional to BC and EF ( 1 1 . BC : EF : : EF : BG, and join GA. AB AB BC... | |
 | Euclides - 1834 - 518 sider
...as DE to EF, so •iZDef. 5. that the side BC may be* homologous toEF: the triangle ABC shall have to the triangle DEF the duplicate ratio of that which BC has to EF. • 11. 6. Take * BG a third proportional to BC, EF, so that BC may be to EF, as EF to BG, and join... | |
 | Euclid - 1835 - 540 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 Con. From this it is manifest, that if three straight lines... | |
 | John Playfair - 1835 - 336 sider
...of that which BC has to EF : and the tnangle ABG is equal to the triangle DEF ; wherefore also *?, triangle ABC has to the triangle DEF the duplicate ratio of that which BC has to EF. COR From this, it is manifest, that if three straight lines be proportionals, as the first is to the... | |
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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... 
