| Anthony Nesbit - 1824 - 434 pagina’s
...both ; then the triangle ABC is to the triangle ADE, as the square of BC to the square of DE. That is, **similar triangles are to one another in the duplicate ratio of their homologous sides.** (Euc. VI. 19. Simp. IV. 24. Em. II. BC THEOREM XIV. In any triangle ABC, double the square of a line... | |
| Peter Nicholson - 1825 - 372 pagina’s
...upon a given straight line similar to one given, and so on. Which was to be done. PHOP. XIX. THEOR. **Similar triangles are to one another in the duplicate ratio of their** homoĦogout sides. Let ABC, DEF be similar triangles, having the angle В equal to the angle E, and... | |
| George Lees - 1826
...triangles, &c. QED Cor. The same may be demonstrated of parallelograms. PROP. XI. THEOREM. Simi'ar **triangles are to one another in the duplicate ratio...having the angle B equal to the angle E, and let AB** : BC : : DE : EF, so that BC is homologous to EF ; then the triangle ABC : triangle DEF : : BC2 : EF2.... | |
| Euclid, John Playfair - 1826 - 320 pagina’s
...so on. Whieh was to be done. PROP. XIX. THEOR. Similar triangles are to one another in the duplieate **ratio of their homologous sides. Let ABC, DEF be similar...angle B equal to the angle E, and let AB be to BC,** ag DE to EF, so that the side BC is homologous to EF (def. 13. 5.): the triangle ABC hag to the triangle... | |
| Euclid - 1826 - 180 pagina’s
...figure AH has been described similar and similarly situated to the given rectilineal figure CE. QEF **PROPOSITION XIX. THEOREM. Similar triangles are to...in the duplicate ratio of their homologous sides.** EF, and let BC be the side homologous to EF ; then the triangle ABC has a duplicate ratio to the triangle... | |
| Euclides - 1826
...figure CE. that at c, also the angle ABG equal to that at CDF; hence the remaining angle. AG в is QEF **PROPOSITION XIX. THEOREM. Similar triangles are to...in the duplicate ratio of their homologous sides.** EF, and let вс be the side homologous to EF ; then the triangle ABC has a duplicate ratio to the... | |
| Robert Simson - 1827 - 513 pagina’s
...already been proved -)- in triangles : t 19. 6. therefore, universally, similar rectilineal figures **are to one another in the duplicate ratio of their homologous sides.** COR. 2. And if to AB, FG, two of the homologous sides, a third f proportional M be taken, AB* has to... | |
| Euclid, Dionysius Lardner - 1828 - 324 pagina’s
...: and it has already been proved in triangles : therefore, universally, similar rectilinear figures **are to one another in the duplicate ratio of their homologous sides.** (629) COR. 2. — And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB... | |
| John Playfair - 1829 - 186 pagina’s
...CoB. 1. In like manner it may be proved that similar figures of four sides, or of any number of sides, **are to one another in the duplicate ratio of their homologous sides;** and it has been proved in triangles. Therefore, universally, similar rectilineal figures are to one... | |
| Pierce Morton - 1830 - 272 pagina’s
...with the homologous sides of the figures, are to one another, each to eich, in the same ratio. But **similar triangles are to one another in the duplicate ratio of their homologous sides.** Therefore the triangles into which the figure А В С DEF is divided, are to the similar triangles... | |
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