 | Anthony Nesbit - 1824 - 476 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 - 1046 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 homo¡ogout sides. Let ABC, DEF be similar triangles, having the angle В equal to the angle E, and... | |
 | George Lees - 1826 - 276 pagina’s
...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 - 326 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 - 234 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 - 226 pagina’s
...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 - 546 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 - 542 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 - 210 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 - 584 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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SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. 
