 | Euclides - 1816 - Liczba stron: 588
...may be described upon a given straight line similar to one given, and so on. Which was to be done. PROP. XIX. THEOR. SIMILAR triangles are to one another...in the duplicate ratio of their homologous sides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC, as... | |
 | John Playfair - 1819 - Liczba stron: 354
...may be described upon a given straight line similar Co one given, and so on. Which was to be done. ^ PROP. XIX. THEOR. Similar triangles are to one another...in the duplicate ratio of their homologous sides. D Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC,... | |
 | John Playfair - 1819 - Liczba stron: 350
...may he described upon a given straight line similar to one given, and so^ou. Which was to be done. PROP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homOlogousjides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let... | |
 | Euclides - 1821 - Liczba stron: 294
...*£-•& follows ex aquo, from the proportionality of the sides about 'the «£^.s composing them. 52 PROP. XIX. THEOR. Similar triangles are to one another...in the duplicate ratio of their homologous sides. Assume on the greater base from either extremity a third proportional to that base and the homologous... | |
 | Anthony Nesbit - 1824 - Liczba stron: 476
...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 - Liczba stron: 1046
...be described 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... | |
 | Euclid - 1826 - Liczba stron: 234
...described similar and similarly situated to the given rectilineal figure CE. QEF PROPOSITION XIX. THEOREM. Similar triangles are to one another 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 - Liczba stron: 226
...the angle ABG equal to that at CDF; hence the remaining angle. AG в is QEF PROPOSITION XIX. THEOREM. Similar triangles are to one another 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... | |
 | George Lees - 1826 - Liczba stron: 276
...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 • of their homologous sides. Let ABC, DEF, be similar triangles, having the angle B equal to the angle E, and let AB : BC : : DE... | |
 | Robert Simson - 1827 - Liczba stron: 546
...similar to one given, and so on. Which was to be done. • 12 Def. •11.6. * 16. 5. t Co1utr. • 11. 5. PROP. XIX. THEOR. Similar triangles are to one another...in the duplicate ratio of their homologous sides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC, as... | |
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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
