| Alexander Ingram - 1799 - 374 Seiten
...fides ; and it has already been proved in triangles. Therefore, univerfally fimilar rectilineal figures **are to one another in the duplicate ratio of their homologous fides.** CoR 2. And if to AB, FG, two of the homologous fides, hio-Def.5. a third proportional M be taken, AB... | |
| John Playfair, Euclid - 1804 - 468 Seiten
...given flraight line fimilar to one given, »nd fo on. Which was to be done. PROP. XIX. THE OR. S IMILAR **triangles are to one another in the duplicate ratio of their homologous fides.** D 13. def-5. Let ABC, DEF be fimilar triangles, havfng the angle B equal to the angle E, and let AB... | |
| Robert Simson - 1804 - 530 Seiten
...fides, and it has already been proved in triangles. Therefore univerfally, fimilar rectilineal figures **are to one another in the duplicate ratio of their homologous fides.** CoR. 2. And if to AB, FG two of the homologous fides a h.io.Def.5. third proportional M be taken, AH... | |
| John Playfair - 1806 - 320 Seiten
...described upon a given straight line similar to one given. 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 two similar triangles, having the angle B equal to the angle E ; and let AB... | |
| John Mason Good - 1813 - 722 Seiten
...rectilineal figure similar, and similarly situated to a given rectilineal figure. Prop. XIX. Tbeor. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. Prop. XX. Theor. Similar polygons may be divided into the same number of similar triangles,... | |
| 1814 - 756 Seiten
...he should have met it before. The demonstration of the 19tb Prop, of Euclid's 6th book, ie " Similar **triangles are to one another in the duplicate ratio of their homologous** sides," requires the previous or the syn hro nous establishment of Props, vi. 11, v. 16, v. 11, vi.... | |
| Euclides - 1816 - 588 Seiten
...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... | |
| John Playfair - 1819 - 354 Seiten
...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... | |
| Euclides - 1821 - 294 Seiten
...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 - 476 Seiten
...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... | |
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