 | Alexander Ingram - Trigonometry - 1799 - 374 pages
...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 - Circle-squaring - 1804 - 468 pages
...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 - Trigonometry - 1804 - 530 pages
...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 - Mathematics - 1806 - 320 pages
...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 - 714 pages
...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 - 760 pages
...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 pages
...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 pages
...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 pages
...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 - Surveying - 1824 - 476 pages
...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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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
