 | John Playfair - 1806 - 320 pagina’s
...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 be to BC,... | |
 | Robert Simson - 1806 - 546 pagina’s
...sides, and it has already been proved in triangles. 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 h 10. iU t'. third proportional M be taken,... | |
 | John Mason Good - 1813 - 714 pagina’s
...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, having... | |
 | 1814 - 760 pagina’s
...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. 15., and... | |
 | Euclides - 1816 - 588 pagina’s
...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 - 354 pagina’s
...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,... | |
 | Euclides - 1821 - 294 pagina’s
...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... | |
 | Euclid - 1822 - 222 pagina’s
...: and the polygons are to each other in the duplicate ratio of their homologous sides. Part 1. For the angles G and E are equal, and the sides about them proportional (1), therefore the tri- ^ Hypoih. angles FGI and AED are similar (2); since the angles %Dcf. i, GIF... | |
 | Anthony Nesbit - 1824 - 476 pagina’s
...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
...sides, and it has already been proved in triangles 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 proportional M be taken, AB has ( 10.... | |
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... are to one another in the duplicate ratio of their homologous sides. 
