 | 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, having... | |
 | Euclides - 1814 - 560 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 he similar triangles, having the angle B equal to the angle E, and let AB be to BC, as DE to EF, so... | |
 | 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. 15., and... | |
 | Euclides - 1816 - 588 pages
...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, k 10 Def. 5. a third proportional M be taken,... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...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 AB be to BC, as DE to EF, so that the side BC is homologous to EF (def. 13. 5.) : the triangle ABC has... | |
 | 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 to BC,... | |
 | Euclid, Robert Simson - Geometry - 1821 - 514 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 similartriangles, having theangle B equal to the angle E, and let AB be to BC, as DE to EF, so that... | |
 | 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 a line... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...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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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
