 | Joseph Fenn - 1769 - 536 σελίδες
...fimilarly fituated. Z>. i. B.6 • • Which was to be done. PR OP OS IT ION XIX. THEOREM XIII. IMILAR triangles (ABC, DEF) are to one another in the duplicate ratio of their homologous fides (CB, FE or AC, DF, &c). Hypothefis. • Thefis. 7be triangles ABC, DEF artßmilar. The Д ABC... | |
 | Robert Simson - 1806 - 546 σελίδες
...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 Playfair - 1806 - 320 σελίδες
...COR. 1. In like manner it may be proved that similar four sided figures, or of any number of sides, are to one another in the duplicate ratio of their homologous sides ; and it has already been proved in triangles. Therefore, universally, similar rectilineal figures... | |
 | John Mason Good - 1813 - 714 σελίδες
...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 σελίδες
...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 σελίδες
...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 - 1819 - 354 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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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... figures are to one another in the duplicate ratio of their homologous sides. 
