| Joseph Fenn - 1769 - 536 páginas
...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 páginas
...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 páginas
...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 páginas
...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 páginas
...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 páginas
...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 páginas
...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 páginas
...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 páginas
...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 páginas
...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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