| University of Cambridge - 1830
...in origin and intensity. SATURDAY MORNING .... 9 to 11. First, Second, Third and Fourth Classes. 1. **SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.** 2. If two straight lines meeting one another, be parallel to two straight lines which meet one another,... | |
| 1835
...reciprocally proportional; ЗУ. being citc'd instead of 35. Therefore, &c. • PROP. 42. (Eue. vi. 10.) **Similar triangles are to one another in the duplicate ratio of their homologous sides.** LetABC.DEF be similar triangles, and let the sides В С, EF be homologous ; the triangle ABC shall... | |
| Euclid - 1835 - 513 pagina’s
...the same has already been proved of triangles. Therefore, universally, «'milar 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, h lO.def. 5. a third proportional M be taken,... | |
| John Playfair - 1836 - 471 pagina’s
...upon a 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...angle B equal to the angle E, and let AB be to BC, as** A DEtoEF,sothat the side BC is homologous to E Fa ; the triangle ABC has to the triangle DEF, the duplicate... | |
| 1836 - 472 pagina’s
...by the extremes be equal to the square of the mean, the three straight lines are proportionals. XIX. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Сок. From this it is manifest, that if three straight lines be proportionals, as the first is to... | |
| John Playfair - 1836 - 114 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 (15. Def.... | |
| Andrew Bell - 1837 - 240 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. — If to AB, FG, two of the homologous sides, a third proportional M be taken, AB has (V.... | |
| Euclid, James Thomson - 1837 - 390 pagina’s
...already been proved (VI. 19.) in respect to triangles. Therefore, universally, similar rectilineal 6gures **are to one another in the duplicate ratio of their homologous sides.** Cor. 2. If to AB, FG, two of the homologous sides, a third proportional M be taken, AB has (V. def.... | |
| Euclid, Robert Simson - 1838 - 416 pagina’s
...upon a 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...the angle B equal to the angle E, and let AB be to** BD, as DE to EF, so that the side BC is homologous to EF (12. def. 5.) ; the triangle ABC has to the... | |
| Euclid - 1838 - 416 pagina’s
...upon a 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...the angle B equal to the angle E, and let AB be to** BD, as DE to EF, so that the side BC is homologous to EF (12. def. 5.) ; the triangle ABC has to the... | |
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