 | 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 sider
...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 - 311 sider
...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 sider
...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 sider
...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 sider
...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 sider
...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 sider
...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 sider
...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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SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. 
