 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...: and it has already been proved in triangles : therefore, universally, similar rectilinear figures are to one another in the duplicate ratio of their homologous sides. (629) COR. 2. — And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB... | |
 | John Playfair - Geometry - 1829 - 210 pages
...other as the rectangles contained by the sides about the equal angles. .• PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be two similar triangles, having the angles at A and D equal; and let AC : AB : : DF :... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...will be be reciprocally proportional ; 39, being cited instead of 35. Therefore, &c. PROP. 42. (Eue. vi. 19.) Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar triangles, and let the sides В С, EF be homologous ; the triangle ABC shall... | |
 | University of Cambridge - 1830 - 554 pages
...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,... | |
 | Euclid - 1835 - 540 pages
...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 ratio of their homologous sides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC, as... | |
 | Mathematics - 1835 - 684 pages
...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... | |
 | John Playfair - Geometry - 1836 - 148 pages
...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 ratio of their homologous sides. Let ABC, DEF be similar triangles having the angle B equal to the angle E, and let AB be to BC, as... | |
 | Mathematics - 1836 - 488 pages
...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... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...be described upon a given straight line similar to one given ; and so on. PROPOSITION XIX. THEOREM. 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... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...described on a given straight line, similar to one given : 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 similar triangles, having the angles B and E equal, and AB : BC : : DE : EF, so that... | |
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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
