| George Lees - 1826 - 266 pages
...triangles, &c. QED Cor. The same may be demonstrated of parallelograms. PROP. XI. THEOREM. Simi'ar **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 : BC : : DE... | |
| Robert Simson - Trigonometry - 1827 - 513 pages
...similar to one given, and so on. Which was to be done. • 12 Def. •11.6. * 16. 5. t Co1utr. • 11. 5. **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... | |
| Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 544 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 - 186 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 :... | |
| University of Cambridge - 1830 - 552 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,... | |
| Pierce Morton - Geometry - 1830 - 584 pages
...with the homologous sides of the figures, are to one another, each to eich, in the same ratio. But **similar triangles are to one another in the duplicate ratio of their homologous sides.** Therefore the triangles into which the figure А В С DEF is divided, are to the similar triangles... | |
| John Playfair - Euclid's Elements - 1832 - 333 pages
...may be described upon a given straight line similar to one given, and so an. Which was to be dona. **PROP. XIX. THEOR, Similar triangles are to one another in the duplicate ratio of** the homologous sides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and... | |
| Euclides - 1834 - 518 pages
...described upon a given straight line similar to one given, and so on. Which was to be done. PROPOSITION **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... | |
| Euclid - 1835 - 540 pages
...may be described 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
...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... | |
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