| John Playfair - 1826 - 326 Seiten
...triangles are to one another in the duplieate 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,** ag DE to EF, so that the side BC is homologous to EF (def. 13. 5.): the triangle ABC hag to the triangle... | |
| Euclid - 1826 - 236 Seiten
...similar and similarly situated to the given rectilineal figure CE. QEF PROPOSITION XIX. THEOREM. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. EF, and let BC be the side homologous to EF ; then the triangle ABC has a duplicate ratio to... | |
| Euclides - 1826 - 226 Seiten
...ABG equal to that at CDF; hence the remaining angle. AG в is QEF PROPOSITION XIX. THEOREM. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. EF, and let вс be the side homologous to EF ; then the triangle ABC has a duplicate ratio... | |
| George Lees - 1826 - 266 Seiten
...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... | |
| Robert Simson - 1827 - 546 Seiten
...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... | |
| John Playfair - 1829 - 210 Seiten
...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 :... | |
| Pierce Morton - 1830 - 584 Seiten
...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... | |
| University of Cambridge - 1830 - 554 Seiten
...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... | |
| Thomas Leybourn - 1830 - 630 Seiten
...distance. SATURDAY MORNING, 9 o'clock to 1 1 . First, Second, Third, and Fourth Classes. 1. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. 2. If a straight line be at right angles to a plane, every plane passing through that straight... | |
| 1835 - 684 Seiten
...the homologous sides of the figures, are to one another, each to each, 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 DKF is divided, are to the similar triangles... | |
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