 | Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...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 - 234 pages
...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 pages
...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 - 276 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... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...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 - Geometry - 1829 - 210 pages
...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 - Geometry - 1830 - 584 pages
...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 pages
...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 - Mathematics - 1830 - 630 pages
...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... | |
 | Mathematics - 1835 - 684 pages
...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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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
