| Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 324 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 :... | |
| Pierce Morton - Geometry - 1830 - 272 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... | |
| 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,... | |
| John Playfair - Euclid's Elements - 1832 - 333 pages
...to a similar, and similarly described triangle upon the second. PROP. XX. THEOR. Similar poly eons **may be divided into the same number of similar triangles,...having the same ratio to one another that the polygons** nave; and the polygons have to one another the duplicate ratio of that which their homologous sides... | |
| Euclid - 1835 - 513 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
...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 - 114 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 - 472 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... | |
| Euclid, James Thomson - Geometry - 1837 - 390 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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