| John Playfair - 1829 - 186 páginas
...CoB. 1. In like manner it may be proved that similar figures of four sides, or of any number of sides, **are to one another in the duplicate ratio of their homologous sides;** and it has been proved in triangles. Therefore, universally, similar rectilineal figures are to one... | |
| University of Cambridge - 1830 - 552 páginas
...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 - 1830 - 584 páginas
...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 - 1832 - 333 páginas
...to another in the duplicate ratio of their homologous sides; and the same has already been proved of **triangles: therefore, universally similar rectilineal...in the duplicate ratio of their homologous sides.** COH. 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB has (def.... | |
| 1835
...similar triangles are to one another as the squares of their homologous sides. PROP. 43. (Eue. vi. 20.) **Similar rectilineal figures are to one another in the duplicate ratio of their homologous sides** ; and their perimeters are as those sides. For it has been seen (32. Cor. 2.) that any two similar... | |
| Euclid - 1835 - 540 páginas
...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... | |
| 1836 - 472 páginas
...another, in the duplicate ratio of their homologous sides ; and the same has already been proved of **triangles : therefore, universally similar rectilineal...in the duplicate ratio of their homologous sides.** 2. And universally, it is manifest, that if three straight lines be proportionals, as the first is... | |
| John Playfair - 1836 - 114 páginas
...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... | |
| Euclid - 1837 - 410 páginas
...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... | |
| Andrew Bell - 1837 - 240 páginas
...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... | |
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