 | John Playfair - Geometry - 1829 - 210 pages
...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 - 554 pages
...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
...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 - 358 pages
...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.... | |
 | Mathematics - 1835 - 684 pages
...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 pages
...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 - 488 pages
...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 - Geometry - 1836 - 148 pages
...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, James Thomson - Geometry - 1837 - 410 pages
...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 - Euclid's Elements - 1837 - 290 pages
...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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... rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
