 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...homologous sides : 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 - 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.... | |
 | John Playfair - Euclid's Elements - 1833 - 346 pages
...same has already been proved of triangles : therefore, universally similar rectilineal figures are,to one another in the duplicate ratio of their homologous...2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB has (def. 11. 5.) to 1VI the duplicate ratio of that which AB has... | |
 | 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... | |
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Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
