| 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
...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
...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,... | |
| 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... | |
| John Playfair - Euclid's Elements - 1832 - 333 pages
...proportionals, they are similar to one another: and in the same manner a rectilineal figure of six, or more, **sides may be described upon a given straight line similar to one given, and so** an. Which was to be dona. PROP. XIX. THEOR, Similar triangles are to one another in the duplicate ratio... | |
| John Playfair - Euclid's Elements - 1833 - 333 pages
...proportionals, they are similar to one another ; and in the same manner a rectilineal figure of six, or more, **sides may be described upon a given straight line...triangles are to one another in the duplicate ratio of** the homologous sides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and... | |
| John Playfair - Euclid's Elements - 1835 - 316 pages
...proportionals, they are similar to one another ; and in the same manner a recD tilineal figure of six, or more, **sides may be described upon a given straight line similar to one given, and so on.** PROP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of the homologous sides.... | |
| 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... | |
| Euclid - 1835 - 513 pages
...the same has already been proved of triangles. Therefore, universally, «'milar rectilineal figures **are to one another in the duplicate ratio of their homologous sides.** COR. 2. And if to AB, FG, two of the homologous sides, h lO.def. 5. a third proportional M be taken,... | |
| John Playfair - Euclid's Elements - 1836 - 471 pages
...proportionals, they are similar to one another ~. and in the same manner a rectilineal figure of six, or more, **sides may be described upon a given straight line...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 A DEtoEF,sothat... | |
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