 | Euclid - 1765 - 492 sider
...all equilateral and equiangular figures are alike deferred upon any right lines. PROP. XIX. THE OR, Similar triangles are to one another in the duplicate ratio of their homologous fides. Let the trianges A B. c, DEF be fimilar, having the angle B equal to the angled ; and let AB... | |
 | Robert Simson - 1775 - 534 sider
...a given ftraight line li« milar to one given, and- fo on. Which was to be done. PROP. XIX. THEO R. SIMILAR triangles are to one another in the duplicate ratio of their homologous ftdes. Let ABC, DEF be fimilar triangles having the angle B equal to the angle E, and let AB be to... | |
 | Euclid - 1781 - 552 sider
...upon a given ftraight line ;.milar to one given, and fo ou. Which was to be doue. PROP. XIX. THEO R. SIMILAR triangles are to one another in the duplicate ratio of their homologous fides. Let ABC, DEF be fimilar triangles, having the angle B equal to the angle E, and let AB he to... | |
 | Euclid, John Playfair - 1795 - 462 sider
...given ftraight line fimilar tct one given, and fo on. Which was to be done. S PROP. XIX. THEO R. IMILAR triangles are to one another in the duplicate ratio of their homologous fides. Let ABC, DEF be fimilar triangles, having the nngle B equal to the angle E, and let AB be to... | |
 | Alexander Ingram - 1799 - 374 sider
...fimilar to CDKFE : and fo on. Which was to be done. PROP. BooK V|. PROP. XIX. THEOR. V>rv-vJ IMILAR triangles are to one another in the duplicate ratio of their homologous fides. Let ABC, DEF be fimilar triangles, having the angle B equal to the angle E, and let AB be to... | |
 | John Playfair - 1806 - 320 sider
...therefore they are similar to each other. In the same manner a rectilineal figure of six, or more, sides may be described upon 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... | |
 | John Mason Good - 1813 - 714 sider
...rectilineal figure similar, and similarly situated to a given rectilineal figure. Prop. XIX. Tbeor. Similar triangles are to one another in the duplicate ratio of their homologous sides. Prop. XX. Theor. Similar polygons may be divided into the same number of similar triangles, having... | |
 | 1814 - 760 sider
...though he should have met it before. The demonstration of the 19tb Prop, of Euclid's 6th book, ie " Similar triangles are to one another in the duplicate ratio of their homologous sides," requires the previous or the syn hro nous establishment of Props, vi. 11, v. 16, v. 11, vi. 15., and... | |
 | Euclides - 1816 - 588 sider
...sides, and it has already been proved in triangles. Therefore, universally, similar 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, k 10 Def. 5. a third proportional M be taken,... | |
 | John Playfair - 1819 - 354 sider
...a rectilineal figure of six, or more, sides may be described upon a given straight line similar Co one given, and so on. Which was to be done. ^ PROP....in the duplicate ratio of their homologous sides. D Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC,... | |
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SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. 
