| Euclides, David Gregory - Mathematics, Greek - 1765 - 464 pages
...homologous fides. This has been a4fe proved of triangles, therefore univerfally fimilar right lined **figures are to one another in the duplicate ratio of their homologous** fides. Euclid's Elements. Book Vf. Corollary. 2. And if a third proportional x be found to AB, FG :... | |
| Joseph Fenn - Mathematics - 1769
...the Jame truth bas already been proved in triangles (P 19), it is tvident universally, that fimüar **rectilineal figures are to one another in the duplicate ratio of their homologous** fides. Wherefore, if te AB, FG two of I be homologous fides a third proportional X be taken ; becaufe... | |
| Robert Simson, Euclid - Trigonometry - 1775 - 520 pages
...their homologous fides, and it has already been proved in triangles. Therefore, univerfally, fimilar **rectilineal figures are to one another in the duplicate ratio of their homologous** fides. CoR. 2. And if to AB, FG, two of the homologous fides, hio.dcf.i. a third proportional M be... | |
| Euclid - 1781 - 520 pages
...their homologous fides, and it has atready been proved in triangles. Therefore, univerfally fimilar **rectilineal figures are to one another in the duplicate ratio of their homologous** fides CoR. 2. And if to AB, FG, two of the homologous fides, hio. def.5. a third proportional M betaken,... | |
| John Playfair - Euclid's Elements - 1795 - 400 pages
...homologous fides, and it has already been proved in triangles. Therefore, univerfaUy fimilar reftilineal **figures are to one another in the duplicate ratio of their homologous** fides. CoR. 2. And if to AB, FG, two of the homologous fides, h 1 1. def. 5. a third proportional M... | |
| Alexander Ingram, Robert Simson - Trigonometry - 1799 - 351 pages
...their homologous fides ; and it has already been proved in triangles. Therefore, univerfally fimilar **rectilineal figures are to one another in the duplicate ratio of their homologous** fides. CoR 2. And if to AB, FG, two of the homologous fides, hio-Def.5. a third proportional M be taken,... | |
| Robert Simson - Trigonometry - 1804
...their homologous- fides, and it has already been proved in triangles. Therefore univerfally, fimilar **rectilineal figures are to one another in the duplicate ratio of their homologous** fides. CoR. 2. And if to AB, FG two of the homologous fides a h.io.Def.5. third proportional M be taken,... | |
| John Playfair - Trigonometry - 1806 - 311 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 two similar triangles, having the angle B equal to the angle E ; and let AB be to BC,... | |
| John Mason Good, Olinthus Gilbert Gregory - 1813
...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
...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... | |
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