 | Euclid - 1765 - 492 頁
...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 - 1769 - 536 頁
...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 - 1775 - 534 頁
...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 - 552 頁
...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,... | |
 | Euclid, John Playfair - 1795 - 462 頁
...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 - 1799 - 374 頁
...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 - 1804 - 530 頁
...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 - 1806 - 320 頁
...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 - 1813 - 714 頁
...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 頁
...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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Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
