| John Keill - Logarithms - 1723 - 444 pages
...tie duplicate Proportion of their homologous Sides. 1" ET ABC, DEF, be fimilar Triangles, having -LJ **the Angle B equal to the Angle E ; and let AB be to BC as DE** is to EF, fo- that BC be the Side homologous to EF. I fay, the Triangle ABC, to the Triangle DEF, has... | |
| Euclid, John Keill - Geometry - 1733 - 444 pages
...PROPOSITION XIX. THEOREM. Similar "Triangles are in the duplicate Ft ofortion of their homologous Sides. **LET ABC, DEF, be fimilar Triangles, having the Angle...B equal to the Angle E ; and let AB be to BC as DE** is to EF, fo that BC be the Side homologous to £ F. I fay, the Triangle ABC, to the Triangle DEF,... | |
| Euclid - Geometry - 1765 - 492 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 : [by i0.... | |
| Joseph Fenn - Mathematics - 1769 - 536 pages
...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 А В... | |
| Robert Simson - Trigonometry - 1775 - 534 pages
...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 - Geometry - 1776 - 318 pages
...Wherefore, &c? PROP. XIX. THEO R. O 1 MILAR triangles are to one another in the duplicate ratiQ. ^ **of their homologous fides. Let ABC, DEF, be fimilar triangles having the** angles at B and E equal ; and AB, to BC, as DE to EF, and BC the fide homologous to EF ; then the triangle^... | |
| Euclid - 1781 - 552 pages
...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 Keill - Geometry - 1782 - 476 pages
...PROPOSITION XIX. THEOREM. Similar Triangles are in the duplicate Proportion of their homologous Sides. **LET ABC, DEF, be fimilar Triangles" having the Angle...equal to the Angle E ; and let AB be to BC, as DE** is to EF, fo that BC he the Side homologous to E F. I fay, the Triangle ABC, to the Triangle DEF, has... | |
| John McGregor (teacher of mathematics.) - Mathematics - 1792 - 532 pages
...fide of each being rt Regular polygons of the like number of fides are fimilar, rind fimilar furfaces **are to one another in the duplicate ratio of their homologous fides** ; but the fides of the polygons in the foregoing table are each of them i ; therefore, as the fquare... | |
| Euclid, John Playfair - Euclid's Elements - 1795 - 462 pages
...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 be taken,... | |
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