...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...

...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,...

...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....

...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...

...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...

...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^...

...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,...

...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...

...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...

...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,...