 | Braithwaite Arnett - 1874
...shall be parallel to the remaining side of the triangle. 10. Define duplicate ratio. Similar triangles are to one another in the duplicate ratio of their homologous sides. 11. Define a plane. State when a straight line is perpendicular to a plane, and when two planes are... | |
 | Euclides - 1874
...homologous sides. Cor. 2. — In like manner it may be proved that any similar figures of four sides are to one another in the duplicate ratio of their homologous sides, and the same has been proved of triangles (VI. 14); therefore, universally, similar rectilineal figures... | |
 | Robert Potts - 1876 - 403 sider
...duplicate ratio of their homologous sides : and it has already been proved in triangles: (vi. 19.) therefore, universally, similar rectilineal figures...in the duplicate ratio of their homologous sides. COB. 2. And if to AB, FG, two of the homologous sides, a third proportional M\K taken, (vi. 11.) AB... | |
 | Euclides - 1876
...homologous sides, as has already been proved in the case of triangles. Therefore, universally, sjmilar rectilineal figures are to one another in the duplicate ratio of their homologous sides. COROLLARY 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB has... | |
 | Richard Wormell - 1876
...circles, or their proportionals the radii of the inscribed circles. THEOREM LXXXV. (¿.) Similar triangles are to one another in the duplicate ratio of their homologous sides. Let А В С, DEF be similar triangles having Z. B = ¿EandAB:DE = BC:EFso that В С and E^F are homologous... | |
 | 1876
...ratio compounded of the ratios of their bases and of their altitudes. THEOR. 15. Similar triangles are to one another in the duplicate ratio of their homologous sides. THEOR. 16. The areas of similar rectilineal figures are to one another in the duplicate ratio of their... | |
 | D. Tierney - 1877
...the triangle required, for it is isosceles and equal to EFG, that is, to ABC. 10. Similar triangles are to one another in the duplicate ratio of their homologous sides. 11. Given a point O in the line AB, find two other points 0, J?, such that a line OP given in direction... | |
 | Samuel H.. Winter - 1877
...are to one another as their altitudes. 7. Define duplicate ratio, and prove that similar triangles are to one another in the duplicate ratio of their homologous sides. On the side AB of a triangle ABC, AD is taken equal to one third of AB ; and on AC, AE is taken equal... | |
 | James Maurice Wilson - 1878
...the triangle ABC is to the triangle DEF in the duplicate ratio of BC to EF. THEOREM 16. The areas of similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. Let ABCDE, PQ_RST\3z similar polygons. JD S Divide each of them into the same number of similar triangles... | |
 | Āryabhaṭa - 1878
...them (As. I). Wherefore if two triangles &c. QED PEOP. xxxrv. THEOREM. (E. 6. 1.9). Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC and DEF be similar triangles, and let the angle ABC be equal to the i^ngle DEF, and let AB... | |
| |
Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
