| 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... | |
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