| Robert Potts - Geometry, Plane - 1876 - 403 pages
...equal to one angle of the other, have their sides about the equal angles reciprocally proportional. 4. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 5. In any right angled triangle, any rectilineal figure described on the side subtending the right... | |
| William Guy Peck - Conic sections - 1876 - 366 pages
...second couplets of (1) and (2) are equal ; hence, ACD : AFD :: AFD : EFD, PROPOSITION XII. THEOREM. Two **similar polygons may be divided into the same number of similar triangles,** similarly placed. Let ACDEF and PQRST be similar polygons, the equal angles in both being taken in... | |
| Dublin city, univ - 1876
...the other segment. If the whole line be 10 feet long, find the lengths of the segments. 2. Prove that **similar triangles are to one another in the duplicate ratio of their** sides. Divide a triangle into three equal parts by right lines drawn parallel to its base. 3. Divide... | |
| Samuel H. Winter - 1877 - 413 pages
...have the same base, 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... | |
| D. Tierney - 1877
...HE, HF. Then EHF is 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... | |
| Āryabhaṭa - 1878
...ACB are equal to 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... | |
| James Maurice Wilson - 1878
...one another in the ratio compounded of the ratios of their bases and of their altitudes. THEOREM 15. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Let ABC, DEF be similar triangles having the angles at A, B, C respectively equal to the angles at... | |
| J. G - 1878 - 372 pages
...TRIGONOMETRY, CONICS. Afternoon Paper. 1. Similar polygons may be divided into the same number of siml **triangles, having the same ratio to one another that the polygons have.** 2. From a fixed point a series of straight lines are drawn to cut two para straight lines. Prove that... | |
| Robert Potts - Algebra - 1879
...triplícala ratios in Geometry correspond to the ratios of the squares and cubes in Algebra : — 1. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** (Eue. VI. 19.) Let а, Ь, с ; a', I', c' represent the sides of two similar triangles ; Then, because... | |
| Robert Potts - 1879
...triplicate ratios in Geometry correspond to the ratios of the squares and cubes in Algebra : — 1. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** (Eue. VI. 19.) Let а, Ь, с ; a', V, ¿ represent the sides of two similar triangles ; Then, because... | |
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