 | Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...to one another the 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... | |
 | Robert Potts - Geometry - 1876 - 446 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 - 376 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 - 420 pages
...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 - 452 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 - 126 pages
...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 - 100 pages
...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 - 450 pages
...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 - 408 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 - 672 pages
...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... | |
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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
