| Richard Wormell - 1876 - 264 páginas
...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... | |
| Samuel H. Winter - 1877 - 448 páginas
...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 - 122 páginas
...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... | |
| James Maurice Wilson - 1878 - 448 páginas
...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 - 96 páginas
...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... | |
| Robert Potts - 1879 - 676 páginas
...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... | |
| Robert Potts - 1879 - 668 páginas
...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... | |
| Isaac Todhunter - 1880 - 400 páginas
...to one another in the duplicate ratio of their homologous sides ; and it has already been shewn for **triangles ; therefore universally, similar rectilineal...in the duplicate ratio of their homologous sides.** COROLLARY 2. If to AB and FG, two of the homologous sides, a third proportional M be taken, [VI. 11.... | |
| Oxford univ, local exams - 1880 - 390 páginas
...middle point of the base to the opposite vertex. z. Euclid VI— XI, and Conic Sections. 10. Similar **figures are to one another in the duplicate ratio of their homologous sides.** Bisect a given triangle by a straight line drawn parallel to the base. 11. The rectangle contained... | |
| Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 páginas
...Prove that АO . OD = BO . 0C (the corners А, C being opposite to one another). 11. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** 1. Prove that am x a" = am + ', m and n being positive integers ; and assuming this formula to hold... | |
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