| 1844
...and u the distance of A" from K. FRIDAY, Jan. 5. 9. ..ll£ SENIOR MODERATOR AND JUNIOR EXAMINER. 1. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 2. Every solid angle is contained by plane angles which are together less than four right angles. 3.... | |
| 1844
...that their common chord will be bisected at right angles by a straight line joining their centres. 4. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 5. About the centre of a given circle describe another circle, equal in area to half the former. TRIGONOMETRY... | |
| James Thomson - 1845 - Liczba stron: 358
...easiest methods, however, of performing this and many other problems, the student PROP. XIX. THEOR. — **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Let ABC, DEF be similar triangles, having the angles B and E equal, and AB : BC : : DE : EF, so that... | |
| Euclid - 1845 - Liczba stron: 199
...given straight line similar to one given, and so on. Which was to be done. PROPOSITION XIX. THEOR. — **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC, as... | |
| Robert Potts - 1845
...described upon a given straight line similar to one given, and so on. QEF PROPOSITION XIX. THEOREM. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC, as... | |
| Dennis M'Curdy - 1846 - Liczba stron: 138
...Recite (a) p. 23, 1 ; (b) p. 32, 1 ; (c) p. 4, 6 ; ( d) p. 22, 5 ; (c) def. 1, 6 and def. 35, 1. 19 Th. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Given the similar triangles ABC, DEF; having the angles at B, E, equal, and AB to BC as DE to EF: then... | |
| Euclides - 1846
...similar, and similarly situated, to a given rectilineal figure of six sides ; &c. QEF PROP. XIX. THEOB. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Let ABC, DEF be similar triangles, having the angle at B equal to the angle at E, and let AB be to... | |
| Joseph Denison - 1846
...ultimately become similar, and consequently the approximating sides homologous, and (6 Euclid 19) because **similar triangles are to one another in the duplicate ratio of their homologous sides;** the evanescent triangles are in the duplicate ratio of the homologous sides; and this seems the proper... | |
| Euclides - 1846
...AEDCB) may be divided into similar triangles, equal in number, and homologous to all. And the polygons **are to one another in the duplicate ratio of their homologous sides.** PART 1. — Because in the triangles FGI and AED, the angles G and E are G ( equal, and the sides about... | |
| Anthony Nesbit - 1847 - Liczba stron: 426
...both ; then the triangle ABC is to the triangle ADE, as the square of BC to the square of D E. That is **similar triangles are to one another in the duplicate ratio of their homologous sides.** (Euc. VI. 19. Simp. IV. 24. Em. II. 18.) THEOREM XIV. In any triangle ABC, double the square of a line... | |
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