| 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... | |
| Euclides - 1845
...has already been proved in triangles: (vi. 19.) therefore, universally, similar rectilineal figures **are to one another in the duplicate ratio of their homologous sides.** COH. 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, (vi. 11.) AB... | |
| Euclid, James Thomson - 1845 - 352 sider
...already been proved (VI. 19) in respect to triangles. Therefore, universally, similar rectilineal figures **are to one another in the duplicate ratio of their homologous sides.** Cor. 2. If to AB, FG, two of the homologous sides a third proportional M be taken, AB has (V. def.... | |
| Dennis M'Curdy - 1846 - 138 sider
...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... | |
| 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... | |
| Euclides - 1846
...And, in like manner, it may be proved, that similar figures of any number of sides more than three **are to one another in the duplicate ratio of their homologous sides** ; and it has already been proved (9. 19) in the case of triangles. Wherefore, universally, Similar... | |
| THOMAS GASKIN, M.A., - 1847
...angle $ = 45. See fig. 121 . 19= See Appendix, Art. 31. ST JOHN'S COLLEGE. DEC. 1843. (No. XIV.) 1. **SIMILAR triangles are to one another in the duplicate ratio of their homologous sides,** 2. Draw a straight line perpendicular to a plane from a given point without it. 3. Shew that the equation... | |
| Anthony Nesbit - 1847 - 426 sider
...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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