| Dennis M'Curdy - Geometry - 1846 - 138 pages
...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... | |
| Dennis M'Curdy - Geometry - 1846 - 138 pages
...to a similar triangle upon the second. The same is true of similar parallelograms, p. 41, 1. 20 Th. **Similar polygons may be divided into the same number of similar triangles, having** to each other the ratio of the polygons; which is the duplicate ratio of their homologous sides. Let... | |
| 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 - Plane trigonometry - 1847 - 426 pages
...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... | |
| Thomas Gaskin - Geometry, Analytic - 1847 - 263 pages
...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... | |
| Samuel Hunter Christie - 1847
...of the ratios of their bases and altitudes : the bases being similar rectilineal figures (Def. 13) **are to one another in the duplicate ratio of their homologous sides** (VI. 20); and the solids being similar, their altitudes are in the simple ratio of the homologous sides:... | |
| Bengal council of educ - 1848
...Morning Paper. 1. Find a mean proportional between two given straight lines. In this case shew how **similar triangles are to one another in the duplicate ratio of their homologous sides.** 2. The parallelograms about the diameter of any parallelogram are similar to the whole and to one another.... | |
| J. Goodall, W. Hammond - 1848
...from the opposite angle. (The first case only of this proposition need be demonstrated.) Section 2. 1. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 2. If one angle of a triangle be equal to the sum of the other two, the greatest side is double of... | |
| Euclides - 1848
...rectilineal figure similar, and similarly situated, to a given rectilineal figure. PROP. XIX. THEOREM. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** COR. From this it is manifest, that if three straight lines be proportionals, as the first is to the... | |
| Great Britain. Committee on Education - 1848
...from the opposite angle. (The first case only of this proposition need be demonstrated.) Section 2. 1. **Similar triangles are to one another in the duplicate ratio of their** homologuous sides. 2. If one angle of a triangle be equal to the sum of the other two, the gteatest... | |
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