| Joseph Denison - 1846 - 106 pages
...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 - 292 pages
...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... | |
| 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... | |
| Euclides - 1846 - 272 pages
...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... | |
| Dennis M'Curdy - Geometry - 1846 - 168 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.... | |
| Thomas Gaskin - Geometry, Analytic - 1847 - 301 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... | |
| 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... | |
| Samuel Hunter Christie - 1847 - 172 pages
...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 - 396 pages
...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 - 388 pages
...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... | |
| |