| Euclid, James Thomson - 1845 - 352 páginas
...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.... | |
| John Playfair - 1846 - 317 páginas
...they are similar to one another ; and in the same manner a rec136 tilineal figure of six, or more, **sides may be described upon a given straight line similar to one given, and so on.** PROP. XIX. THEOR. Similar triangles are to one anotlier %n the duplicate ratio of the Iiomologous sides.... | |
| Dennis M'Curdy - 1846 - 138 páginas
...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
...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... | |
| 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 - 426 páginas
...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, 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... | |
| 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:... | |
| 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... | |
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