 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...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.... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...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 - Geometry - 1846 - 166 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... | |
 | 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
...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 - 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... | |
 | Anthony Nesbit - Plane trigonometry - 1847 - 492 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 - 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... | |
 | 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:... | |
 | Euclides - 1848 - 52 pages
...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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SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. 
