| Euclides - 1884 - 434 pages
...figure BLMN similar and oppositely situated to the figure BAGH be obtained? PROPOSITION 19. THEOREM. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** G Let ABC and DEF be similar triangles, having L. B = LE, and LC — LF, so that BC and EF are homologous... | |
| Dalhousie University - 1884 - 184 pages
...= 0, between 1 and 2. GEOMETRY AND MENSURATION.— SECOND YEAR. APRIL 15iH.— 10 AM TO 1 p. M. I. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Prove this : and represent the ratio of the two triangles by means of two straight lines whereof one... | |
| 1884 - 610 pages
...magnitude. • 5. Describe a triangle ABC such that each of the angles B and 6' is double of the angle A. 6. **Similar triangles are to one another in the duplicate ratio of their homologous sides.-** Give Euclid's proof of this proposition, and also shew that it may be established without using any... | |
| John Harris - Geometry - 1884 - 188 pages
...area of) the eq. triangle DAB of four to nine. It demonstrates therefore (by inspection) the theorem ; **Similar triangles are to one another in the duplicate ratio of their** respondent sides. (Euclid, IV. 19.) It also demonstrates that if from an eq. triangle a lesser eq.... | |
| United States. Congress. Senate - United States - 1880 - 1304 pages
...point on the curve. I the tangents at A, B in D, E ; prove that AB is a mean proportional betwi 12. **Similar triangles are to one another in the duplicate ratio of their** sides. TRIGONOMETRY. Examiner,— Prof. C. NIVEN. Lieutenants qualifying for gunnery and torpedo officers.... | |
| Sir Norman Lockyer - Electronic journals - 1886 - 684 pages
...book. To mention one only- the proof which he judiciously gives of the fundamental proposition that " **similar triangles are to one another in the duplicate ratio of their homologous sides** " depends directly on the ist Proposition only of the Sixth Book, instead of the chain being carried... | |
| Dalhousie University - 1887 - 206 pages
...YEAR. APRIL 18.— 10 AM TO 1 PM 1. Explain " duplicate ratio " and prove that, " similar tranples **are to one another in the duplicate ratio of their homologous sides." 2.** If four straight lines be proportionals, the similar rectilineal figures descriled on them shall also... | |
| Association for the Improvement of Geometrical Teaching - Euclid's Elements - 1888 - 208 pages
...in D, prove that the rectangle contained by BD and BF is .equal to twice the area of ABC. THEOR. n. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Let ABC, DEF be two similar triangles, having the sides BC, EF homologous^ then shall the triangle... | |
| Canada. Department of the Interior - 1888 - 756 pages
...rectangles under the sides containing the equal angles. 15. From tho last deduce tho proposition " **similar triangles are to one another in the duplicate ratio of their homologous sides.''** No. of Mark-. 13 10 13 13 li 13 13 13 PLANE TRIGONOMETRY. Time, 3 hours. 1. Find the number of degrees... | |
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