| Euclid, Isaac Todhunter - 1883 - 400 pagina’s
...; and it has already been shewn for triangles ; therefore universally, similar rectilineal figures **are to one another in the duplicate ratio of their homologous sides.** COROLLARY 2. If to AB and FG, two of the homologous sides, a third proportional M be taken, [VI. 11.... | |
| Euclides - 1884
...could a 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
...= 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... | |
| John Harris - 1884 - 144 pagina’s
...to (the 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 - 1880
...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 - 1886
...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
...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... | |
| Canada. Department of the Interior - 1888
...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... | |
| Association for the Improvement of Geometrical Teaching - 1888
...F. Compare the areas of the triangles AGB, FGE. THKOR. 12. The areas of similar rectilineal figures **are to one another in the duplicate ratio of their homologous sides. Let** ABCD, HKLM be two similar figures, having the sides AB, HK homologous : then shall the figure ABCD... | |
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