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" SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. "
The school edition. Euclid's Elements of geometry, the first six books, by R ... - Pagina 271
door Euclides - 1864
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

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....
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

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...
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Calendar of Dalhousie College and University

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...
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Some Propositions in Geometry: In Five Parts

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....
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Senate Documents, Otherwise Publ. as Public Documents and ..., Volume 3

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....
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Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term ...

Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term,1885.Volume XIV - 1885
...straight lines. Prove that the sum of the given lines is greater than twice their mean proportional. 9. Similar triangles are to one another in the duplicate ratio of their homologons sides. H в THURSDAY, December 11, 1884. Щ—3. For candidates ander the new regulations....
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Nature, Volume 34

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...
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Calendar of Dalhousie College and University

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...
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Annual Report

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...
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The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II ...

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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