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" Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Side 180
av Robert Simson - 1806 - 518 sider
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 400 sider
...to one another in the duplicate ratio of their homologous sides ; and it has already been shewn for triangles ; therefore universally, similar rectilineal...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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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883
...ratio compounded of the ratios of their bases and of their altitudes. THEOR. 15. Similar triangles are to one another in the duplicate ratio of their homologous sides. THEOR. 16. The areas of similar rectilineal figures are to one another in the duplicate ratio of their...
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Some Propositions in Geometry: In Five Parts

John Harris - 1884 - 144 sider
...the square on A c, including the diagonal A e of the square on A b. Then because similar trianglcs are to one another in the duplicate ratio of their homologous sides (Euclid VI. 19) and the triangles A eb and Afc are similar, the " '' triangle A eb has the ratio to...
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Calendar of Dalhousie College and University

Dalhousie University - 1884
...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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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884
...that these triangles have each to each the same ratio which the polygons have ; and that the polygons are to one another in the duplicate ratio of their homologous sides. Join BE, EC, GL, LH. Because the polygon ABCDE is similar to the polygon FGHKL, .-. LA = LF, and BA...
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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
...first given line and the third proportional is greater than the second given line. 9. Similar triangles are to one another in the duplicate ratio of their homologous sides. THURSDAY, December 11, 1884. 12^—3. For candidates under the old regulations. EUCLID. (B) 1. How...
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Nature, Volum 34

Sir Norman Lockyer - 1886
...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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The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II ...

Association for the Improvement of Geometrical Teaching - 1888
...bisect the sides BC, AC in E and 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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Annual Report

Canada. Department of the Interior - 1888
...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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Treatise on Trigonometry ...

William Ernest Johnson - 1889 - 504 sider
...have been proportional to the product of two lengths. This is equivalent to Euclid's statement that " Similar rectilineal figures are to one another in the duplicate ratio of their homologous sides." 24. The area of any rectilineal figure may be found by dividing it into triangles : and applying the...
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