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" SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Page 167
by Euclides - 1814
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Senate Documents, Otherwise Publ. as Public Documents and ..., Volume 3

United States. Congress. Senate - United States - 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 - Electronic journals - 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 - Euclid's Elements - 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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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - Mathematics - 1889
...will touch the circle circumscribing ABC in the point A. 8. Describe a circle about a given square. 9. Similar triangles are to one another in the duplicate ratio of their homologous sides. 10. In a right-angled triangle if a line be drawn from the right angle perpendicular to the base it...
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Annual Report of the Schools of New Brunswick

New Brunswick. Board of Education - Education - 1889
...another, are proportionals ; and those which are opposite to the equal angles, are homologous sides. fi. Similar triangles are to one another in the duplicate ratio of their homologous sides. T. ALGEBRA. Time, 1 hour SO mitt. Ei-Jiibit the work. 1. Find the value of x in each of the following...
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Treatise on Trigonometry ...

William Ernest Johnson - Plane trigonometry - 1889 - 504 pages
...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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Mathematical Papers for Admission Into the Royal Military College for the ...

Eldred John Brooksmith, Robert Moir Milne - 1890 - 132 pages
...one another, and shall have those angles equal about which the sides are proportionals. 6. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. If ABC be an obtuse-angled triangle, having the obtuse angle BAC; and if AD, AE, be drawn to meet BC...
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