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" ... polygons are to each other in the duplicate ratio of their homologous sides. "
The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ... - Page 32
by Euclides - 1833
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Annual Report

Canada. Topographical and Air Survey Bureau - 1908 - 758 pages
...Prove geometrically that in any triangle a" = b- + c2 - 2bc Cos A. 14 11. Show that similar figures are to each other in the duplicate ratio of their homologous sides. 14 12. Find the locus of the apex of the triangles having a common base and whose sides about the apex...
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The Lady's and Gentleman's Diary

Almanacs, English - 1852 - 492 pages
...to 40,0., and }O,O3 ; and since the triangles C,CaC3 and O,02O3 are similar, and similar triangles are to each other in the duplicate ratio of their homologous sides, therefore " if three right lines," &c. LEICESTER COTTAGE, NEAR PORTSEA, May, 1856. ( To be continued....
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Parliamentary Papers, Volume 24

Great Britain. Parliament. House of Commons - Great Britain - 1876 - 570 pages
...— -.a + b + e. x + ax - a x + bx - b Ix-a 3. Define duplicate ratio. Prove that similar triangles are to each other in the duplicate ratio of their homologous sides. 4. In a given triangle draw a straight line parallel to one of the sides, so that it may be a mean...
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Knowledge: An Illustrated Magazine of Science, Volume 2

Science - 1882 - 546 pages
...he cannot gain credit and prizes without being able to write Latin verses or to show that triangles are to each other in the duplicate ratio of their homologous sides, he will give all his studying time to these things, just as he would give it to the study of chess...
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