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... rectilineal figures are to one another in the duplicate ratio of their homologous sides.
The Elements of Euclid - Página 131
por Euclid - 1838 - 416 páginas
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## Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term ...

...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, Volumen34

Sir Norman Lockyer - 1886 - 684 páginas
...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 - 208 páginas
...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 - 756 páginas
...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 - 574 páginas
...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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## Annual Report of the Schools of New Brunswick ... by the Chief ...

New Brunswick. Board of Education - 1889 - 1006 páginas
...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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## Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - 1889 - 354 páginas
...AC the two sides including the right angle : prove that _JL= l 4.JL AD* AB* AC*n. Similar triangles are to one another in the duplicate ratio of their homologous sides. II. ARITHMETIC. (Including the use of Common Logarithms.) [NB — Great importance will be attached...
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## Sandhurst Mathematical Papers for Admission Into the Royal Military College ...

Royal Military College, Sandhurst - 1890 - 144 páginas
...parts, having first proved the proposition in Euclid on which your method depends. 6. Similar triangles are to one another in the duplicate ratio of their homologous sides. Explain the following terms : homologous sides, ex asquali, alternando, duplicate ratio. 7. Two equal...
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## The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 páginas
...da ::CD : DA'./ [VI. 4Again v LS bac, cad= L s BAC, CAD; PROPOSITION 19. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let As ABC, DEF have LS A, B, C equal to LS D, E, F respectively, so that BC is homologous to EF; then...
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## A Rudimentary Treatise on Land and Engineering Surveying: For Students and ...

Thomas Baker - 1891 - 264 páginas
...ABC is to the triangle AED a* the square of AB is to tlte square of AE : that is, similar triangles are to one another in the duplicate ratio of their homologous sides. (Euc. VI. 19.) THEOREM VIII. All similar figures are to one another as the squares of then homologous,...
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