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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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Annual Report of the Schools of New Brunswick

New Brunswick. Board of Education - 1889
...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
...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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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 sider
...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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Sandhurst Mathematical Papers for Admission Into the Royal Military College ...

Royal Military College, Sandhurst - 1890 - 132 sider
...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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A Rudimentary Treatise on Land and Engineering Surveying: For Students and ...

Thomas Baker - 1891 - 231 sider
...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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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - 1892
...drawn through O parallel to BC, CA, and AB, show that HK BC LM CA ' AB PQ _ = 2. 7. Similar triangles are to one another in the duplicate ratio of their homologous sides. 8. Given the base of a triangle, the perpendicular, and the sum of the sides, construct it. !). If...
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Examinations Papers

1893
...vertex, and show how to divide the circumference of a circle into fifteen equal parts. 0. The areas of similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. Hence show that any rectilineal figure described on the hypothenuse of a right-angled triangle is equal...
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The Manitoba School Question

Frederick Coate Wade - 1895 - 122 sider
...cut them proportionally ; and conversely. Is this converse universally true ? 10. Similar triangles are to one another in the duplicate ratio of their homologous sides. Bisect a triangle by a line drawn parallel to one of its sides. ALGEBRA. 1. Investigate a rule for...
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Proceedings of the Edinburgh Mathematical Society, Volumer 17-18

Edinburgh Mathematical Society - 1899
...the square on the mean, the three straight lines are proportional. EUCLID VI. 19. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DBF be two similar triangles, having the angles at B, C equal to the angles at E, F respectively...
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Examination Papers

University of Toronto - 1900
...mean proportional AE between AD and AB ; draw EF \\ BC ; EF is the required line. 4. Similar triangles are to one another in the duplicate ratio of their homologous sides. 5. If three straight lines be proportionals, the ratio of the first to the third is equal to the ratio...
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