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" Similar triangles are to one another in the duplicate ratio of their homologous sides. "
Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory, and N ... - Page 95
by John Mason Good - 1813
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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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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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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 pages
...AB : BC 1 and cd : 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 - Railroads - 1891 - 231 pages
...then, the tnanr/ff 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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Plane and Solid Geometry

Seth Thayer Stewart - Geometry - 1891 - 406 pages
...vi., PROP, n.) Conclusion : A and B, being any regular polygons, etc. PROPOSITION XII. 4O3. Theorem : Similar polygons may be divided into the same number of similar triangles similarly placed. Statement : Similar polygons, ABD and GHJ, may be divided into the same number of...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 518 pages
...DEF; Proved. .'. the A ABC : the A DEF in the duplicate ratio of BC : EF. QED PROPOSITION 20. THEOREM. Similar polygons may be divided into the same number of similar triangles, having the same ratio each to each that the polygons have; and the polygons are to one another in the duplicate ratio of...
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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - Education - 1892
...LM, and PQ are 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

1894
...parallel to AD. 4. Similar triangles are to one another in the duplicate ratio of their homologous sides. Similar triangles are to one another in the duplicate ratio of their corresponding altitudes. 6. Shew how to solve two equations which contain two unknown quantities when...
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The Manitoba School Question

Frederick Coate Wade - Church and state - 1895 - 122 pages
...produced, it will 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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