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" SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. "
The school edition. Euclid's Elements of geometry, the first six books, by R ... - Pagina 271
door Euclides - 1864
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Annual Report of the Schools of New Brunswick

New Brunswick. Board of 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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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - 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 - 1889 - 504 pagina’s
...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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Sandhurst Mathematical Papers for Admission Into the Royal Military College ...

Royal Military College, Sandhurst - 1890 - 132 pagina’s
...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 pagina’s
...OABCD : oabcd :: AOAB : Aoab, ie in dupl. ratio of OA : oa. COR. i. — Similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. COR. ii. — If to the homologous sides BC, EF of two similar rectilineal figures P and Q a third proportional...
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A Rudimentary Treatise on Land and Engineering Surveying: For Students and ...

Thomas Baker - 1891 - 231 pagina’s
...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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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1892 - 518 pagina’s
...Similarly it AB may BH be shewn : CD : DE that Also BA and GH AG HB : DC : FE CF, VI ED; 4. PROPOSITION 19. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. B Let ABC, DEF be similar triangles, having the i.ABC equal to the L. DEF, and let BC and EF be homologous...
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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - 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 - 1895 - 122 pagina’s
...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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