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" SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Strona 159
autor: Euclides - 1814
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Sandhurst Mathematical Papers for Admission Into the Royal Military College ...

Royal Military College, Sandhurst - 1890 - Liczba stron: 144
...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 - Liczba stron: 538
...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 - Liczba stron: 262
...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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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - 1892 - Liczba stron: 508
...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 - Liczba stron: 788
...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 - Liczba stron: 168
...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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Proceedings of the Edinburgh Mathematical Society

Edinburgh Mathematical Society - 1899 - Liczba stron: 340
...extremes be equal to 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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Special Reports on Educational Subjects, Tomy 6-7

Great Britain. Board of Education - 1900 - Liczba stron: 906
...point on a circle described with 0 as centre and OM as radius, then AM will bisect the angle PAQ. 9. Similar triangles are to one another in the duplicate ratio of their homologous sides. SCHOOL SCHOLAESHIP EXAMINATION. — June, 1899. i ALGEBRA. 1. Find the square root of the expression...
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Sessional Papers, Tom 22,Część 2

Great Britain. Parliament. House of Commons - 1900 - Liczba stron: 686
...point on a circle described with 0 as centre and OM as radius, then AM will bisect the angle PAQ. 9. Similar triangles are to one another in the duplicate ratio of their homologous sides. RUGBY SCHOOL SCHOLARSHIP EXAMINATION. — June, 1899. ALGEBRA. 1. Find the square root of the expression...
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Examination Papers

University of Toronto - 1900 - Liczba stron: 1164
...in D and find a 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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