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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 ... - Page 167
by Euclides - 1814
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 pages
...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 - 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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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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Proceedings of the Edinburgh Mathematical Society, Volumes 17-18

Edinburgh Mathematical Society - Mathematics - 1899
...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, Volumes 6-7

Great Britain. Board of Education - Education - 1900
...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, Volume 22, Part 2

Great Britain. Parliament. House of Commons - Great Britain - 1900
...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
...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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Report of the Committee of Council on Education in Scotland...[without Appendix]

Education - 1900
...side of я triangle, it will cut the other sides (or the other sides produced) proportionately. 7. Similar triangles are to one another in the duplicate ratio of their homologous sides. ABC is a triangle right angled at A, D is the midpoint of EG, and AE. EF are drawn perpendicular to...
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