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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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Proceedings of the Edinburgh Mathematical Society, Volumes 17-18

Edinburgh Mathematical Society - Electronic journals - 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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Annual Report of the Commissioners ..., Volume 65

1899
...will be accepted. Dr. MORAN, Head Insi>ector. Mr. PEDLOW, District Inspector. SECTION A. 1. Prove that similar polygons may be divided into the same number of similar triangles, and that these triangles have the same ratio to one another that the polygons have. 2. Describe a rectilineal...
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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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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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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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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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Calendar

University of Sydney - 1901
...forty seconds to one minute. 7. Triangles of the same altitude are to one another as their bases. 8. Similar triangles are to one another in the duplicate ratio of their homologous sides. 0. Find the diameter of a cylindrical pipe, two feet long, containing a volume of 000 cubic inches....
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Plane Geometry

Arthur Schultze - 1901
...and the lines joining their homologous vertices meet in a point. PROPOSITION XXVI. THEOREM 303. Two similar polygons may be divided into the same number of similar triangles similar each to each and similarly placed. A" —— / A —"""——. E Hyp. Polygon ABCDE ~ polygon...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 370 pages
...and the lines joining their homologous vertices meet in a point. x PROPOSITION XXVI. THEOREM 303. Two similar polygons may be divided into the same number of similar triangles similar each to each and similarly placed. Hyp. Polygon ABODE ~ polygon A'B'OD'E'. To prove A ABC ~...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 370 pages
...and the lines joining their homologous vertices meet in a point. PROPOSITION XXVI. THEOREM 303. Two similar polygons may be divided into the same number of similar triangles similar each to each and similarly placed. A* E' Hyp. Polygon ABCDE ~ polygon A'B'OD'E'. To prove A...
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