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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 Durham University Journal, Volume 1

University of Durham - 1879
...eight times either angle at the base. 6. Define similar triangles, duplicate ratio : — Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 8. Define a conic section, the tangent to a conic section : — If S be the focus, P any point on the...
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Proceedings of the Edinburgh Mathematical Society, Volumes 18-20

Edinburgh Mathematical Society - Electronic journals - 1900
...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, DEFbetwu similar triangles, having the angles at В, С equal to the angles at E, F respectively :...
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A Treatise on Practical Mensuration

Anthony Nesbit - Measurement - 1859 - 450 pages
...both ; then the triangle ABC is to the triangle ADE, as the square of BC to the square of DE. That is, similar triangles are to one another in the duplicate ratio of their homologous sides. (Euc. "3 c VI. 19. Simp. IV. 24. Em. II. 18.) THEOREM XTV. In any triangle the double of the square...
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The Calendar of Owens college, Manchester

Manchester univ - 1877
...Explain this. Prove that equal magnitudes have the same ratio to the same magnitude and conversely. 10. Similar triangles are to one another in the duplicate ratio of their homologous sides. Bisect a triangle by a line perpendicular to one of the sides. 11. Enunciate and prove the general...
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Report of Her Majesty's Civil Service Commissioners: Together ..., Volumes 15-16

1870
...Di.i'AUTM i \r. triangles, having ! h.- same ratio to one another that the polygons Jan. 1870. have7. Similar triangles are to one another in the duplicate ratio of their homologous sides. 8. If from any point without a circle lines be drawn touching it, the angle contained by the tangents...
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Parliamentary Papers, Volume 19

Great Britain. Parliament. House of Commons - Bills, Legislative - 1861
...describe a segment of a circle, which Khali contain an angle equal to a given rectilineal angle. 3. Similar triangles are to one another in the duplicate ratio of their homologous sides. 4. Investigate a rule for finding the greatest common measure of two algebraical expressions. 5. Reduce...
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