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" Similar triangles are to one another in the duplicate ratio of their homologous sides. "
Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory, and N ... - Page 95
by John Mason Good - 1813
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...deducing the truth of I. 37, since VI. 6 does not depend on I. 37. PKOP. XIII.— THEOREM. (Euc. VI. 19.) Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC and OPQ be similar triangles, having the angle B equal to the angle P, and AB to BC as OP to...
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Recent military, naval, and civil service examination papers in mathematics ...

Braithwaite Arnett - 1874
...proportionally, this line shall be parallel to the remaining side of the triangle. 10. Define duplicate ratio. Similar triangles are to one another in the duplicate ratio of their homologous sides. 11. Define a plane. State when a straight line is perpendicular to a plane, and when two planes are...
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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 349 pages
...proportionals are said to be homologous to one another; so also are the consequents. PROPOSITION (q). Similar triangles are to one another in the duplicate ratio of their homologous sides. Let the similar triangles ABC, AHK be placed so as to have the sides AB, AC along the homologous sides...
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Annual Report of the Commissioners ..., Volume 40

1874
...Explain the term duplicate ratio, and illustrate its meaning as you would to a class. (b.) Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 2. Describe a circle which will pass through a given point, and touch a given circle in a given point....
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...described upon a given straight line similar to one given, and so on. QEF PROPOSITION 19.— Theorem. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF lie similar triangles, having the angle B equal to the angle E, and let AB be to BC, as...
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Rudimentary treatise on mensuration and measuring

Thomas Baker (C.E.) - 1874
...then, the triangle ABC is to the triangle AED as the square of A. B is to the 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 their homologous,...
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Plane and solid geometry, by G.E. Webster and A. Gardiner

George E. Webster - 1874
...area is possessed by the figure which has the largest number of sides. (7) Similar rectilineal figures are to one another in the duplicate* ratio of their homologous^ sides. (8) If three straight lines oe proportionals, as the first quantity is to the third quantity, so is...
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Elements of Geometry Containing Books I. to VI. and Portions of Books XI ...

James Hamblin Smith - Geometry - 1876
...the figure A is similar to the figure B. VI. Def. 1. y. ED PROPOSITION XXI. THEOREM. (Eucl. vi. 20.) Similar polygons may be divided into the same number...similar triangles, having the same ratio to one another, which the polygons have ; and the polygons are to one another in the duplicate ratio of their homologous...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876
...circumscribed circles, or their proportionals the radii of the inscribed circles. THEOREM LXXXV. (¿.) Similar triangles are to one another in the duplicate ratio of their homologous sides. Let А В С, DEF be similar triangles having Z. B = ¿EandAB:DE = BC:EFso that В С and E^F are homologous...
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SYLLABUS OF PLANE GEOMETRY

1876
...to one another the ratio compounded of the ratios of their bases and of their altitudes. THEOR. 15. Similar triangles are to one another in the duplicate ratio of their homologous sides. THEOR. 16. The areas of similar rectilineal figures are to one another in the duplicate ratio of their...
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