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Llibres Llibres 91 - 100 de 176 sobre 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 homologous sides. "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - PÓgina 167
per Robert Simson - 1762 - 466 pÓgines
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THE EDINBURGH UNIVERSITY CALENDAR 1871-72

EDWARD RAVENSCROFT - 1871
...of it without the circle, is equal to the square of the line which touches it. 6. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. Given (b) the base of a triangle, find an expression for the base of a similar triangle whose...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - 349 pÓgines
...sides may be described, on a given line, similar to a given fig. QEF PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar AS, having L s at A, B, C= s.sa.tD,E,F respectively, so that BC and...
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The elements of geometry, in eight books; or, First step in applied logic

L J V. Gerard - 1874
...have an equal angle formed by proportional sides, are similar to each other. Let ABC and DEF be two triangles having the angle B equal to the angle E, and let AB be to DE as BC is to E F. If AB be equal to DE, the side BC is equal to EF [Gen. Def. 28] : therefore the...
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Euclidian Geometry

Francis Cuthbertson - 1874 - 349 pÓgines
...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...
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Recent military, naval, and civil service examination papers in mathematics ...

Braithwaite Arnett - 1874
...base shall have the same ratio which the other sides of the triangle have to one another. 7. Similar triangles are to one another in the duplicate ratio of their homologous sides. 8. A and B are fixed points, and P is a moveable point such that PA always bears a fixed ratio...
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Annual Report of the Commissioners ..., Volum 40

1874
...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...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...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...
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Rudimentary treatise on mensuration and measuring

Thomas Baker (C.E.) - 1874
...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...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...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...
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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...
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