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" SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. "
The school edition. Euclid's Elements of geometry, the first six books, by R ... - Pagina 271
door Euclides - 1864
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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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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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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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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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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...homologous sides. Cor. 2. — In like manner it may be proved that any similar figures of four sides are to one another in the duplicate ratio of their homologous sides, and the same has been proved of triangles (VI. 14); therefore, universally, similar rectilineal figures...
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Euclidian Geometry

Francis Cuthbertson - 1874 - 349 pagina’s
...ratio of AB to AH. Hence, proceeding as in Proposition VIII., it may be proved that Similar polygons are to one another in the duplicate ratio of their homologous sides. PROPOSITION (r). If four straight lines are proportional, the duplicate ratio of the first two is the...
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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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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...has already been proved in triangles (VI. 19) ; therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. COT. 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken (VI. 11), 1....
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1876 - 349 pagina’s
...same way a fig. of six or more sides may be described, on a given line, similar to a given fig. QEF PROPOSITION XIX. THEOREM. Similar triangles are to...the duplicate ratio of their homologous sides. Let ABC,DEF be similar AS, having / s at A, B, C= L s at D, E, F respectively, so that BC and EF are 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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