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If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means; And if the rectangle contained by the extremes be equal to the rectangle contained by the means, the four straight lines...
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Pągina 133
per John Playfair - 1846 - 317 pągines
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THE QUADRATURE OF THE CIRCLE, THE SQUARE ROOT OF TWO, AND THE RIGHT-ANGLED ...

WILLIAM ALEXANDER MYERS - 1874
...6 therefore the rectangle contained by A and G is equal to the rectangle contained by B and D ; but if the rectangle contained by the extremes be equal...means, the four straight lines are proportionals; [FI. 16.] therefore A is to B as D is to (7. But B is equal to D] [Construction.'] Therefore A is to...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 403 pągines
...rectangle contained fy the extremes is equal to the rectangle contained by the means: and conversely, if the rectangle contained by the extremes be equal...proportionals. Let the four straight lines AB, CD, E, /"be proportionals, viz. as AB to CD, so E to F. The rectangle contained by AB, F, shall be equal to...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin SMITH - 1876 - 349 pągines
...in D, and the circle in C, prove that the square on CE is equal to twice the AEBC. And Conversely, If the rectangle contained by the extremes be equal...means, the four straight lines are proportionals. Let rect. AB, GH"=rect. CD, EF. Then must AB be to CD as EF is to GH. For, the same construction being...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876
...rectangle contained by the extremes is equal to the rectangle contained by the means. Сonversely, if the rectangle contained by the extremes be equal...means, the four straight lines are proportionals. Since rectangles are equiangular parallelograms, the proof in this case is identical with that of the...
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SYLLABUS OF PLANE GEOMETRY

1876
...the rectangle contained by the means; and, conversely, if the rectangle contained by the extremes is equal to the rectangle contained by the means the four straight lines are proportional. COR. If three straight lines are proportional the rectangle contained by the extremes...
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Elementary geometry

James Maurice Wilson - 1878
...the rectangle contained by the means; and, conversely, if the rectangle contained by the extremes is equal to the rectangle contained by the means the four straight lines are proportional. BC D I Let A be to B as C to D ; then will the rectangle contained by A and D be equal...
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First Public Examination in Literis Graecis Et Latinis

University of Oxford - 1879
...lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means ; and if the rectangle contained by the...means, the four straight lines are proportionals. II. Elements of Geometry. II. 1. Define secant and tangent of an angle, and prove that (1) sin2 A =...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - 1879 - 266 pągines
...Theorem.—If four straight lines be proportional, the redangle of the extremes is equal to the rectangle of the means ; and if the rectangle contained by the...contained by the means, the four straight lines are proportional. Let A, B, C, D be four straight lines, so that A : B :: C: D; then the rectangle contained...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 400 pągines
...lines be proportionals, the rectangle contained by the extremes is equal to the square on the mean; and if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines are proportionals. Let the three straight lines A, B,...
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The Cambridge Examiner, Volum 4

1884
...lines be proportiouals, the rectangle contained by the extremes is equal to the square on the mean ; and if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines are proportionals. 16. If two straight lines which meet...
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