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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 ... - Pāgina 133
per John Playfair - 1846 - 317 pāgines
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 318 pāgines
...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...; the rectangle contained by AB, F is equal to the rect angle contained by CD, E. From the points A, C draw (11. 1.) AG, CH at right angles to AB, CD...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 318 pāgines
...lines be proportionals, the rectangle contained by the extremes it equal to the rectangle contained by the means; And if the rectangle contained by the extremes...means, the four straight lines are proportionals. From the points A, C draw(11. 1.) AG, CH at right angles to AB, CD ; and make AG equal to F, and CH...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...rectangle contained by the extremes is equal to the rectangle contained by the means ; and conversely, if the rectangle contained by the extremes be equal...means, the four straight lines are proportionals. First, let the four straight lines AB, СD, E and F bо proportionals, viz., AB to СD, as E to F....
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1856 - 318 pāgines
...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...to CD, so E to F ; the rectangle contained by AB, F,is equal to the reel angle contained by CD, E. From the points A, C draw(ll. l.)AG, CH at right angles...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1858 - 12 pāgines
...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. 3. Solve the following equations (1) JK __ X+l _ 13 x 6 (2) x* + xy = 15 ; xy-y* = 2. 4. The slant...
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The Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

W. Davis Haskoll - 1858 - 324 pāgines
...lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean, and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals. PROBLEM 2. Fig. 16. On the ground from...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 361 pāgines
...rectangle contained by 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, Fbe 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 the First Six Books of Euclid : with a ...

John Playfair - 1860 - 317 pāgines
...THEOR. If four straight lines be proportionals, the rectangle contained by the extremes it equaltothe rectangle containedby the means; And if the rectangle...means, the four straight lines are proportionals. From the points A, C draw(ll. l.)AG, CH at right angles to AB, CD ; and make AG equal to F, and CH...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...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. Given that the three straight lines...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...rectangle contained by the extremes is equal to the rectangle contained by the means ; and conversely, if the rectangle contained by the extremes be equal...to the rectangle contained by the means, the four st. lines are proportionals. CON. 11, L 3, L 3l, I.' DEM. 7, V. 14, VI. Def. 1, II. A reet, is contained...
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