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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 ... - Pàgina 133
per John Playfair - 1846 - 317 pàgines
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...: F), the rectangle (AB'F) contained by the extremes, is equal to the rectangle (CD'E) contained by the means : and, if the rectangle contained by the...contained by the means, the four straight lines are proportional. From A and C, the extremities of AB and CD, draw the perpendiculars AG and CH, and make...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 pàgines
...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. Let the three straight lines A, B,...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...the rectangle contained by the means : and if the rectangle contained by the extremes be equivalent to the rectangle contained by the means, the four...CD, so E to F : the rectangle contained by AB, F is equivalent to the rectangle contained by c D, E. EUC. B. VI. OF GEOMETRY. sides about equal angles...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 pàgines
...lines lie 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. Let the three straight lines, A, B,...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...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 CD, so E to F. The rectangle contained by AB, F, shall be equal to the rectangle contained by CD, E. H— From the points A, C draw AG, CH at right...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 pàgines
...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. Let the three straight lines A, B,...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...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. First, let the three straight lines...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...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. PROP. XVII. THEOREM. If three straight lines be proportionals, the rectangle contained by the extremes...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853
...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. Let the three straight lines A, B,...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 pàgines
...lines be proportionals, tlie rectangle contained by the extreme» 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. LET the three straight lines a, b,...
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