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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 school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...: and converselg, if the rectangle contained bg the extremes be iqual to the rectangle contained bg the means, the four straight lines are 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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The college Euclid: comprising the first six and the parts of the eleventh ...

Euclides - 1865
...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. 1 7. If three straight lines be proportionals, the rectangle contained by the extremes is equal...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1855 - 317 pągines
...proportionals, the rectangle contained by the extremes it equal to the rectangle conla.ine.dlty themeans; And if the rectangle contained by the extremes be...; the rectangle contained by AB, F is equal to the rect angle contained by CD, E. From the points A, C draw (11. l.)AG, CH at right angles to AB, CD ;...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 pągines
...[Construction. therefore the rectangle contained by A and 6' is equal to the rectangle contained by B and D. But if the rectangle contained by the extremes be equal...the means, the four straight lines are proportionals ; [VI. 16. therefore A is to B as D is to (7. But B is equal to D ; [CorutnicHon. Therefore A is to...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 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, 13,...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 pągines
...rectangle contained bit the extremes is equal to the rectangle contained by the meant: 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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Examination for women. Examination papers, with lists of syndics and examiners

Cambridge univ, exam. papers - 1870
...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. Two chords AB, CD of a circle intersect in 0, prove that AO is to CO as DO is to BO. 5. Prove that...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - 349 pągines
...circle in C, prove that the square on CE is equal to twice the quadrilateral AEBC. And Conversely, If the rectangle contained by the extremes be equal to the rectangle contained by the means, the jywr straight lines are proportionals. Let rect. AB, GH=rect. CD, EF. Then must AB be to CD as EF is...
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The Quadrature of the Circle: The Square Root of Two, and the Right-angled ...

William Alexander Myers - 1873 - 164 pągines
...[Hypothesis.] therefore the 'rectangle contained by A and C is equal to the rectangle contained by B and D; but if the rectangle contained by the extremes be equal...rectangle contained by the means, the four straight lines ate proportionals; [FT. 16.] therefore A is to B as D is to C. But B is equal to D; [Construction.]...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...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...F be proportionals, viz., as AB to CD, so E to F. Then the rectangle contained by AB, F, shall be equal to the rectangle contained by CD, E. Construction....
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