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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 Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - 1882 - 266 pągines
...— 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...equal to the rectangle contained by the means, the Jour straight lines are proportional. . Let A, B, C, D be four straight lines, so that A : B : : C...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 400 pągines
...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, tftefuur straight lines are proportionals. Let the four straight lines AB, CD, E, F, be proportionals,...
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883
...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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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1883
...the quadrilateral AEBC. And Conversely, If the rectangle contained by the extremes be equal to tbe rectangle contained by the means, the four straight lines are proportionals. Let rect. AB, GJT=rect. CD, EF. Then mwt AB be to CD as EF is to GH. For, the same construction being made,...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884
...the rectangle contained by the extremes is equal to the rectangle contained by the means. Conversely: If the rectangle contained by the extremes be equal...contained by the means, the four straight lines are proportional. BG •H c(1) Let AB:CD = EF: GH: it is required to prove AB . GH = CD . EF. From A draw...
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Cambridge University Examination Papers

University of Cambridge - 1884
...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. _ J TUESDAY, June 3, 1884. 9— Щ....
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The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II ...

Association for the Improvement of Geometrical Teaching - 1888
...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. Let OA, OB, OC, OD be four straight lines, such that OA : OB : : OC : OD : then shall...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 pągines
...rectangle contained by the extremes is equal to the rectangle contained by the means. (2) Conversely : — If the rectangle contained by the extremes be equal...means, the four straight lines are proportionals. (1) Let A, B, C, D be four st. lines, such that A : B :: C : D, then rect. A, D = rect. B, C. G rL-....
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1892 - 518 pągines
...to the rectangle contained by the means: Conversely, if the rectangle contained by the extremes is equal to the rectangle contained by the means, the four straight lines are proportional. Let the st. lines AB, CD, EF, GH be proportional, so that AB : CD :: EF : GH. Then shall...
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Proceedings of the Edinburgh Mathematical Society, Volums 17-18

Edinburgh Mathematical Society - 1899
...rectangle contained by the extremes is equal to the rectangle contained by the means. Conversely : If the rectangle contained by the extremes be equal...contained by the means, the four straight lines are proportional. (1) Let the four straight t lines AB, AC, AD, AE be proportional, so that AB : AC = AD...
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