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" If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square... "
An Elementary Treatise on the Geometrical and Algebraical Investigation of ... - Page 56
by Daniel Cresswell - 1817 - 436 pages
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...sum and difference. M ^5' PROP. VI. THEOR. IF a straight line be bisected, and produced to any point: the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which...
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Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - Geometry - 1817 - 454 pages
...of another problem of the same nature ; in which it is required to produce a straight line AB, such that the rectangle contained by the whole line thus produced and the part produced, shall be equivalent to the square of the line AB itself. Divide AB, by this proposition,...
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A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 410 pages
...ofL. 94. COR. By the help of this proposition and (E. 14. 2.), a given straight line may be produced, so that the rectangle contained by the whole line...the part of it produced, shall . be equal to a given rectilineal figure. PROP. LXXIV. 95. THEOREM. IJ\ from the bisection of any given arch of a circle,...
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A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 490 pages
...and which is equal to the tangent, itself also touches the circle. " --> PROP. LXXIII. 93. PROBLEM. To produce a given straight line, so that the rectangle contained by the whole lint? thus produced, and the part of it produced, shall be equal to a given square. Let AB be a given...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...following pYoblem, more simple, and, as was observed in the former instance very little less general . " To produce a given straight line, so that the rectangle '• contained by the segments, between the extremities of the given. " line, and the point to which it is produced, may...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...Proposition VI. Theoretn. If a straight line be bisected, and produced .to any point : the recangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 pages
...PROPOSITION X. THEOREM. If a right line be cut into two equal parts, and produced to any point, the square of the whole line thus produced, and the part of it produced, shall be together double to the square of the half line, and of' the line made up of the half and the part produced....
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 228 pages
...PROPOSITION X. THEOREM. If a right line be cut into two equal parts, and produced to any point, the square of the whole line thus produced, and the part of it produced, shall be together double to the square of the half line, and of the line made up of the half and the part produced....
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...their sum and difference. PROP. VI. THEOR. If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which...
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Hirsch's Geometry: Or, A Sequel to Euclid

Meyer Hirsch - Geometry - 1827 - 294 pages
...proof of this construction is founded on Eue. VI. 13, 17. SECTION LXXIII. PROB. To produce a given line, so that the rectangle contained by the whole line thus produced, and the part produced, may be equal to the square of a given line. SOLUT. Let the line AB be given (g. 86) : lengthen...
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