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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... "
A Supplement to the Elements of Euclid - Page 175
by Daniel Cresswell - 1819 - 410 pages
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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...also subtend equal angles, at the center of the circle. (LXVII.) To produce a given straight line, so that the rectangle contained by the whole line...the part of it produced, shall be equal to a given square. (LXVII i.) If, from the bisection of any given arch of a circle, a straight line be drawn cutting...
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Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - Geometry - 1817 - 456 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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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...CD3 = (AC + CD) (AC-CD)." 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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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 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 - 234 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 - 226 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 - 546 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 Collection of Examples Formulae and Calculations on the Literal ...

Hirsch - Algebra - 1827 - 690 pages
...this construction is founded on Eue. VI. 13, 17. SECTION LXXIII. Рвов. То 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 (ßg. 86) : lengthen...
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Hirsch's Geometry: Or, A Sequel to Euclid

Meyer Hirsch - Geometry - 1827 - 288 pages
...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 (ßg. 86) : lengthen...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1832 - 358 pages
..."(AC+CD)(AC-CD)" PROP. VI. THEOR. If a straight line be bisected, and produced to any point; therect angle 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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