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" If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line. "
The English Journal of Education - Page 272
1851
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The Element of Geometry

John Playfair - 1836 - 114 pages
...about the diagonal of a square are likewise squares. / G H / CPROP. XXI. THEOR. If a straight line lie divided into two equal parts, and also into two unequal...section, is equal to the square of half the line. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 pages
...line being bisected, the rectangle of the parts is equal to the square of one of them. PROP. V. THEOR. IF a straight line be divided into two equal parts,...section, is equal to the square of half the line. Let the straight line AB be bisected in C, and divided unequally in D : the rectangle AD.DB, together...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 pages
...square of AB is equal to the squares of AC, CB, and twice the rectangle AC-CB. PROPOSITION V. THEOREM. . If a straight line be divided into two equal parts,...section, is equal to the square of half the line. Let the straight line AB he divided into two equal parts in the point C, and into two unequal parts...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 pages
...(a+i)2 =a*+2a6+62. PROP. V. THEOR. If a straight line le divided into two equal parts, andalsointo two unequal parts; the rectangle contained by the...section, is equal to the square of half the line. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 pages
...AC2 + CB2 + figs. AG + GE, and that these are = AC* + CB8 + 2 AC x CB. D H M PROPOSITION V. Theorem. If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle A contained by the unequal parts, I together with the square of the line between the points of section,...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...square on half the line. PROP. V THEOR. If a straight line be divided into two equal parts, and aim into two unequal 'parts ; the rectangle contained...section, is equal to the square of half the line. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts...
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The Elements of Euclid

Euclid - 1838 - 416 pages
...demonstration it is manifest, that the parallelograms about the diameter of a square are likewise squares. two unequal parts: the rectangle contained by the...section, is equal to the square of half the line. Let the straight line AH be divided into two equal parts in the point C, and into two unequal parts...
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The parent's guide to a liberal ... education; containing a selection of ...

Robert Simson (master of Colebrooke house acad, Islington.) - 1838
...square of the hypotenuse is equal to the sum of the squares of the other two sides. 14. If a right line be divided into two equal parts, and also into two unequal parts, what equations will result? 15. The base of a right-angled triangle is 300 feet, and the sum of the...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...half. PROP. V. THEOR. If a straight line (AB) be bisected (in c), and be also divided unequally (in D), the rectangle contained by the unequal parts, together with the square of the part intermediate between the points of section, is equal to the square of half the line. Upon AC describe...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...square of the half. PROP. V. THEOR. If a straight line be bisected, and be also divided unequally, the rectangle contained by the unequal parts, together with the square of the part intermediate between the points of section, is equal to the square of half the line. P E_ AD PROP....
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