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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 Elements of Euclid, the parts read in the University of Cambridge [book ... - Page 62
by Euclides - 1846
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1762 - 466 pages
...likewife fquares. PROP, BooklL PRO PV THEO R. IF a ftraight line be divided into two equal parts, and alfo into two unequal parts ; the rectangle contained by the unequal parts, together with the fquare of the line between the points of fe&ion, is equal to the fquare of half the line. Let the ftraight...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - Trigonometry - 1775 - 520 pages
...likcwife fquares. PROP. Book II. PRO PV THEO R. Fa ftraight line be divided into two equal parts, and alfo into two unequal parts ; the rectangle contained by the unequal parts, together with the fquare of the line between the points of fection, is equal to the fquare of half the line. Let the...
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Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1804 - 440 pages
...are likewife fquares. PROP. V. THEO R. IF a ftraight line be divided into two 'equal parts, and alfo into two unequal parts ; the rectangle contained by the unequal parts, together with the fquare of the line between the points of fection, is equal to the fquare of half the line. Let the...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804
...'• . c- 43. '• PROP. V. THE OR. • IF a ftraight line be divided into two equal parts, and alfo into two unequal parts ; the rectangle contained by the unequal parts, together with the fquare of the line between the points of fe&ion, is equal to the fquare of half the line. Let the ftraight...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Euclid's Elements - 1806 - 518 pages
...paralJelograms about the diameter of a square are likewise squares. PROP. V. THEOR. IF a straight line be divided into two equal parts, and also into two...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 at the point D ; the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...parallelograms about the diameter of a square are likewise squares. . PROP. V. THEOR. IF a straight line be divided into two equal parts, and also into two...square of the line between the points of section, are equal to the square of half the line. Let the straight line AB be divided into two equal parts...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1810 - 518 pages
...square are likewise squares. PROP. V. THEOR. IF a straight line be divided into two equal parts, aid also into two unequal parts ; the rectangle contained...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 at the point D; the...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...parts, together •with twice the rectangle contained by the parts. Prop. V. Theor. If a straight line be divided into two equal parts, and also into two...section, is equal to the square of half the line. Prop. VI. Theor. If a straight line be bisected, and produced to any point; the rectangle contained...
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An Easy Introduction to the Mathematics: In which the Theory and ..., Volume 2

Charles Butler - Mathematics - 1814
...product a+or.a— «•= aa — xx ; to each of these equals add xx, and a+xa — x+xx=aa, that b, the rectangle contained by the unequal parts, together with the square of (x) the line between the points of section is equal to the square of (a) half the line. QED In the...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - Euclid's Elements - 1816 - 528 pages
...parallelograms about the diameterof a square are likewise squares. PROP. V. THEOR. IF a straight line be divided into two equal parts, and also into two...the square of half the line. Let the straight line AB be divided into two e qual parts in the point C, and into two unequal parts at the point D ; the...
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