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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 on the line between the points of section, is equal to the square on half the line. "
The Element of Geometry - Page 25
by John Playfair - 1836 - 114 pages
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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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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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Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Circle-squaring - 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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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 unequal...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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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...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 unequal...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 - 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 unequal...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 rectangle AD, DB, together...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 333 pages
...squares. PROP. V. THEOR. If a straight line be divided into two equal parts, and also into two uneqtial parts ; the rectangle contained by the unequal parts,...equal parts in the point C, and into two unequal parts in the point D ; the rectangle AD.DB, together with the square of CD, is equal to the square of CB,...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 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 unequal...half the line. Let the straight line AB be divided into%two equal parts in the point C, and into two unequal parts in the point D ; the rectangle AD.DB,...
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