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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. "
Euclid's Elements [book 1-6] with corrections, by J.R. Young - Page 61
by Euclides - 1838
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1762 - 488 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 - 534 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 First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 552 pages
...of the line between the points of fe&ion, is equal to the fquare of half the. line. Let the ftraight line AB be divided into two equal parts in the point C, and into two unequal parts at the point 1); the rectangle AD, DI3, together with the fquare of CD, is equal to the fquare of CB. Upon CB d<:fcribe...
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Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

John Playfair, Euclid - Circle-squaring - 1804 - 468 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 - 530 pages
...'• . 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 ...

John Playfair - Mathematics - 1806 - 320 pages
...are likewise squares. . PROP. V. THEOR. IF a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by...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 - 714 pages
...contained by the parts. Prop. V. Theor. If a straight line be divided into two equal parts, and also into two unequal parts) the rectangle contained by...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 - 528 pages
...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 - 588 pages
...are likewise squares. PROP. V. THEOR. IF a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by...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 - 350 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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