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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. "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Page 49
by Euclid, John Playfair - 1846 - 317 pages
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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
...PROP. V. THEOR. IF a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together...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 - 1819 - 354 pages
...PROP. V. THEOR. If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together...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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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 800 pages
...parts, and also into two um quäl parts j the rectangle contained by the unequal parts, togotherVrith the square of the line between the points of section, is equal to the square of half the line. Prop. VI. Theor. If a straight line be bisected, and produned to any point; the rectangle contained...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 514 pages
...PROP. V. THEOR. IP a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together...section, is equal to the square of half the line. i H M Let the straight line AB be divided into two equal parts in the point C, and into two unequal...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...Proposition V. Tlieorem. If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together...equal parts in the point C, and into two unequal parts at the point D ; the rectangle AD.DB, together with the square of CD, is equal to the square ot CB....
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...of the intermediate distance, is equal to the square made of half the line. Let the right line лв be divided into two equal parts in the point c, and into two unequal parts at the point D; the rectangle AD, DB, toether with the square or For describe 2 CEFD, the square of...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...straight line be divided into two equal parts, and also into two unequal parts ; the reetangle eontained by the unequal parts, together with the square of the line between the points of seetion, is equal to the square of half the line. Let the straight line AB be divided into two equal...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...PROP. V. THEOR. If a straight line be divided into two equal parts and also into two unequal parts ; the rectangle contained by the •unequal parts, together...equal parts in the point C, and into two unequal parts at the point D : the rectangle AD, DB, together with the square of CD, shall be equal to the square...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...PROP. V. THEOR. If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together...equal parts in the point C, and into two unequal parts at the point D ; the rectangle AD, DB, together with the square of CD, is equal to the square of CB....
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