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" If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line, which is... "
Euclid, books i. & ii., with notes, examples, and explanations, by a late ... - Page 109
by Euclides - 1879
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...unequal lines AC, CD, is equal to the rectangle contained by their sum and difference. PROP. VI. THEOR. IF a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 320 pages
...rectangle contained by their sum and difference, or that AC*— -CD2=AC+CD. AC— CD." ' / PROP. VI. THEOR. IF a straight line be bisected, and produced to any ^ point, the rectangle contained by the whole line thus produced and the part of it produced, together with the...
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Pantologia. A new (cabinet) cyclopśdia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...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 produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced, together with the...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...lines AC, CD, is equal to the rectangle contained by their sum and difference. M ^5' PROP. VI. THEOR. IF a straight line be bisected, and produced to any point: the rectangle contained by the whole line thus produced, and the part of it produced, together with the...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
..." contained by their sum and difference, or that AC3 — CD3 = (AC + CD) (AC-CD)." PROP. VI. THEOR. If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced, together with the...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...the squares of 'AD, DB are double of the squares of AC, CD. If therefore a straight Пае, &C. ÷.ED Proposition X. Theorem. If a straight line be bisected, and produced to any point, fhe square of the whole line thus produced, and the square of the part of it produced, are together...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...unequal lines, AC, CD, is equal to the rectangle contained by their sum and difference. PROP. VI. THEOR. If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1832 - 358 pages
...away the equal rectangles 2BC.CD and 2AC.CD, there re" mains AD"+DBa =2AC-+2CD'. " PROP. X. THEOR. Jf a straight line be. bisected, and produced to any point, the square of the. whole line thus produced, and the square of the ^part of 'it produced, are together double...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1833 - 346 pages
...taking away the equal rectangles 2BC. CD and 2AC.CD, there re" mains AD2+DB2=2ACH2CD2." PROP. X. THEOR. If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...lines AC, CD, is equal to the rectangle contained by their sum AD and difference DB. PROP. VI. THEOR. If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together ivith the...
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