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" IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section. "
Gradations in Euclid : books i. and ii., with an explanatory preface [&c ... - Page 232
edited by - 1870
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...BC* + BC.AC = AB.BCb ; therefore AD2=AC2+ U3.2. 4AB.BC. QED" Book II. PROP. IX. THEOR. IF a straight line be divided into two equal, and also into two...the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section....
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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
...together in one straight line. Wherefore, if a straight line, &c. QED PROP. IX. THEOR. IF a straight line be divided into two equal, and also into two...the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section....
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory, and N ...

John Mason Good, Olinthus Gilbert Gregory - 1813
...square of the straight line which is made up of the whole and that part. Prop. IX. Theor. If a straight line be divided into two equal, and also into two unequal parts; the tqniMN of the two unequal parts arc together double of the square of half the line, and of the square...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - Euclid's Elements - 1816 - 528 pages
...Wherefore, if a straight line, &c. QED TIL F ACBT z .... 6 K / P R / PROP. IX. THEOR. IF a straight line be divided into two equal, and also into two...the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section....
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Geometrical Problems Deducible from the First Six Books of Euclid: Arranged ...

Miles Bland - Geometry - 1819 - 377 pages
...nil lines drawn from that point meeting the three lines be harmonically divided. 23. If a straight line be divided into two equal and also into two unequal parts, and be |>roduced, so that the part produced may have to the whole line so produced, the same ratio...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Geometry - 1819 - 377 pages
...all lines drawn from that point meeting the three lines be harmonically divided. 23. If a straight line be divided into two equal and also into two unequal parts, and be produced, so that the part produced may have to the whole line so produced, the same ratio that...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...in one straight line. ^herefore, if a straight line, &c. QED Proposition IX. Theorem, If a straight line be divided into two equal, and also into two...the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section....
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Solutions of the Cambridge Problems: From 1800 to 1820, Volume 2

John Martin Frederick Wright - Mathematics - 1825 - 653 pages
...given rectilinear figure, having an angle equal to a given rectilinear angle. 2. If a straight Hue be divided into two equal, and also into two unequal,...the squares of the two unequal parts are together double of the square of half the line, and of the square of the Une between the points of section....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1826 - 320 pages
...BO+RC.AC=\B.BC (3.2.) and therefore AD3==AC + 4\B.BC. Q, E, D," -V PROP. IX. THEOR. ., If a straight line be divided into two equal, and also into two...the squares of the two, unequal parts are together double of the square of half the line, and of the square of the line between the points of section....
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...together in one straight line. Wherefore, if a straight line, &c. GED PROP. IX. THEOR. If a straight line be divided into two equal, and also into two...unequal parts; the squares of the two unequal parts arc together double of the square of half the line, and of the square of the line between the points...
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