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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. "
A Collection of Cambridge Mathematical Examination Papers: Papers in the ... - Page 233
by John Martin Frederick Wright - 1831
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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
...QED 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 are together...square of the line between the points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts...
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Elements of geometry: containing the first six books of Euclid, with a ...

John Playfair - Trigonometry - 1806 - 311 pages
...II. 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 are together...square of the line between the points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts....
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1810 - 518 pages
...F 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 are together...half the line, and of the square of the line between tlie points, of section. Let the straight line AB be divided at the point C into two equal, and at...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory, and N ...

John Mason Good, Olinthus Gilbert Gregory - 1813
...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...square of the line between the points of section. Prop. X. Theor. If a straight line be bisected, and produced to any point, the square of tht; whole...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...R / 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 are together...square of the line between the points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts:...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Trigonometry - 1819 - 333 pages
...QED" PROP. IX. THEOR. If a straight line be divided into too equal, and also into tzeo unequal parts ; the squares of the two unequal parts are together...square of the line between the points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...PROP. IX. THEOR. 'If /a straight line be divided into two equal, and also into too untquai parts ; the squares of the two unequal parts are together double of the square of half the iinCi ahd of th-e square of the line between the points of section. • » v. Let the straight line...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...Proposition IX. Theorem, If a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together...square of the line between the points of section. Let the straight line AB be divided at the point С into two equal, »nd at D into two unequal parts...
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Solutions of the Cambridge Problems: From 1800 to 1820, Volume 2

John Martin Frederick Wright - Mathematics - 1825
...rectilinear angle. 2. If a straight Hue be divided into two equal, and also into two unequal, parts ; the squares of the two unequal parts are together...square of half the line, and of the square of the Une between the points of section. 3. If two straight lines within a circle cut one another, the rectangle...
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Elements of arithmetic, algebra and geometry

George Lees - 1826
...a straight line AB be divided into two equal parts AC, CB, and also into two unequal parts AD, DB ; the squares of the two unequal parts are together...square of half the line, and of the square of the tine CD, between the points of section. • . ; Or, AD2 + DB2 = 2AC2 .+ 2CD2. From the point C, draw...
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