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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. "
Solutions of the Cambridge Problems: From 1800 to 1820 - Page 654
by John Martin Frederick Wright - 1825 - 653 pages
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 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 unequal...square of half the line, and of the square of the line between the points of section. Let the straight line AB be divided at the point C into two equal,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Mathematics - 1806 - 320 pages
...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 unequal...square of half the line, and of the square of the line between the points of section. Let the straight line AB be divided at the point C into two equal,...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...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 - 1816 - 588 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 unequal...square of half the line, and of the square of the line between the points of section. Let the straight line AB be divided at the point C into two equal,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...AD2=AC-+4AB.BC. 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...square of half the line, and of the square of the line between the points of section. Let the straight line AB be divided at the point C into two equal,...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...ADs=AC3+4AB.BC. q. ED" 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 - 1046 pages
...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 unequal...square of half the line, and of the square of the line between the points of section. Let the straight line AB be divided at the point С into two equal,...
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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
...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 unequal...square of half the line, and of the square of the line between the points of section. Let the straight line AB he divided at the point C into two equal,...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 pages
...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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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 234 pages
...PROPOSITION IX. ТНЕОПЕМ. J/1 a rzgAf Kne ie any how cut into two equal and two unequal parts, then the squares of the two unequal parts are, together, double of the square of the half line, and the square of the intermediate part. Let any right line AB be cut into two equal...
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