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" To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part. "
Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ... - Page 91
by Euclid - 1890 - 400 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...because DG=DB; therefore AD2+DB2=2AC2+ 2CD2. Wherefore, if a straight line, &c, QE D, PROP. XI. PROB. TO divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square of the other part. Let AB be the given straight line ; it is...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...double of the squares of AC, CD. Wherefore, wr a straight line, &c. QED PROP. XI. PROB. TO clivjde a given straight line into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. Let AB be the given straight line ; it...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1810 - 518 pages
...AD, DB are double of the squares of AC, CD. \Vherefore, if a straight line, &c. QED PR6P. XI. PROB. TO divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. Let AB be the given straight line ; it...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...double of the squares of AC, CD. Wherefore, if a straight line, úc. QED "46. 1 Ho. 1 PROP. XI. PROB. To divide a given straight line into two parts, so...that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. Let AB be the given straight line; it...
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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...tangents to the two circles, drawn from any point of the line, shall be equal to one another. (LXXV.) To divide a given straight line into two parts, so that the square of the one shall be equal to the rectangle contained by the other and a given straight line....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1819 - 333 pages
...DG=DB: Therefore, AD3 +DB3=2AC3+2CD3. Wherefore, if a straight line, &c. Q, ED . . PROP. XI. PROB. To divide a given straight line into two parts, so...that the rectangle contained by the -whole, and one of the parts, may be equal to the square of the other part. Let AB be the given straight line ; it...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 442 pages
...squares may be equal to a given square, and their rectangle equal to a given rectangle. 9. To divide a straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square of a given line, which is less than the line to be divided....
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A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 410 pages
...them without the circles, shall (E. 36. 3. and S. 80. 3.) be equal to one another. PROP. LXXXI. 106. PROBLEM. To divide a given straight line into two parts, so that the square of the one shall be equal to the rectangle contained by the other and a given straight line....
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 444 pages
...squares may be equal to a given square, and their rectangle equal to a given rectangle. 9. To divide a straight line into two parts, so that the rectangle contained by the whole aud one of the parts may be equal to the square of a given line, which is less than the line to be...
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A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 486 pages
...manifest from this proposition, and from E. 1O. 4., that if the semi-diameter of a circle be divided into two parts, so that the rectangle contained by the whole and the lesser part may be equal to the square of the greater part, the greater segment shall be equal...
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