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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, may be equal to the square of the other part. "
Euclid's Elements [book 1-6] with corrections, by J.R. Young - Page 70
by Euclides - 1838
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 560 pages
...the squares of AC, CD. Wherefore, if a straight line, &c. QED Boon II. '46. 1 '10.1 PROP. XI. PROB. To divide a given straight line into two parts, so...parts, shall be equal to the square of the other part. Upon AB describe3 the square ABDC; bisect b AC in E, and join BE; produce CA to F, and make c EF equal...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...equal to the square of the other part. Let AB be the given straight line; it is required to divide it into two parts, so that the rectangle contained by...the whole, and one of the parts, shall be equal to thcsquare of the other part. Upon AB describe* the square ABDC ; bisect b AC in E, and join BE ; produce,...
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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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An Introduction to Algebra: With Notes and Observations : Designed for the ...

John Bonnycastle - Algebra - 1818 - 326 pages
...It is required to divide a line, of 20 inches in length, into two such jiarts that the rectangle of the whole and one of the parts shall be equal to the square of the other. Ans. lOv/6-10 5. It is required to divide the number 60 into two such parts, that their product shall...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 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...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 required to...
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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. 10. To divide...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 800 pages
...made up of the half and the part produced. Prop. XI. Prob. To divide a given straight lint into tu'o parts, so that the rectangle contained by the whole, and one of the parts, shall be equal tu the fquare of the other part. Prop. XII. Theor. In obtuse angled triangles, if a perpendicular be...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...AD3+DB==2AC3+2CD3. Wherefore, if a straight line, &c. Q, ED PROP. XI, PROB. To divide a given straight line into too parts, so that the rectangle contained by the whole, and one of the parts, niay be equal to the square of the other part. Let AB be the given straight line ; it is required to...
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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
...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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