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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. "
The Elements of Euclid, the parts read in the University of Cambridge [book ... - Pagina 69
di Euclides - 1846
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pagine
...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 Introduction to Algebra: With Notes and Observations : Designed for the ...

John Bonnycastle - 1818 - 326 pagine
...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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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 800 pagine
...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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A Supplement to the Elements of Euclid

Daniel Cresswell - 1819 - 486 pagine
...such, that the rectangle contained by the whole line and one of its parts, shall have a given ratio to the square of the other part. Let AB be the given straight line : It is reAB % quired to divide it into two parts, such that the rectangle contained by AB and one of the parts...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1819 - 444 pagine
...DB are equal to the square of AB, ie to the given square. (9.) To divide a straight line into ttvo 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. L,etAB be the...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1819 - 442 pagine
...AD, DB are equal to the square of AB, ie to the given square. (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 fhe line to be divided. Let AB he tlie...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pagine
...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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A Supplement to the Elements of Euclid

Daniel Cresswell - 1819 - 446 pagine
...DAH > the L HAG ; and so on. . PROP. XXXIII. 47. PROBLEM. To trisect av given finite straight line. Let AB be the given straight line: It is required to divide it into three equal parts. Upon AB describe (E. 1.1.) the equilateral A CAB ; bisect (E. 9. 1.) the two equal...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 350 pagine
...has^ieen inscribed. Which was to be done. x Otherwise. •' Divide the radius of the given circle, so that the rectangle contained by the whole and one of the parts may be equal to the square of the other (11. 2.). Apply in the circle, on each side of a given point,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1821 - 514 pagine
...line: it is required to divide it into two parts, so that the rectangle contained by the whole and dne of the parts shall be equal to the square of the other part. Upon AB describe (46. 1.) the square ABDC; bisect (10. 1.) AC in E, and join BE; produce CA to F, and...
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