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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 first six books of the Elements of Euclid, with numerous exercises - Page 42
by Euclides - 1853 - 147 pages
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 560 pages
...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 that the rectangle contained...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 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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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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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 442 pages
...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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...+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 is required to...
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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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A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 446 pages
...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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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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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 444 pages
...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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