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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 on the other part. "
A treatise on the elements of algebra, by G. Ainsworth and J. Yeats - Page 107
by G. Ainsworth, J. Yeats - 1854
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Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1804 - 440 pages
...PROP. XI. PR OB. TO divide a given ftraight line into two parts, fo that the.rectangle contained by the whole, and one of the parts, may be equal to the fquare of the other part. Let AB be the given ftraight line ; it is required to divide it into two...
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Geometrical Problems Deducible from the First Six Books of Euclid: Arranged ...

Miles Bland - Geometry - 1819 - 377 pages
...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 given line to be divided. Upon...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Geometry - 1819 - 377 pages
...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 given line to be divided. Upon...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan - Algebra - 1824 - 516 pages
...remainder, minus 1, will be 9 times the number sought. Ans. 1 1 , or 3] . Prob. 22. It is required to divide 20 into two such parts, that the product of the whole and one of the parts, shall be equal to the square of the other. Ans. lOv/5— 10, and 30— lOy/5. Prob. 23. A labourer...
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An Elementary Treatise on Algebra, Theoretical and Practical ...

James Ryan - Algebra - 1824 - 516 pages
...remainder, minus 1, will be 9 times the number sought. Ans. II, or 3], Prob. 22. It is required to divide 20 into two such parts, that the product of the whole and one of the parts, shall be equal to the square of the other. Ans. lOv/5 — 10, and 30— 10^/5, Prob. 23. A labourer...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1826 - 320 pages
...to be done. Otherwise : "Divide the radius of the given eirele, so that the reetangle eontained by the whole and one of the parts may be equal to the square ef the other (tl. 2.). Apply in the eirele, on eaeh side of a given point, a line equal to the greater...
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A collection of examples in pure and mixed mathematics, with hints and ...

1845
...Cape, ii. 38.) 59. 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 a given line, which is less than the line to be divided. (Euclid, iii. 1 6, 36. Cape, ii. 38 and iii....
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A Theoretical and Practical Treatise on Algebra ...

Horatio Nelson Robinson - Algebra - 1848 - 320 pages
...four droves was 1121. How many were in each drove? Ans. 1st, 162 ; 2d, 40 ; 3d, 606 ; 4th, 313. 99. Divide the number 20 into two such parts, that the product of their squares shall be 0216. Ans. 12 and 8. 30. Divide the number a into two such parts that the produ.-t...
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Minutes of the Committee of Council on Education, with Appendices, Volume 2

Great Britain. Committee on Education - 1850
...Euc. II. 11. To divide a given finite straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the squire of the other part. 4. Prove Euc. III. 22. The opposite angles of any quadrilateral figure inscribed...
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Algebra for High Schools and Colleges: Containing a Systematic Exposition ...

James B. Dodd - Algebra - 1859 - 306 pages
...servants; also the whole sum taken with them was $3456. What was the number of gentlemen ? Ans. 12. 21. Divide the number 20 into two such parts, that the product of the whole number and one of the parts shall be equal to the square of the other. Ans. 10/ 5— 10, and 30 —...
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