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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 ...

Euclid, Robert Simson - Geometry - 1821 - 514 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 dne of the parts shall be equal to the square of the other part. Upon AB describe (46. 1.) the square...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...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 dug two trenches, one of which was 6 yards...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan - Algebra - 1824 - 550 pages
...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 dug two trenches, one of which was 6 yards...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...AC, CD. Wherefore, if a straight line, &c. QED Proposition Xf. Problem. 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 'o the square of the other part. Let AB be the given straight line ; it is required to divide it into...
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An Introduction to Algebra: With Notes and Observations, Designed for the ...

John Bonnycastle - Algebra - 1825 - 336 pages
...is required to divide a line, of 20 inches in length, into two such parts that the rectangle of (he whole and one of the parts shall be equal to the square of the other. Ans. 10^5-10, and 30—10^/5 6. It is required to divide the number 60 into two such parts that their...
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A Supplement to the Elements of Euclid

Daniel Cresswell - Euclid's Elements - 1825 - 616 pages
...therefore (dividendo), : BC* :: AB : BD. PROP. VIII. 8. PROBLEM. To divide a given Jinite straight line into two parts, so that the rectangle, contained by the whole line, and the difference of those two parts, shall be in a given ratio to the square of the less of...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 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...parts, shall be equal to the square of the other part. Upon AB describe* the square ABDC; bisect* AC in E, ahd join BE : produce CA to F, and make* EF equal...
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Geometrical Problems Deducible from the First Six Books of Euclid: Arranged ...

Miles Bland - Euclid's Elements - 1827 - 462 pages
...the whole line produced and the part produced may be equal to a 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 the line to be divided. 10. To divide...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...PROPOSITION IX. PROBLEM. To divide a given straight line into two parts which shall be in any given ratio. Let AB be the given straight line; it is required to divide AB into two parts which shall be in a given ratio. From the point A draw a line AC, making any angle...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1832 - 358 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, sha'l be equal to the square of the other part. Upon AB describe (40. 1.) the square ABDC;...
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