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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 ... - Página 69
por Euclides - 1846
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - 1824 - 542 páginas
...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 - 1824 - 550 páginas
...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 - 1825 - 1046 páginas
...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 - 1825 - 336 páginas
...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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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 546 páginas
...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,...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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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 210 páginas
...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 - 1832 - 358 páginas
...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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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 páginas
...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,...parts, shall be equal to the square of the other part. e 47. 1. Upon AB describe » the square ABDC ; bisect5 AC in E, Book ir. and join BE ; produce CA to...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - 1835 - 544 páginas
...square of the other part. Let AB be the given straight Hue; it is required to divide it into two part", so that the rectangle contained by the whole, and...parts, shall be equal to the square of the other part. c 3. ']. ' e 47. 1. Upon AB describe * the square ABDC ; bisect b AC in E, Book II and join BE ; produce...
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The Element of Geometry

John Playfair - 1836 - 148 páginas
...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...parts shall be equal to the square of the other part. Upon AB describe (16. 2.) the square ABDC; bisect (8. 1.) AC in E, and join BE ; produce CA to F, and...
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