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" 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 the square of the other part. "
The Principles of Analytical Geometry ... - Page 7
by Henry Parr Hamilton - 1826 - 326 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...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 the square of the other part, e 47. 1. Upon AB describe" the square ABDC ; bisectb AC in E, Book II. and join BE ; produce CA to...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...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 the square of the other part. a 46. 1. Upon AB describe a the square ABDC ; bisect 1• AC in E, ami b 10. 1. jo1n BE ; produce CA...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 722 pages
...Prob. To divide a given straight line into two parts, so that thé rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. Prop. XII. Theor. In obtuse angled triangles, if a perpendicular be drawn from any of the acute angles...
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A Treatise on Algebra: In Practice and Theory, ... with Notes and ..., Volume 1

John Bonnycastle - Algebra - 1813 - 456 pages
...required to divide a line, of 20 inches in length, into two such parts, that the rectangle of the whole and one of the parts shall be equal to the square of the other. Ans. 10/5 — 10 5. It is required to divide the number 60 into two such parts, that their product...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...PROB. 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 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...
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An Introduction to Algebra: With Notes and Observations : Designed for the ...

John Bonnycastle - Algebra - 1818 - 260 pages
...required to divide a line, of 20 inches in length, into two such parts that the rectangle of the whole and one of the parts shall be equal to the square of the other. Ans. 10^/5-10 5. It is required to divide the number 60 into two such parts, that their product shall...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1819 - 333 pages
...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 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,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 514 pages
...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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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan - Algebra - 1824 - 516 pages
..., 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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An Elementary Treatise on Algebra, Theoretical and Practical ...

James Ryan, Robert Adrain - Algebra - 1824 - 516 pages
...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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