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" To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment. "
Treatise on the elements of algebra - Page 294
by James Bryce - 1837
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Easy Introduction to Mathematics, Volume 2

Charles Butler - Mathematics - 1814
...introduced under a different form in another part of the Elements, (viz. 11.2.) there, we have merely to divide a straight line, so that the rectangle contained by the whole and the less segment, may equal the square of the greater ; we have to determine the properties of a figure,...
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Hirsch's Collection of Examples, Formulae, & Calculations, on the ..., Volume 1

Hirsh - 1827 - 304 pages
...ACB; further, ACL = \AQL = AOE = GDE ; consequently ABC - ACB = GDE. QE I). SECTION LXXII. Рков. To divide a straight line, so that the rectangle contained by the two parts may be equal to a given square. SOLDT. The given line AB = a (g. 85) is required to be...
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Hirsch's Geometry: Or, A Sequel to Euclid

Meyer Hirsch - Trigonometry - 1827 - 264 pages
...ABC - ACB; further, ACL = $AOL = AOE = GDE ; consequently ABC - ACB = GDE. QED SECTION LXXII. PROB. To divide a straight line, so that the rectangle contained by the two parts may be equal to a given square. SOLUT. The given line AB = a (g. 85) is required to be...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 272 pages
...required value of y. Hence AD, and therefore AC and А В are found, and the triangle is determined. 18. To divide a straight line, so that the rectangle contained by the two parts may be equal to the square upon a given line 6. Let А В = a AP = x Then the rectangle AP,...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...required value of y. Hence AD, and therefore А С and AB are found, and the triangle is determined. 18. To divide a straight line, so that the rectangle contained by the two parts may be equal to the square upon a given line b. L,et AB = a д p — - у Then the rectangle...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...expressed in numbers ; in other words, there is no number capable of being divided so that the product of the whole and one part, shall be equal to the square of the other part. When a line is thus divided (in extreme and mean ratio, as it is termed in the Sixth Book), the rectangle...
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846
...PROBLEM. To divide a given finite right line ( AB) so that the rectangle contained under the whole line and one part, shall be equal to the square of the other part. From A draw AC, perpendicular to the given line AB, and let AC be equal to AB, and bisect it in E,...
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The English journal of education, ed. by G. Moody, Volume 1

George Moody - 1847
...the other two sides of it, the angle contained by these two sides is a light angle. SECTION Il. — 1. To divide a straight line, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 2. In every triangle the square of the...
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Minutes of the Committee of Council on Education, Volume 1

Great Britain. Committee on Education - School buildings - 1847
...upon the other two sides of it, the angle contained by these two sides is a right angle. SECTION II. 1. To divide a straight line, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 2. In every triangle the square of the...
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Calendar of Queen's [afterw.] University college, Cork

Cork city, univ. coll - 1851
...Trigonometry. 1. Show geometrically how to divide a straight line so that the rectangle of the whole line and one part shall be equal to the square of the other part. Deduce the same method also by algebra. Explain why the line thus divided is said to be divided in...
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