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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. "
Euclid's Elements of geometry, books i. ii. iii. iv - Side 65
av Euclides - 1862
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A Treatise on Algebra: Symbolical algebra and its applications to the ...

George Peacock - 1845 - 480 sider
...the following problem. Its first case stated and solved. " To divide a given line into two such parts that the rectangle contained by the whole and one of the parts shall be equal to the square of the other." If we call x the greater of the two parts, and, therefore, a - x the other, the equation...
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A collection of examples in pure and mixed mathematics, with hints and ...

Alfred Wrigley - 1845 - 222 sider
...drawn from one of these points. (Euclid, iii. 18. 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....
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 382 sider
...partu of whioh are, by the same curolla'y, tli» PROP. XI. PROB. — 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. Let AB be the given straight line ; it is required to...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 sider
...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...and one of the parts shall be equal to the square of the other part. Upon AB describe the square ACDB ; bisect AC in E, and join BE ; produce CA to F,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1846 - 334 sider
...proposition is evident from this algebraical equality. PROP. XI. PROB. 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. Let AB be the given straight line ; it is required to...
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An Elementary Course of Mathematics: Designed Principally for Students of ...

Harvey Goodwin - 1846 - 500 sider
...(l + n) ' ma ' na n (a> + mx) = Ex. 5. Divide the quantity a into two parts such that the product of the whole and one of the parts shall be equal to the square of the other part. Let a? = one part ; .-. a- n' = the other; .-. by the question, ax = (a — at):...
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Minutes of the Committee of Council on Education, Volum 1

Great Britain. Committee on Education - 1847 - 606 sider
...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 side subtending either of the acute angles...
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The English Journal of Education, Volum 1

1847 - 508 sider
...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 side subtending either of the acute angles...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 sider
...line made up of the half and the part produced. PROP. XI. PROBLEM. To divide a given straight line into two parts, so that the rectangle contained by...and one of the parts, shall be equal to the square of the other part. PROP. XII. THEOREM. In obtuse-angled triangles, if a perpendicular be drawn from...
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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848 - 390 sider
...triangle between the perpendicular and the obtuse angle. Section 4. 1. Divide a given straight line into two parts, so that the rectangle contained by...and one of the parts shall be equal to the square of the other part. 2. Describe a square that shall be double a given triangle. 3. Prove that the diagonals...
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