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Books Bücher 41 - 50 von 195 in To divide a given straight line into two parts, so that the rectangle contained by...
" 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. "
Military examinations. Mathematical examination papers, set for entrance to ... - Seite 34
von Woolwich roy. military acad, Walter Ferrier Austin - 1880
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 Seiten
...double of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROPOSITION XI. PROB. — To divide a given straight line into two parts, so that...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...
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Report of the Committee of Council on Education (England and Wales ..., Band 2

Great Britain. Council on Education - 1845
...rectangle contained by the whole and that part, together with the square of the other part. 62. To divide a given straight line into two parts, so that...and one of the parts, shall be equal to the square of the other part. 63. Show that if — B he substracted from A, the result is A + B. 64. Perform the...
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The first six and the eleventh and twelfth books of Euclid's Elements; with ...

James Thomson - 1845 - 358 Seiten
...expression, the first and third partu of whioh are, by the same curolla'y, tli» PROP. XI. PROB. — To divide a given straight line into two parts, so that...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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A collection of examples in pure and mixed mathematics, with hints and ...

1845
...of contact, and the diameter drawn from one of these points. (Euclid, iii. 18. Cape, ii. 38.) 59. To divide a given straight line into two parts, so that...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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A Treatise on Algebra: Symbolical algebra and its applications to the ...

George Peacock - 1845
...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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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...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 ...

John Playfair - 1846 - 317 Seiten
...(2a+i)2+J2=2o2+2(a+4)2, and the proposition is evident from this algebraical equality. PROP. XI. PROB. To divide a given straight line into two parts, so that...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 - 468 Seiten
...(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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The English journal of education, ed. by G. Moody, Band 1

George Moody - 1847
...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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Minutes of the Committee of Council on Education, Band 1

Great Britain. Committee on Education - 1847
...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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