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" Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other... "
Arithmetic, algebra, differential and integral calculus, by W. Rutherford ... - Página 153
por Royal Military Academy, Woolwich - 1853
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Proceedings

Scotland free church, gen. assembly - 1847
...on the other two sides, these sides contain a right angle. 3. Divide a given line into two parts, so that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. 4. The angle in a semicircle is a right angle. 5. Of...
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The British Annals of Education for ...: Being The Scholastic ..., Volúmenes1-2

1844
...line. 7. 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. 8. If in a circle two straight lines cut one another, which do not both pass through the centre, they...
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Report of the Committee of Council on Education (England and Wales ..., Volumen2

Great Britain. Council on Education - 1845
...part. 62. 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. 63. Show that if — B he substracted from A, the result is A + B. 64. Perform the operations indicated...
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A Treatise on Algebra: Symbolical algebra and its applications to the ...

George Peacock - 1845
...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 will become...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 páginas
...line, &c. QED PROPOSITION VIII. THEOR. — If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line, which is made...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...the problem may be possible. 7. Divide a given straight line into two parts, such that the squares of the whole line and one of the parts shall be equal to twice the square of the other part. 8. Divide a given line, so that the square of the greater part...
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An Elementary Course of Mathematics: Designed Principally for Students of ...

Harvey Goodwin - 1846 - 468 páginas
...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): = o2 - Zax + a?2, x- -...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...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 the square ACDB ; bisect AC in E, and join BE ; produce CA to F, and make EF equal...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1846 - 317 páginas
...equality, by transposition. PROP. VIII. THEOR. If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made...
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The English Journal of Education, Volumen1

1847
...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 is less than the...
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