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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 ... - Pągina 11
per Henry Parr Hamilton - 1826 - 326 pągines
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## The British Annals of Education for ...: Being The Scholastic ..., Volum 1

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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## Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 pągines
...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 ABDC ; bisectf AC in • 46. i. E, and join BE; produce CA to F, and makeJ...
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## Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Robert Potts - 1845
...PROBLEM. 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 AB into two parts, so that the rectangle...
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## Report of the Committee of Council on Education (England and Wales ..., Volum 2

...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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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - 317 pągines
...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, the parts read in the University of Cambridge [book ...

Euclides - 1846
...PROII. To divide a yifen straight line into tioo 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 Elementary Course of Mathematics: Designed Principally for Students of ...

Harvey Goodwin - 1846 - 468 pągines
...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,...
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## The English journal of education, ed. by G. Moody, Volum 1

George Moody - 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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## The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...PROBLEM. 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. PROP. XII. THEOREM. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute...
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