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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. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Page 3-16
by Euclides - 1814
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1844 - 338 pages
...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...into two parts, so that the rectangle contained by Ji ^j. the whole, and one of the parts, shall be equal to the square of the other part. Upon AB describe...
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Report of the Committee of Council on Education (England and Wales ..., Volume 2

Great Britain. Council on Education - 1845 - 696 pages
...whole and that part, together with the square of the other part. 62. To divide a given straight line into two parts, so that the rectangle contained by...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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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...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 contained by...parts, shall be equal to the square of the other part. H KD Upon AB describe the square ACDB; (i. 46.) bisect AC in E, (i. 10.) and join BE, produce CA to...
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A Treatise on Algebra: Symbolical algebra and its applications to the ...

George Peacock - Algebra - 1845 - 480 pages
...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...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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A collection of examples in pure and mixed mathematics, with hints and ...

Alfred Wrigley - 1845 - 222 pages
...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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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...X. PROB. — To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line ; it is required to divide it into two equal parts. 14 t 24 Def. Constr. 4. 1. • 3. 1. t 1. 1. I Constr. || 24 Def. 8. 1. 10 Def. \ D...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 380 pages
...was to be done. PROP. XXX. PROB. — To divide a given straight line in extreme and mean ratio. Let AB be the given straight line ; it is required to divide it in extreme and mean ratio. Divide AB (II. 11 ) in the point C, so that the rectangle AB.BO may be equal...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...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...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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An Elementary Course of Mathematics: Designed Principally for Students of ...

Harvey Goodwin - Mathematics - 1846 - 500 pages
...(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): = o2 - Zax + a?2,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1846 - 334 pages
...PROP. X. PROB. To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line ; it is required to divide it into two equal parts. Describe (1. 1.) upon it an equilateral triangle ABC, and bisect (9. 1.) the angle ACB...
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