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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: The Errors, by which Theon, Or Others, Have Long Ago ... - Page 60
by Robert Simson - 1806 - 518 pages
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 351 pages
...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...parts, shall be equal to the square of the other part. Upon AB describe* the square ABDC; bisect* AC * 46. 1. in E, and join BE; produce CA to F, making*...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...equivalent to double the squares of AC, CD. If therefore a straight line, &c. QED PROP. XI. PROB. To divide a given straight line into two parts, so that the...contained by the whole, and one of the parts, shall be equivalent to the square of the other part. Let AB be the given straight line : it is required to divide...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 317 pages
...(2a-f*)2+*2=2a2+2(a+i)2, and the 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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Proceedings

Scotland free church, gen. assembly - 1847
...the squares described 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...
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The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

Education - 1844
...contained by the whole and each of the parts are together equal to the square of the whole line. 7. Divide a given straight line into two parts, so that 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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1844 - 317 pages
...straight line ; it is required to divide it 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 (46. 1.) the square ABDC ; bisect (10. 1.) AC in E, and join BE ; produce CA to F,...
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Report of the Committee of Council on Education (England and Wales ..., Volume 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 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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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 199 pages
...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...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 ...

Euclides - 1845
...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
...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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