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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 first six books of the Elements of Euclid, with numerous exercises - Seite 42
von Euclides - 1853 - 147 Seiten
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...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 rectangle 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 - 1842 - 317 Seiten
...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 ..., Bände 1-2

1844
...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 rectangle contained...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 - 1844 - 317 Seiten
...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 ..., Band 2

Great Britain. Council on Education - 1845
...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 rectangle contained...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 - 1845 - 199 Seiten
...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 - 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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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 Seiten
...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 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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