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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. "
Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ... - Page 157
by Miles Bland - 1819 - 377 pages
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The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

Education - 1844 - 688 pages
...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 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,...
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A collection of examples in pure and mixed mathematics, with hints and ...

Alfred Wrigley - 1845 - 222 pages
...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...given line, which is less than the line to be divided. (Euclid, iii. 1 6, 36. Cape, ii. 38 and iii. 79.) 60. To draw a straight line, which shall touch a...
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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
...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 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...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...Wherefore, if a straight line, &c. QED PROPOSITION XI. 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...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...Wherefore, if a straight line, &c. QED PROPOSITION 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 equal to the square of the other part. Let AB be the given straight line; it is required to...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 382 pages
...given lines are equal. PROP. XXIII. PROR. — To divide a given straight line into two parts, such that the rectangle contained by the whole and one of the parts may have a given ratio to the square of the other. Let AB (see the last figure) be the given line ; it...
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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 of the parts shall be equal to the square of the other." If we call x the greater of the two parts, and, therefore,...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...AC, CD. 'Wherefore, If a straight line %c. PROP. XI. 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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...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 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...
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Minutes of the Committee of Council on Education, Volume 1

Great Britain. Committee on Education - School buildings - 1847 - 606 pages
...the angle contained by these two sides is a right angle. SECTION II. 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...
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