 | Trinity College (Dublin, Ireland) - 1911 - 614 pages
...another the angle subtended by the first is greater than that subtended by the second. 5. Divide a line into two parts so that the rectangle contained by the whole line and one part shall be equal to the square of the other part. 6. Prove that the rectangle contained... | |
 | Great Britain. Board of Education - Mathematics - 1912 - 632 pages
...used.) 1. Prove that the diagonals of a parallelogram bisect one another. 2. Divide a straight line so that the rectangle contained by the whole and one of the parts shall be equal to the square on the remaining part. Prove that the difference of the squares on the whole and on the remaining part is... | |
 | Great Britain. Board of Education - Education - 1912 - 1044 pages
...middle points of BC, B'C', respectively, prove that AU is less than A'O1. 2. Divide a straight line so that the rectangle contained by the whole and one of the parts shall be equal to the square on the remaining part. Prove that the difference of the squares on the whole and on the remaining part is... | |
 | Newfoundland Council of Higher Education - 1912 - 300 pages
...sides, prove that the angle contained by those two sides is a right angle. Show, without proof, how to divide a given straight line into two parts, so that the sum of the squares on the two parts may be to the square on the whole line as 9 is to 16. (12) 7. Prove... | |
 | Florian Cajori, Letitia Rebekah Odell - Algebra - 1915 - 240 pages
...geometric construction. In proposition 11, of Book II, of the Elements, Euclid solved by drawing lines the problem : To divide a given straight line into two...parts, so that the rectangle contained by the whole line and one part of it may be equal to the square on the other part. In algebra, this problem demands... | |
 | Muḥammad ibn Mūsá Khuwārizmī - Literature, Medieval - 1915 - 206 pages
...square on the remaining segment. " Let AB be the given straight line ; thus it is required to cut AB so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment. 1 References and citations from the Elements... | |
 | Jay Hambidge - Decoration and ornament - 1920 - 212 pages
...(who flourished about 300 BC), the following propositions occur: (i) "To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment" (Book II, proposition II); (2) "To cut a... | |
 | David E. Smith - Mathematics - 1958 - 756 pages
...also gives in the Elements such geometric problems as the following : To cut a given straight line so that the rectangle contained by the whole and one of the segments shall be equal to the square on the remaining segment.3 This may be represented algebraically... | |
 | Saskatchewan. Department of Education - Education - 1910 - 260 pages
...sides, prove that the square on the longer diagonal is three times the square on the shorter. 4. (a) To divide a given straight line into two parts, so...rectangle contained by the whole and one of the parts may be equal to the square on the other part. II. 11. (6) Divide a given straight line externally in... | |
 | Morris Kline - Mathematics - 1990 - 434 pages
...EUCLID AND APOLLONIUS H D Figure 4. 10 Figure 4. 11 Proposition 1 1 . To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment. This requires that we divide AB (Fig. 4.10)... | |
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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. 
