| Trinity College (Dublin, Ireland) - 1911 - 616 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 - 1048 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 - 296 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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