 | Great Britain. Board of Education - 1912 - 632 Seiten
...BD. If the sides AB, AC are 28, 9'6 centimetres respectively, calculate the leugths of BD, DC, AD. 4. Divide a given straight line into two parts so that the square on one part may be equal to the rectangle contained by the whole line and the other part. Prove... | |
 | Florian Cajori, Letitia Rebekah Odell - 1915 - 240 Seiten
...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 - 1915 - 206 Seiten
...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 - 1920 - 212 Seiten
...(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 - 1958 - 756 Seiten
...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 - 1910 - 260 Seiten
...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 that...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 - 1990 - 434 Seiten
...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)... | |
 | David Bennett - 1997 - 212 Seiten
...beauty. It was neatly summarised by Euclid in two of his propositions: "to cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the square m the remaining segment" and "to cut a given finite line in extreme... | |
 | John J. Roche - 1998 - 364 Seiten
...Euclid book II, proposition 1 1 is an example of a construction problem: 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'. Heath points out24 that this is equivalent,... | |
 | Johannes de Muris, Hubertus Lambertus Ludovicus Busard - 1998 - 398 Seiten
...radius of the circle (Campanus IV. 15 Porism). Prop. 3 reads as follows: 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 (Campanus 11.11). From Prop. 4: If the radius... | |
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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. 
