 | Saskatchewan. Department of Education - 1910 - 260 Seiten
...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 the 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... | |
 | 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... | |
 | 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,... | |
 | Reinhard Laubenbacher, David Pengelley - 2000 - 292 Seiten
...Hint: See Figure 5.6. Exercise 5.9: Proposition 1 1 in Book II states: 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. Which type of quadratic equation can be solved... | |
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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. 
