| Morris Kline - 1990 - 434 sider
...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 sider
...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 sider
...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, ROCHE - 1998 - 364 sider
...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 sider
...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... | |
| Georgia Lynette Irby-Massie, Paul T. Keyser, Paul Turquand Keyser - 2002 - 440 sider
...proportion used in the Parthenon, which we call (sqrt(5)+1)/2 = 1.618...] To cut a given straight line **so that the rectangle contained by the whole and one of the** segments is equal to die square on the remaining segment. Let AB be die given straight line (Figure... | |
| Teun Koetsier, Luc Bergmans - 2004 - 716 sider
...that this proportion occurs: in Book II, prop. 11, Euclid instructs us 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". 10 This implies that the division of AB... | |
| Israel Kleiner - 2007 - 168 sider
...algebraically as (a + b)2 — a2 + 2ab + b2. Proposition II. 1 1 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." It asks, in algebraic language, to solve... | |
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