| Reinhard Laubenbacher, David Pengelley - Mathematics - 2000 - 292 pages
...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... | |
| Euclid - 2001 - 420 pages
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| Georgia Lynette Irby-Massie, Paul Turquand Keyser - History - 2002 - 440 pages
...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 - Mathematics - 2004 - 716 pages
...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 - Mathematics - 2007 - 168 pages
...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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