 | Morris Kline - Mathematics - 1990 - 434 pages
...segments. 1 KLL <igure4.8 66 F 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... | |
 | David Bennett - Bridges - 1997 - 212 pages
...mysteries of aesthetic 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... | |
 | John J. Roche - Mathematics - 1998 - 364 pages
...2 times 4 times 6'. 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... | |
 | Johannes de Muris, Hubertus Lambertus Ludovicus Busard - History - 1998 - 398 pages
...hexagon is equal to the 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.... | |
 | Reinhard Laubenbacher, David Pengelley - Mathematics - 2000 - 292 pages
...added straight line. 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... | |
 | Georgia Lynette Irby-Massie, Paul Turquand Keyser - History - 2002 - 440 pages
...[constructing the 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... | |
 | Jean Christianidis - Mathematics - 2004 - 502 pages
...once, I fully agree with them. Let us now examine how it was used. The problem II 1 1 reads: To cut a given straight line so that the rectangle contained by the whole and one of its segments is equal to the square ofthe remaining segment. If the given straight line... | |
 | Teun Koetsier, Luc Bergmans - Mathematics - 2004 - 716 pages
...first time, though, 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... | |
 | Israel Kleiner - Mathematics - 2007 - 168 pages
...proposition can be stated 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,... | |
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If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square... 
