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AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
The Educational Record of the Province of Quebec: The Medium Through which ... - Side 186
1891
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## Mathematical Thought from Ancient to Modern Times: Volume 1

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)...
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## The Architecture of Bridge Design

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...
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## De arte mensurandi

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...
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## The Mathematics of Measurement: A Critical History

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,...
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## Mathematical Expeditions: Chronicles by the Explorers

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...
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## Greek Science of the Hellenistic Era: A Sourcebook

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...
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## Mathematics and the Divine: A Historical Study

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...
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## A History of Abstract Algebra

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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