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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. "
Elements of geometry, based on Euclid, books i-iii - Page 71
by Edward Atkins - 1876 - 119 pages
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Mathematical Expeditions: Chronicles by the Explorers

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...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid - 2001 - 420 pages
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Apollonius of Perga's Conica: Text, Context, Subtext

Michael N. Fried, Sabetai Unguru - Architecture - 2001 - 520 pages
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Greek Science of the Hellenistic Era: A Sourcebook

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...
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Mathematics and the Divine: A Historical Study

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...
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Montanregion Harz

Laure Lévêque - Europe - 2006 - 498 pages
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Craftsmanship in the Teaching of Elementary Mathematics

F. W. Westaway - Mathematics - 2007 - 688 pages
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A History of Abstract Algebra

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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Amazing Traces of a Babylonian Origin in Greek Mathematics

Jöran Friberg - Mathematics - 2007 - 476 pages
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