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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. "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Page 60
by Robert Simson - 1806 - 518 pages
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Dynamic Symmetry: The Greek Vase

Jay Hambidge - Decoration and ornament - 1920 - 161 pages
...(who flourished about 300 BC), the following propositions occur: (i) "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" (Book II, proposition II); (2) "To cut a...
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History of Mathematics, Volume 2

David E. Smith - Mathematics - 1958 - 736 pages
...also gives in the Elements such geometric problems as the following : To cut a given straight line so that the rectangle contained by the whole and one of the segments shall be equal to the square on the remaining segment.3 This may be represented algebraically...
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Mathematical Thought from Ancient to Modern Times: Volume 1

Morris Kline - Mathematics - 1990 - 428 pages
...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 - Technology & Engineering - 1997 - 198 pages
...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 - History - 1998 - 392 pages
...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 James Roche, ROCHE - Mathematics - 1998 - 330 pages
...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 - Mathematics - 2000 - 278 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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Greek Science of the Hellenistic Era: A Sourcebook

Georgia Lynette Irby, Georgia Lynette Irby-Massie, Paul Turquand Keyser - History - 2002 - 392 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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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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