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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 first six books of the Elements of Euclid, with numerous exercises - Seite 42
von Euclides - 1853 - 147 Seiten
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Elementary Algebra: First[-second] Year Course, Band 1

Florian Cajori, Letitia Rebekah Odell - 1915
...of Book II, of the Elements, Euclid solved by drawing lines the problem : To divide a given straight line into two parts, so that the rectangle contained by the whole line and one part of it may be equal to the square on the other part. In algebra, this problem demands...
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Dynamic Symmetry: The Greek Vase

Jay Hambidge - 1920 - 161 Seiten
...(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, Band 2

David E. Smith - 1958 - 736 Seiten
...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 - 1990 - 428 Seiten
...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 - 198 Seiten
...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 - 392 Seiten
...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 - 1998 - 330 Seiten
...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 - 278 Seiten
...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 - 2002 - 392 Seiten
...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 Seiten
...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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