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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; viz. the first six books, together with the eleventh ... - Página 52
por Euclides - 1814
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Introduction and books 1,2

Euclid - 1908
...square on the remaining segment. Let AB be the given straight line ; thus it is required to cut AB so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment. For let the square ABDC be described on AB...
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Robert of Chester's Latin translation of the Algebra of al-Khowarizmi

Muḥammad ibn Mūsá Khuwārizmī, Muhammad ibn Mūsa (al-Khuwārazmī) - 1915 - 164 páginas
...square on the remaining segment. " Let AB be the given straight line ; thus it is required to cut AB so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment. 1 References and citations from the Elements...
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Dynamic Symmetry: The Greek Vase

Jay Hambidge - 1920 - 161 páginas
...(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, Volumen2

David E. Smith - 1958 - 736 páginas
...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 páginas
...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 páginas
...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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The Mathematics of Measurement: A Critical History

John James Roche, ROCHE - 1998 - 330 páginas
...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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De arte mensurandi

Johannes de Muris, Hubertus Lambertus Ludovicus Busard - 1998 - 392 páginas
...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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Mathematical Expeditions: Chronicles by the Explorers

Reinhard Laubenbacher, David Pengelley - 2000 - 278 páginas
...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 páginas
...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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