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" If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square on the half. "
The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History - Página 11
de Reviel Netz - 2003 - 352 páginas
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School Science and Mathematics, Volume 20

1920
...illustration of the algebraical content of one of these theorems, let us examine Euclid II, 5: "If a line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole, together with the square on the straight line between the points of section, is equal to the square...
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Introduction and books 1,2

Euclid - 1908
...with twice the rectangles contained by every pair of the parts. PROPOSITION 5. If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square...
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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
...following Heath, The Thirteen Books of Euclid's Elements, reads as follows : " If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square...
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A Source Book in Medieval Science

Edward Grant - 1974 - 864 páginas
...(DC)*; therefore, CE = 1. 84. Elements, Book II, Proposition 5 (Heath, 1, 382): "If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square...
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The Beginnings of Greek Mathematics

A. Szabó - 1978 - 358 páginas
...II. 6, let me begin by quoting both of these propositions: Proposition II. 5: "If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square...
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The Emergence of Number

John N. Crossley - 1987 - 222 páginas
...propositions are as follows (in Heath's translation: Book II, Proposition 5. If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square...
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Mathematical Expeditions: Chronicles by the Explorers

Reinhard Laubenbacher, David Pengelley - 2000 - 278 páginas
...a gnomon. FIGURE 5.2. Gnomon. CD B FIGURE 5.3. Proposition 5. PROPOSITION 5. If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square...
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Galois' Theory of Algebraic Equations

Jean-Pierre Tignol - 2001 - 333 páginas
...the Elements. For instance, Proposition 5 of Book II states [30, v. I, p. 382]: If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square...
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From Discrete to Continuous: The Broadening of Number Concepts in Early ...

K. Neal - 2002 - 175 páginas
...the standard version given in Heath leaps out. The proof is usually stated as "If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square...
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Classics in the History of Greek Mathematics

Jean Christianidis - 2004 - 474 páginas
...= ¿ Let us now proceed to the promised examples. Proposition 11.5 states: ‘If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments ofthe whole together with the square on the straight line between the points of section is equal to...
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