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" That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. "
Introduction and books 1,2 - Страница 188
написао/ла Euclid - 1908
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Cognitive Dimensions of Social Science

Mark Turner Professor of English and Member of the Doctoral Faculty in Neuroscience and Cognitive Science University of Maryland - 2001 - 192 страница
...propositions, he made use of the parallel axiom: "If a straight line falling on two straight lines makes the interior angles on the same side less than two...produced indefinitely, meet on that side on which the angles are less than two right angles." This axiom seemed to many geometers to lack the necessary...
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Mathematics and the Roots of Postmodern Thought

Vladimir Tasiæ - 2001 - 208 страница
...All right angles are mutually congruent. P5. If a straight line falling on two straight lines makes the interior angles on the same side less than two...produced indefinitely. meet on that side on which the angles are less than the two right angles. iLe.. whenever there is a line L and a point P not on...
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A Mathematics Sampler: Topics for the Liberal Arts

William P. Berlinghoff, Kerry E. Grant, Dale Skrien - 2001 - 672 страница
...Euclid's Fifth Postulate, which says: If a straight line falling on two straight lines makes the sum of the interior angles on the same side less than two right angles, then the two straight lines, if extended indefinitely, meet on that side on which the angle sum is...
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Time and Space

Barry Dainton - 2001 - 406 страница
...version. Euclid's version is "If a straight line falling across two straight lines makes the sum of the interior angles on the same side less than two right angles, then the two straight lines intersect, if sufficiently extended on that side." 3. In a letter to Bessel,...
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Mathematics and Its History

John Stillwell - 2004 - 576 страница
...equivalent statements of Axiom />i, some obviously fairly close to it, for example, Euclid's own: That if a straight line falling on two straight lines, make...on that side on which are the angles less than the two right angles. [Heath (1925), p. 202] Other statements of Axiom P{ are less obviously equivalent...
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All the Mathematics You Missed: But Need to Know for Graduate School

Thomas A. Garrity - 2002 - 378 страница
...Euclid's beginnings. Fifth Postulate: That, if a straight line falling on two straight lines makes the interior angles on the same side less than two...on that side on which are the angles less than the two right angles. Certainly by looking at the picture necessary point / ol intersection we see that...
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Geometry: Our Cultural Heritage

Audun Holme - 2002 - 408 страница
...5. That, if a straight line falling on two straight lines make the interior angles on the same line less than two right angles, the two straight lines,...on that side on which are the angles less than the two right angles. These are the five postulates of Euclid. Among them the fifth postulate occupies...
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Mathematical Evolutions

Abe Shenitzer, John Stillwell - 2002 - 318 страница
...If a straight line falling on two straight lines makes the interior angles on the same side together less than two right angles, the two straight lines,...produced indefinitely, meet on that side on which the angles are together less than two right angles. "Now whatever else this postulate may be, self-evident...
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Greek Science of the Hellenistic Era: A Sourcebook

Georgia Lynette Irby-Massie, Paul Turquand Keyser - 2002 - 440 страница
...equal one to another, [space is homogenous] 5. If a straight line intersecting two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, extended indefinitely, intersect on the side of the angles less than two right angles, [compare Toth...
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Geometry: Our Cultural Heritage

Audun Holme - 2002 - 408 страница
...circle with any center and distance. 4. That all right angles are equal to one another. 5. That, if a straight line falling on two straight lines make the interior angles on the same line less than two right angles, the two straight lines, if produced indefinitely meet on that side...
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