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" If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles... "
Elements of geometry, based on Euclid, books i-iii - Side 9
av Edward Atkins - 1876 - 119 sider
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The Monist, Volum 13

1903
...is only one form of the conception of parallelism. So it was formulated axiomatically as follows : " If a straight line meet two straight lines, so as...lines being continually produced, shall at length meet upon that side on which are the angles which are less than two right angles." This dogmatic statement...
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A Text-book of Euclid's Elements for the Use of Schools, Bok 1

Euclid - 1904 - 456 sider
...another, are equal. 10. Two straight lines cannot enclose a space. 11. All right angles are equal. 12. If a straight line meet two straight lines so as to make the interior angles on one side of it together less than two right angles, these straight lines will meet...
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EUCLID'S PARALLEL POSTULATE: ITS NATURE, VALIDITY, AND PLACE IN GEOMETRICAL ...

JOHN WILLAIM WITHERS - 1905
...They are as follows: 10, Two straight lines cannot inclose a space; n, All right angles are equal; 12, If a straight line meet two straight lines, so...continually produced, shall at length meet on that side on which are the angles which are less than two right angles. 8 In nearly all modern editions,...
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Euclid's Parallel Postulate: Its Nature, Validity, and Place in Geometrical ...

John William Withers - 1905 - 192 sider
...They are as follows: 10, Two straight lines cannot inclose a space; n, All right angles are equal; 12, If a straight line meet two straight lines, so...continually produced, shall at length meet on that side on which are the angles which are less than two right angles.8 In nearly all modern editions,...
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School Science and Mathematics, Volum 18

1918
...parallel can be drawn to a given straight line." Either form is much simpler than Euclid's statement: "If a straight line meet two straight lines so as...continually produced, shall at length meet on that side on which are the angles which are less than two right angles." Playfair himself laid no claim...
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Henley's Encyclopædia of Practical Engineering and Allied Trades: A ...

Joseph Gregory Horner - 1906
...equal to one another. 9. The whole is greater than its part. 10. Two straight lines cannot enclose a space. 11. All right angles are equal to o,ne another....continually produced, shall at length meet on that side on which are the angles which are less than two right angles. Axis. — This term has numerous...
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Henley's Encyclopaedia of Practical Engineering and Allied Trades ...

1906
...equal to one another. 9. The whole is greater than its part. 10. Two straight lines cannot enclose a space. 11. All right angles are equal to one another....continually produced, shall at length meet on that side on which are the angles which are less than two right angles. Axis. — This term has numerous...
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Space and Geometry in the Light of Physiological, Psychological and Physical ...

Ernst Mach - 1906 - 144 sider
...system is found the so-called Fifth Postulate (also called the Eleventh Axiom and by some the Twelfth) : "If a straight line meet two straight lines, so as...lines being continually produced, shall at length meet upon that side on which are the angles which are less than two right angles." Euclid easily proves...
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Space and Geometry in the Light of Physiological, Psychological and Physical ...

Ernst Mach - 1906 - 144 sider
...system is found the so-called Fifth Postulate (also called the Eleventh Axiom and by some the Twelfth) : "If a straight line meet two straight lines, so as...lines being continually produced, shall at length meet upon that side on which are the angles which are less than two right angles." Euclid easily proves...
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Winged Words

Henry Heathcote Statham - 1907 - 281 sider
...248-252. t It may save some readers the trouble of referring to their Euclid to print the axiom here : " If a straight line meet two straight lines so as to make the interior angles on one side of it together less than two right angles, these straight lines will meet...
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