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" If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles... "
The Elements of Euclid, containing the first six books, with a selection of ... - Side 6
av Euclides - 1874
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School Science and Mathematics, Volum 18

1918
...given straight line." Either form is much simpler than Euclid's statement: "If a straight line meet two straight lines so as to make the two interior...lines, being 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...
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Euclid's Parallel Postulate: Its Nature, Validity, and Place in Geometrical ...

John William Withers - 1905 - 192 sider
...Two straight lines cannot inclose a space; n, All right angles are equal; 12, If a straight line meet two straight lines, so as to make the two interior...lines being 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 WILLAIM WITHERS - 1905
...less than two right angles, these straight lines being 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, except the most recent, these are called " axioms "• and classed,...
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Space and Geometry in the Light of Physiological, Psychological and Physical ...

Ernst Mach - 1906 - 144 sider
...Fifth Postulate (also called the Eleventh Axiom and by some the Twelfth) : "If a straight line meet two straight lines, so as to make the two interior...the angles which are less than two right angles." Euclid easily proves that if a straight line falling on two other straight lines makes the alternate...
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Space and Geometry in the Light of Physiological, Psychological and Physical ...

Ernst Mach - 1906 - 144 sider
...Fifth Postulate (also called the Eleventh Axiom and by some the Twelfth) : "If a straight line meet two straight lines, so as to make the two interior...the angles which are less than two right angles." Euclid easily proves that if a straight line falling on two other straight lines makes the alternate...
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Henley's Encyclopaedia of Practical Engineering and Allied Trades ...

1906
...cannot enclose a space. 11. All right angles are equal to one another. 12. If a straight line meet two straight lines, so as to make the two interior...lines, being 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...
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Henley's Encyclopædia of Practical Engineering and Allied Trades: A ...

Joseph Gregory Horner - 1906
...cannot enclose a space. 11. All right angles are equal to o,ne another. 12. If a straight line meet two straight lines, so as to make the two interior...lines, being 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...
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A Short Account of the History of Mathematics

Walter William Rouse Ball - 1908 - 522 sider
...Among Euclid's axioms and postulates is one on parallel lines, which is usually stated iu the form that if a straight line meets two straight lines, so as to make the sum of the two interior angles on the same side of it taken together less than two right angles, then...
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A Short History of Science

William Thompson Sedgwick, Harry Walter Tyler - 1917 - 474 sider
...known as Axioms 11 and 12, — "All right angles are equal " ; and the famous parallel axiom : — "If a straight line meets two straight lines, so as...make the two interior angles on the same side of it together less than two right angles, these straight lines will meet if produced on that side." The...
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Lectures on the Philosophy of Mathematics

James Byrnie Shaw - 1918 - 206 sider
...non-Euclidean geometry. Euclid had among his postulates one which read thus : If a straight line meet two straight lines so as to make the two interior...continually produced, shall at length meet upon that side of the line on which are the angles which are less than two right angles. For ages mathematicians endeavored...
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