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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... "
The first six books of the Elements of Euclid, with numerous exercises - Seite 4
von Euclides - 1853 - 147 Seiten
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Principles of Class Teaching

Joseph John Findlay - 1902 - 442 Seiten
...proposition (it is numbered as the first part of Proposition 28) : — If a straight line meet two other straight lines, so as to make the two interior angles on the same side supplementary, the lines will never meet, although produced ever so far. You can prove it by assuming...
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A Text-book of Euclid's Elements for the Use of Schools, Bücher 1

Euclid - 1904 - 456 Seiten
...straight lines is based upon his twelfth Axiom, which we here repeat. AXIOM 12. If a straight line cut two straight lines so as to make the two interior angles on the same side of it together less than two right angles, these straight lines, being continually produced, will at length...
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School Science and Mathematics, Band 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 Seiten
...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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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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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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A Short Account of the History of Mathematics

Walter William Rouse Ball - 1908 - 522 Seiten
...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 Seiten
...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 Seiten
...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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Solid Geometry

Charles Austin Hobbs - 1921 - 192 Seiten
...corresponding angles equal, the two lines are parallel. Prop. 41. If two lines are cut by a transversal so as to make the two interior angles on the same side of the transversal supplementary, the lines are parallel. Prop. 41, Cor. II. Two lines respectively perpendicular...
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