| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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