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