... far prolonged, the same distance apart, that is, never intersect. They have the properties of the Euclidean parallels, and may be called and defined as such. It likewise follows, now, from the properties of triangles and rectangles, that two straight... Lectures on Fundamental Concepts of Algebra and Geometry - Page 26by John Wesley Young, William Wells Denton, Ulysses Grant Mitchell - 1911 - 247 pagesFull view - About this book
| Webster Wells - Geometry - 1886 - 371 pages
...two of its angles, it is perpendicular to the other diagonal. 4. If two lines are cut by a third so **as to make the sum of the interior angles on the same side of the** secant line less than two right angles, the lines will meet if sufficiently produced. 6. If exterior... | |
| Edward C. Hegeler - Philosophy - 1904
...properties of triangles and rectangles, that two straight lines which are cut by a third straight line so **as to make the sum of the interior angles on the same side of** them less than two right angles will meet on that side, but in either direction from their point of... | |
| Ernst Mach - Mathematics - 1906 - 144 pages
...properties of triangles and rectangles, that two straight lines which are cut by a third straight line so **as to make the sum of the interior angles on the same side of** them less than two right angles will meet on that side, but in either direction from their point of... | |
| Ernst Mach - Mathematics - 1906 - 144 pages
...properties of triangles and rectangles, that two straight lines which are cut by a third straight line so **as to make the sum of the interior angles on the same side of** them less than two right angles will meet on that side, but in either direction from their point of... | |
| JOHN WESLEY YOUNG - 1911
...up a valid geometry ? " * Gt POINCABE, loc. cit.9 p. 39. LECTURE III ON THE HISTOKY OF THE PAEALLEL **POSTULATE Euclid's Attitude toward his Fifth Postulate....are cut by a transversal in such a way as to make** the sum of the interior angles on the same side of the transversal less than two right angles, then... | |
| Morris Kline - Mathematics - 1981 - 482 pages
...rested. As stated by Euclid, the axiom runs as follows: 1f two lines in one plane intersect a third in **such a way as to make the sum of the interior angles on** one side of the third line less than two right angles, then these two lines will meet on that side... | |
| Education - 1897
...which the conclusion is reached. He says: If parallel lines meet at infinity, then two lines which **are cut by a transversal in such a way as to make** equal alternate interior angles are parallel, and he is vastly interested in establishing his conclusion,... | |
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