 | American Academy of Arts and Sciences - 1913 - 1092 страница
...and most of the relations connecting them will be the same as in Euclidean plane geometry. Thus : 4 1°. Through two points one and only one line can...translations and rotations, of which the former alone arc the same for our geometry. It seems desirable, therefore, to discuss first and in some detail the... | |
 | American Academy of Arts and Sciences - 1913 - 1092 страница
...and most of the relations connecting them will be the same as in Euclidean plane geometry. Thus : 4 1°. Through two points one and only one line can...than did Euclid. The transformations of Euclidean geomi'trjf may be divided into translations and rotations, of which the former alone are the same for... | |
 | Richard Courant, Herbert Robbins - 1996 - 596 страница
...rays, is by no means obvious. This is the famous postulate of the unique parallel, which states that through any point not on a given line one and only one line can be drawn parallel to the given line. The remarkable feature of this axiom is that it makes... | |
 | Constance Reid - 2004 - 306 страница
...axioms. The most easily grasped statement is a later one, known as the Postulate of the Unique Parallel: Through any point not on a given line, one and only one line can he drawn which will never meet the given line. Now let us make a contrary assumption and let... | |
 | Aryeh Carmell - 1976 - 552 страница
...still produce consistent but non-Euclidean Geometries. (The Euclidean parallel postulate states that through any point not on a given line one and only one line can be drawn parallel to the given line. The nonEuclidean cases are that either none or any number... | |
| |
Thus : 4 1°. Through two points one and only one line can be drawn. 2°. Two lines intersect in one and only one point, except that 3°. Through any point not on a given line one and only one parallel (non-intersecting) line can be drawn. 4°. The line... 