 | George Holmes Howison, Joseph Ray - 1869 - 622 Seiten
...diameters, we shall have an inscribed parallelogram. Thus the diagram of Art. 478 is verified ; for, as only one parallel to a given line can be drawn through a given point, lines drawn through the extremities of conjugate diameters so as to form their parallelogram must be... | |
 | William Guy Peck - 1876 - 412 Seiten
...DE, and at A draw AC perpendicular to AD ; then will AC be parallel to DE. It is assumed that only one parallel to a given line can be drawn through a given point ; hence, if a line is perpendicular to one of two parallels, it is also perpendicular to the other.... | |
 | 1877 - 626 Seiten
...there is no question raised. One of the most immediate consequences of the eleventh axiom is that only one parallel to a given line can be drawn through a given point. But in the non-Euclidian Geometry the line cuts the fundamental conic in two points, and cither of... | |
 | Eugene Randolph Smith, William Henry Metzler - 1918 - 232 Seiten
...true. But if C is true, H may be either true or untrue without bringing in a contradiction ; and if H is untrue, C may be true or untrue without bringing...the method of reasoning from statements covering all possibilities, which will be given later. NOTE. It should be observed in these examples of the methods... | |
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To prove the conclusion, it is necessary to use the additional geometrical principle that but one parallel to a given line can be drawn through a given point. 