 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...line intersect one of two parallel right lines it must also intersect the other.' ' Only one right line can be drawn through a given point parallel to a given right line.' The axiom expressed by the first of these ways appears to me to be as unobjectionable,... | |
 | Euclides - 1858 - 248 pages
...axiom and its converse should be so obvious as not to require demonstration. 3. ' ' The Twelfth A xiom may be expressed in any of the following ways : —...must also intersect the other : or, Only one rt. line cau be drawn through a given point parallel to a given rt. line." — LARDNER, p. 316. 4. The least... | |
 | Euclides - 1870 - 270 pages
...both the assumed axiom and its converse should be so obvious as not to require demonstration. 3. " The Twelfth Axiom may be expressed in any of the following...drawn through a given point parallel to a given rt. line." — LARDXER, p. 316. 4. The least objectionable definition of parallel st. lines is — " Parallel... | |
 | Gerardus Beekman Docharty - Calculus - 1865 - 328 pages
...parallel to a given line, then the angle which the line makes with the axis is known, and only one line can be drawn through a given point parallel to a given line. Illustration. If we were required to draw a line through the point P, whose abscissa AB is 8,... | |
 | Henry Martyn Taylor - 1893 - 486 pages
...intersecting straight lines cannot both be parallel to the same straight line. 2. Only one straight line can be drawn through a given point parallel to a given straight line. 3. If two straight lines, each of which is parallel to a third straight line, meet,... | |
 | Webster Wells - Geometry - 1894 - 400 pages
...plane are parallel.] (§ 411.) But through C, only one parallel can be drawn to AB. [But one straight line can be drawn through a given point parallel to a given straight line.] (§ 53.) Whence, CD is perpendicular to MN. 413. COB. II. If each of two straight lines... | |
 | George Clinton Shutts - Geometry - 1894 - 412 pages
...greater than one of two equal magnitudes is less or greater, respectively, than the other. 18. Only one line can be drawn through a given point parallel to a given line. POSTULATE i. — A line can be revolved about a given point until it embraces another point or... | |
 | Henry Martyn Taylor - Euclid's Elements - 1895 - 708 pages
...intersecting straight lines cannot both be parallel to the same straight line. 2. Only one straight line can be drawn through a given point parallel to a given straight line. 3. If two straight lines, each of which is parallel to a third straight line, meet,... | |
 | Webster Wells - Geometry - 1898 - 284 pages
...cannot meet however far they may be produced; as AB and CD. ® D 53. Ax. We assume that but one straight line can be drawn through a given point parallel to a given straight line. PROP. XI. THEOREM. 54. Two perpendiculars to the same straight line are parallel. I... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...one another, however far they may be produced; as AB and CD. A B D 60. AXIOMS. 1. But one straight line can be drawn through a given point parallel to a given straight line. 2. Since parallel lines cannot approach one another, they are everywhere equally distant... | |
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We assume that but one straight line can be drawn through a given point parallel to a given straight line. 
