 | Thomas Smith (D.D.) - 1902 - 244 Seiten
...the truth of the story. It ought to be true ! But the definition of parallel straight lines as being "such as are in the same plane, and which, being produced ever so far both ways, do not meet," is the field on which the trumpet has blared and the clang of deadly weapons has rung for generations,... | |
 | Elisha Mitchell Scientific Society (Chapel Hill, N.C.) - 1904 - 766 Seiten
...those who sought to substitute a new definition of parallels for Euclid's, which reads (I, Def. 35): "•Parallel straight lines are such as are in the same plane, and which being' produced ever so fur both -Mays do not meet." To cite a few classic definitions, Wolf, Boscovich, and T. Simpson use... | |
 | Elisha Mitchell Scientific Society (Chapel Hill, N.C.) - 1905 - 518 Seiten
...those who sought to substitute a. new definition of parallels for Euclid's, which reads (I, Def. 35): "Parallel straight lines are such as are in the same plane, and which being produced ever so far both -Mays do not meet." To cite a few classic definitions, Wolf, Boscovich, and T. Simpson use the following:... | |
 | James Welton, Alexander James Monahan - 1911 - 544 Seiten
...apply to negative definitions.2 Euclid's definition of parallel straight lines as " those which lie in the same plane, and which, being produced ever so far both ways, never meet " offends against this principle, as does his definition of a point as " that which has... | |
 | Florian Cajori - 1917 - 344 Seiten
...proving the parallelpostulate from the nature of the straight line and plane angle. Euclid's definition, parallel straight lines are such as are in the same...being produced ever so far both ways do not meet, still holds its place as the best definition for use in elementary geometry. A new definition, used... | |
 | Theophilus Parsons - 1859 - 516 Seiten
...of two finite right lines, which constitutes their parallelism. According to Euclid, parallel right lines are such as are in the same plane, and which,...being produced ever so far, both ways, do not meet. This is not a definition of the position of two finite right lines, which constitutes their parallelism,... | |
 | Lancelot Hogben - 1968 - 662 Seiten
...practical man is Euclid's definition of the word parallel. Parallel, straight lines, as defined by him, are ' such as are in the same plane and which, being produced ever so far both ways, do not meet'. Having defined them in this obscure way, he then inverts the proper order of definition and proof by... | |
 | J. M. Dubbey, John Michael Dubbey - 2004 - 248 Seiten
...another, cannot be both parallel to the same straight line.'44 It having already been defined that 'Parallel straight lines are such as are in the same...which, being produced ever so far both ways, do not meet.'45 P. Barlow wrote on the Theory of Numbers46 in 1811 in which he solved some indeterminate equations... | |
 | Florian Cajori - 2007 - 337 Seiten
...nature of the straight line and plane angle. Euclid's definition, parallel straight lines are sneh as are in the same plane, and which being produced ever so far both ways do not meet, still holds its place as the best definition for use in elementary geometry. A new definition, used... | |
 | Benjamin Franklin Finkel - 1894 - 908 Seiten
...intersect, how far soever they IMS produced. Hoisted '« Looattchewtkift Geometry. Page 12. Art. 4. •_'<!. Parallel straight lines are such as are in the same...being- produced ever so far both ways, do not meet 3d. Paralles are everywhere equidistant. From . 1 draw AD perpendicular to /if, aod through A draw... | |
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Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet. 
