| Elisha Mitchell Scientific Society (Chapel Hill, N.C.) - Natural history - 1904
...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.) - Natural history - 1905
...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:... | |
| Florian Cajori - Mathematics - 1917 - 304 pages
...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 - Judges - 1859 - 476 pages
...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 Thomas Hogben - Mathematics - 1968 - 648 pages
...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 - Science - 2004 - 244 pages
...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 - Mathematics - 2007 - 336 pages
...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... | |
| Mathematicians - 1894
...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... | |
| Elisha Mitchell Scientific Society (Chapel Hill, N.C.) - Natural history - 1907
...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...which being produced ever so far both ways do not** meet.'1'' To cite a few classic definitions, Wolf, Boscovich, and T. Simpson use the following: "Straight... | |
| Physics - 1853
...Alumina . . . 31-87 Glucina . . . 21-43 Peroxide of iron . 1-31 Peroxide of tin . •35 " Parallel right **lines are such as are in the same plane, and which, being produced** continually in both directions, would never meet." Adopting this definition, we are forced to give... | |
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