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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. "
A Treatise on Surveying, Containing the Theory and Practice: To which is ... - Page 26
by John Gummere - 1814 - 346 pages
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Journal of the Elisha Mitchell Scientific Society, Volumes 20-23

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...
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Journal of the Elisha Mitchell Scientific Society, Volumes 21-23

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:...
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A History of Elementary Mathematics: With Hints on Methods of Teaching

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...
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Memoir of Theophilus Parsons: Chief Justice of the Supreme Judicial Court of ...

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,...
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Mathematics for the Million

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...
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The Mathematical Work of Charles Babbage

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...
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A History of Elementary Mathematics

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...
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The American Mathematical Monthly: Devoted to the Interests of Collegiate ...

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...
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Journal of the Elisha Mitchell Scientific Society, Volume 23

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...
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The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science

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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