英语词汇“parallel postulate”的英英意思、用法、释义、翻译、读音、例句、短语、词组-英语词典

parallel postulate n. Geometry the fifth postulate of the first book of Euclid's Elements, which states that if two straight lines are cut by a third, and the sum of the interior angles on one side of the third line is less than two right angles, then the two straight lines meet on that side of the third, or (equivalently), given a straight line and a point not on the line, there exists only one straight line through the point parallel to the given line.

ΚΠ

1878 Amer. Jrnl. Math. 1 261 The Parallel-Postulate was generally supposed to be a consequence of the nature of straight lines.

1942 G. M. Merriman To discover Math. vi. 152 Historically the non-Euclidean geometries..arose from attempts to establish Euclid's parallel postulate as a theorem based on his other more acceptable assumptions.

1991 C. B. Boyer & U. C. Merzbach Hist. Math. (ed. 2) xxiii. 521 In the paper of 1829 he [sc. Lobachevsky] became the first mathematician to take the revolutionary step of publishing a geometry specifically built on an assumption in direct conflict with the parallel postulate: Through a point C lying outside a line AB there can be drawn more than one line in the plane and not meeting AB.

单词	parallel postulate
释义	> as lemmas parallel postulate parallel postulate n. Geometry the fifth postulate of the first book of Euclid's Elements, which states that if two straight lines are cut by a third, and the sum of the interior angles on one side of the third line is less than two right angles, then the two straight lines meet on that side of the third, or (equivalently), given a straight line and a point not on the line, there exists only one straight line through the point parallel to the given line. ΚΠ 1878 Amer. Jrnl. Math. 1 261 The Parallel-Postulate was generally supposed to be a consequence of the nature of straight lines. 1942 G. M. Merriman To discover Math. vi. 152 Historically the non-Euclidean geometries..arose from attempts to establish Euclid's parallel postulate as a theorem based on his other more acceptable assumptions. 1991 C. B. Boyer & U. C. Merzbach Hist. Math. (ed. 2) xxiii. 521 In the paper of 1829 he [sc. Lobachevsky] became the first mathematician to take the revolutionary step of publishing a geometry specifically built on an assumption in direct conflict with the parallel postulate: Through a point C lying outside a line AB there can be drawn more than one line in the plane and not meeting AB. extracted from paralleln.adj.adv. < as lemmas
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