Euclid and His Modern RivalsCourier Corporation, 5. mars 2014 - 320 sider The author of Alice in Wonderland (and an Oxford professor of mathematics) employs the fanciful format of a play set in Hell to take a hard look at late-19th-century interpretations of Euclidean geometry. Carroll's penetrating observations on geometry are accompanied by ample doses of his famous wit. 1885 edition. |
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Side 1
... Lines, which make equal angles with one Line, do so with all Lines. He might just as well say that a young lady, who was inclined to one young man, was 'equally and similarly inclined ' to all young men ! Rhad. She might ' make equal ...
... Lines, which make equal angles with one Line, do so with all Lines. He might just as well say that a young lady, who was inclined to one young man, was 'equally and similarly inclined ' to all young men ! Rhad. She might ' make equal ...
Side 17
... a Parallel. Although it has been proved in I. 27 that such things as parallel Lines exist, that does not tell us that, for every Line and for every point without that Line, there exists a real Line, parallel to the given Line and ...
... a Parallel. Although it has been proved in I. 27 that such things as parallel Lines exist, that does not tell us that, for every Line and for every point without that Line, there exists a real Line, parallel to the given Line and ...
Side 26
... given a Line and a point, it is possible to draw a Line, through the given point, intersectional with the given Line. 4. A Pair of intersectional Lines are unequally inclined to any transversal. Cor. I. In either pair of alternate ...
... given a Line and a point, it is possible to draw a Line, through the given point, intersectional with the given Line. 4. A Pair of intersectional Lines are unequally inclined to any transversal. Cor. I. In either pair of alternate ...
Side 27
... given a Line and a point without it, it is possible to draw a Line, through the given point, separational from the given Line. [I. 31.] 8. A Pair of intersectional Lines are such that any two points on one, which are on the same side of ...
... given a Line and a point without it, it is possible to draw a Line, through the given point, separational from the given Line. [I. 31.] 8. A Pair of intersectional Lines are such that any two points on one, which are on the same side of ...
Side 28
... given a Line and a point without it: it is possible to draw a Line, through the given point, having a direction different from that of the given Line. 17. A Line, which has a point in common with one of two coincidental Lines has a ...
... given a Line and a point without it: it is possible to draw a Line, through the given point, having a direction different from that of the given Line. 17. A Line, which has a point in common with one of two coincidental Lines has a ...
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admit adopted allow already assert assume Axiom axiomatic beginners better Certainly coincide common point conclusion consider construct contain course curve define Definition demonstration different directions discussed draw drawn edition equal equally inclined equidistant Euclid examining exist fact fear figure Geometry give given Line grant greater instance intersectional length less limit logical magnitude Manual mathematical matter mean meet method moving necessary NIEMAND opposite Pair of Lines parallel pass perpendicular Plane position possible principle Problems produced proof Prop proposed Propositions prove question reason refer remaining remark right angles right Line Rivals separational sequence side straight Line suppose surely Table teaching Theorem thing third tion transversal Triangle true turn Unabridged republication whole Wilson writer دو