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 xxvi
... Lines and Angles. Treatment of Line 217 Angle :— ' declination from ' accepted . . . .218 must be less than sum of two right angles . ,, ' multiple angles ' in VI. 33 . . . „ proof for Ax. 10 accepted . . . .211) 6. Omissions ...
... Lines and Angles. Treatment of Line 217 Angle :— ' declination from ' accepted . . . .218 must be less than sum of two right angles . ,, ' multiple angles ' in VI. 33 . . . „ proof for Ax. 10 accepted . . . .211) 6. Omissions ...
Side 1
... Right Lines are said to be parallel when they are equally and similarly inclined to the same right Line, or make equal angles with it towards the same side.' Min. That is very soothing. So far as I can make it out, Mr. Cooley quietly ...
... Right Lines are said to be parallel when they are equally and similarly inclined to the same right Line, or make equal angles with it towards the same side.' Min. That is very soothing. So far as I can make it out, Mr. Cooley quietly ...
Side 17
... right would you have, in I. 47, to say ' draw a Square ' ? How would you know it to be possible ? Min. We could ... Line and for every point without that Line, there exists a real Line, parallel to the given Line and passing through the ...
... right would you have, in I. 47, to say ' draw a Square ' ? How would you know it to be possible ? Min. We could ... Line and for every point without that Line, there exists a real Line, parallel to the given Line and passing through the ...
Side 19
... right Line joining them ; and, by 'the distance of a point from a Line/ the length of the perpendicular drawn, from the point, to the Line. Now the properties of a Pair of Lines may be ranged under four headings : — (1) as to common or ...
... right Line joining them ; and, by 'the distance of a point from a Line/ the length of the perpendicular drawn, from the point, to the Line. Now the properties of a Pair of Lines may be ranged under four headings : — (1) as to common or ...
Side 27
... right angles. T 17.] 5. A Pair of Lines, which have a common point and are equally inclined to a certain transversal ... Line and a point without it, it is possible to draw a Line, through the given point, separational from the given ...
... right angles. T 17.] 5. A Pair of Lines, which have a common point and are equally inclined to a certain transversal ... Line and a point without it, it is possible to draw a Line, through the given point, separational from the given ...
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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