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 v
... beginners" (p. 59). According to Professor Benjamin Peirce (spelled "Pierce" in the text) of Harvard (pp. 144-147), "Parallel Lines are straight Lines which have the same Direction." And how did he define Direction? "The Direction of a ...
... beginners" (p. 59). According to Professor Benjamin Peirce (spelled "Pierce" in the text) of Harvard (pp. 144-147), "Parallel Lines are straight Lines which have the same Direction." And how did he define Direction? "The Direction of a ...
Side vi
... beginners, we ought not to take as axiomatic any Theorem which can be proved by the Axioms we already possess." There is much to be said for his standpoint that the degree of rigor in Euclid's Elements is just right for high school: a ...
... beginners, we ought not to take as axiomatic any Theorem which can be proved by the Axioms we already possess." There is much to be said for his standpoint that the degree of rigor in Euclid's Elements is just right for high school: a ...
Side xvi
... . . . . .55 „ Angle . . . . . .57 ,. Parallels ......,, Test for meeting of finite Lines . . . .58 Manual unsuited for beginners . . . . .59 SCENE III. Treatment of Parallels by angles made with transversals. xviii ARGUMENT OF DRAMA.
... . . . . .55 „ Angle . . . . . .57 ,. Parallels ......,, Test for meeting of finite Lines . . . .58 Manual unsuited for beginners . . . . .59 SCENE III. Treatment of Parallels by angles made with transversals. xviii ARGUMENT OF DRAMA.
Side xxi
... beginners . . . . ,, § 3. WlLLOCK. Treatment of Parallels 150 Virtual assumption of Axiom ' different Lines may have the same direction '.....„ Assumption of Axiom ' separational Lines have the same direction ' . . . . . . .152 General ...
... beginners . . . . ,, § 3. WlLLOCK. Treatment of Parallels 150 Virtual assumption of Axiom ' different Lines may have the same direction '.....„ Assumption of Axiom ' separational Lines have the same direction ' . . . . . . .152 General ...
Side 6
... beginners, we may as well limit our discussion to the subject-matter of Books I and II. Min. I am quite of that opinion. Euc. The first point to settle is whether, for purposes of teaching and examining, you desire to have one fixed ...
... beginners, we may as well limit our discussion to the subject-matter of Books I and II. Min. I am quite of that opinion. Euc. The first point to settle is whether, for purposes of teaching and examining, you desire to have one fixed ...
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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