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Ideas of Euclid, by Text
[Greek, 330 - 270 BCE, Born in Alexandria. Studied at the Academy in Athens. Died in Alexandria.]
290BCE
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Elements of Geometry
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p.1
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9603
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An assumption that there is a largest prime leads to a contradiction [Brown,JR]
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p.2
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8623
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Proof reveals the interdependence of truths, as well as showing their certainty [Frege]
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p.21
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22278
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Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter]
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p.24
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8673
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Euclid's parallel postulate defines unique non-intersecting parallel lines [Friend]
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p.55
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6297
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Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Resnik]
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p.87
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8738
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Postulate 2 says a line can be extended continuously [Shapiro]
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p.106
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13907
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If you pick an arbitrary triangle, things proved of it are true of all triangles [Lemmon]
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p.183
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10250
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Euclid needs a principle of continuity, saying some lines must intersect [Shapiro]
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p.259
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10302
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Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Bernays]
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p.404
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14157
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Modern geometries only accept various parts of the Euclid propositions [Russell]
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7 Def 1
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p.194
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9894
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A unit is that according to which each existing thing is said to be one
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72a17
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p.149
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1600
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Euclid's common notions or axioms are what we must have if we are to learn anything at all [Roochnik]
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