< Page:Carroll - Euclid and His Modern Rivals.djvu
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xxix
ARGUMENT OF DRAMA.
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Reasons for retaining it:—
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needed to prove I. 8
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not included in new I. 8
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proves rigidity of Triangle
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I. 7, 8 analogous to III. 23, 24
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bears on practical science
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Omission of II. 8 suggested
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Reason for retaining it, its use in Geometrical Conic Sections
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Alterations suggested:—
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New proofs for I. 5:—
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'hypothetical construction'
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superposition
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treating sides as 'obliques'
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„ as radii of a Circle
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Inversion of order of I. 8, 24 rejected
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„ I. 18,19,20; do.
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Fuller proof of I. 24; accepted
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Algebraical proofs of II.; rejected
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Additions suggested:—
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New Axiom; accepted
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Two new Theorems; do.
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§ 7. The summing-up.
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Euclid's farewell speech
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