Page:Carroll - Euclid and His Modern Rivals.djvu/33

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ARGUMENT OF DRAMA.
xxix

PAGE

 
Reasons for retaining it:—
 
needed to prove I. 8
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 220
 
not included in new I. 8
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 220„
 
proves rigidity of Triangle
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 220„
 
I. 7, 8 analogous to III. 23, 24
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 221
 
bears on practical science
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 221„
Omission of II. 8 suggested
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 221„
 
Reason for retaining it, its use in Geometrical Conic Sections
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 221„
Alterations suggested:—
 
New proofs for I. 5:—
 
'hypothetical construction'
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 222
 
superposition
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 222„
 
treating sides as 'obliques'
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treating sides„ as radii of a Circle
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 223
 
Inversion of order of I. 8, 24 rejected
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Inversion of order of„ 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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 223„
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.

Euclid's farewell speech
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