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

From Wikisource
Jump to navigation Jump to search
This page has been proofread, but needs to be validated.
ARGUMENT OF DRAMA.
xxix

PAGE

 
Reasons for retaining it:—
 
needed to prove I. 8
....................................................................................................................................................................................................................................................
220
 
not included in new I. 8
....................................................................................................................................................................................................................................................
220
 
proves rigidity of Triangle
....................................................................................................................................................................................................................................................
220
 
I. 7, 8 analogous to III. 23, 24
....................................................................................................................................................................................................................................................
221
 
bears on practical science
....................................................................................................................................................................................................................................................
221
Omission of II. 8 suggested
....................................................................................................................................................................................................................................................
221
 
Reason for retaining it, its use in Geometrical Conic Sections
....................................................................................................................................................................................................................................................
221
Alterations suggested:—
 
New proofs for I. 5:—
 
'hypothetical construction'
....................................................................................................................................................................................................................................................
222
 
superposition
....................................................................................................................................................................................................................................................
222
 
treating sides as 'obliques'
....................................................................................................................................................................................................................................................
222
 
treating sides as radii of a Circle
....................................................................................................................................................................................................................................................
223
 
Inversion of order of I. 8, 24 rejected
....................................................................................................................................................................................................................................................
223
 
Inversion of order of I. 18,19,20; do.
....................................................................................................................................................................................................................................................
223
 
Fuller proof of I. 24; accepted
....................................................................................................................................................................................................................................................
223
 
Algebraical proofs of II.; rejected
....................................................................................................................................................................................................................................................
223
Additions suggested:—
....................................................................................................................................................................................................................................................
 
New Axiom; accepted
....................................................................................................................................................................................................................................................
224
 
Two new Theorems; do.
....................................................................................................................................................................................................................................................
224

§ 7. The summing-up.


Euclid's farewell speech
....................................................................................................................................................................................................................................................
225