Page:Carroll - Euclid and His Modern Rivals.djvu/19

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

PAGE

Other subjects of enquiry:—
....................................................................................................................................................................................................................................................
15
(3)
Superposition;
 
(4)
Use of diagonals in Euc. II;
 
(5)
Treatment of Lines;
 
(6)
Treatment of Angles;
 
(7)
Euclid's Propositions omitted;
 
(8)
Euclid's Propositions newly treated;
 
(9)
New Propositions;
 
(10)
Style, &c.
 
List of authors to be examined, viz.:—
....................................................................................................................................................................................................................................................
16
 
Legendre, Cooley, Cuthbertson, Henrici, Wilson, Pierce, Willock, Chauvenet, Loomis, Morell, Reynolds, Wright, Syllabus of Association for Improvement of Geometrical Teaching, Wilson's 'Syllabus'-Manual.
 

§ 3. The combination, or separation of Problems and Theorems.


Reasons assigned for separation
....................................................................................................................................................................................................................................................
18
Reasons for combination:—
....................................................................................................................................................................................................................................................
19
(1)
Problems are also Theorems;
 
(2)
Separation would necessitate a new numeration,
 
(3)
and hypothetical constructions.
 

§ 4. Syllabus of propositions relating to Pairs of Lines.


Three classes of Pairs of Lines:—
....................................................................................................................................................................................................................................................
20
(1)
Having two common points;