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

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Other subjects of enquiry:— ....................................................................................................................................................................................................................................................

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(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.:— ....................................................................................................................................................................................................................................................

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Legendre, Cooley, Cuthbertson, Henrici, Wilson, Pierce, Willock, Chauvenet, Loomis, Morell, Reynolds, Wright, Syllabus of Association for Improvement of Geometrical Teaching, Wilson's 'Syllabus'-Manual.

 

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

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Reasons assigned for separation ....................................................................................................................................................................................................................................................

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Reasons for combination:— ....................................................................................................................................................................................................................................................

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(1)

Problems are also Theorems;

(2)

Separation would necessitate a new numeration,

(3)

and hypothetical constructions.

 

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

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Three classes of Pairs of Lines:— ....................................................................................................................................................................................................................................................

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(1)

Having two common points;