Page:Carroll - Euclid and His Modern Rivals.djvu/18

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Scene II.

[Minos and Euclid.]

 

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§ I. A priori reasons for retaining Euclid's Manual.

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We require, in a Manual, a selection rather than a complete repertory of Geometrical truths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Discussion limited to subject-matter of Euc. I, II. ....................................................................................................................................................................................................................................................

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One fixed logical sequence essential ....................................................................................................................................................................................................................................................

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One system of numbering desirable ....................................................................................................................................................................................................................................................

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A priori claims of Euclid's sequence and numeration to be retained ....................................................................................................................................................................................................................................................

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New Theorems might be interpolated without change of numeration ....................................................................................................................................................................................................................................................

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§ 2. Method of procedure in examining Modern Rivals.

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Proposed changes which, even if proved to be essential, would not necessitate the abandonment of Euclid's Manual:— ....................................................................................................................................................................................................................................................

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(1)

Propositions to be omitted;

(2)

Propositions„ to be replaced by new proofs;

(3)

New Propositions to be added.

Proposed changes which, if proved to be essential, would necessitate such abandonment:— . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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(1)

Separation of Problems and Theorems;

(2)

Different treatment of Parallels.