Читать книгу Euclid and His Modern Rivals - Charles Lutwidge Dodgson - Страница 2

London

MACMILLAN AND CO.

Oxford

PREFACE TO SECOND EDITION.

PREFACE TO FIRST EDITION.

ARGUMENT OF DRAMA.

ACT I.

Preliminaries to examination of Modern Rivals.

ACT II.

Manuals which reject Euclid's treatment of Parallels.

ACT III.

Manuals which adopt Euclid's treatment of Parallels.

ACT IV.

Manual of Euclid.

APPENDICES.

I.

II.

III.

IV.

ACT I.

Scene I.

ACT I.

Scene II.

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

§ 2. Method of procedure in examining Modern Rivals .

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

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

§ 5. Playfair's Axiom .

§ 6. The Principle of Superposition .

§ 7. The omission of diagonals in Euc. II. .

ACT II.

Manuals which reject Euclid's treatment of Parallels .

Scene I.

ACT II.

Scene II.

Treatment of Parallels by methods involving infinite series .

ACT II.

Scene III.

Treatment of Parallels by angles made with transversals .

ACT II.

Scene IV.

Treatment of Parallels by equidistances .

ACT II.

Scene V.

Treatment of Parallels by revolving Lines .

ACT II.

Scene VI.

Treatment of Parallels by direction .

ACT II.

Scene VI.

ACT III.

Scene I.

ACT III.

Scene I.

ACT III.

Scene I.

ACT III.

Scene I.

ACT III.

Scene I.

ACT III.

Scene I.

ACT III.

Scene II.

ACT III.

Scene II.

ACT IV.

§ 1. Treatment of Pairs of Lines .

§ 2. Euclid's Constructions.

§ 3. Euclid's Demonstrations .

§ 4. Euclid's Style .

§ 5. Euclid's treatment of Lines and Angles .

§ 6. Omissions, alterations, and additions, suggested by Modern Rivals .

§ 7. The summing-up .

ERRATUM.