Page:Carroll - Euclid and His Modern Rivals.djvu/30

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General survey:— ....................................................................................................................................................................................................................................................

189

A 'Theorem' is a 'statement of a Theorem' ....................................................................................................................................................................................................................................................

189„

Rule of Conversion ....................................................................................................................................................................................................................................................

190

Miscellaneous inaccuracies ....................................................................................................................................................................................................................................................

191

Summing-up ....................................................................................................................................................................................................................................................

194

 

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§2. Wilson's 'Syllabus'-Manual.

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Introductory ....................................................................................................................................................................................................................................................

195

A Theorem is a 'statement of a Theorem' ....................................................................................................................................................................................................................................................

196

Rule of Conversion ....................................................................................................................................................................................................................................................

196„

Every Theorem a 'means of measuring' ....................................................................................................................................................................................................................................................

196„

'Straight angles' ....................................................................................................................................................................................................................................................

196„

Miscellaneous inaccuracies ....................................................................................................................................................................................................................................................

196„

The Manual's one great merit ....................................................................................................................................................................................................................................................

197

No test for meeting of finite Lines ....................................................................................................................................................................................................................................................

198

Propositions discussed in detail:—

An important omission ....................................................................................................................................................................................................................................................

199

An illogical conversion ....................................................................................................................................................................................................................................................

199„

'Un enfant terrible' ....................................................................................................................................................................................................................................................

201

Summary of results:— ....................................................................................................................................................................................................................................................

206

Of 73 Propositions of Euclid, this Manual has

14 omitted;

43 done as in Euclid;

10 done by new but objectionable methods, viz.—

1 illogical;

1 'hypothetical construction';

2 needlessly using 'superposition';

2 algebraical;

4 omitting the diagonals of Euc. II.;

6 done by new and admissible methods.