Page:Carroll - Euclid and His Modern Rivals.djvu/236

198 in some future fit of inspiration he should bring out a yet more agonising version of it.

But it has the usual hiatus of a system which replaces Euclid's Axiom by Playfair's: it provides no means of proving that the Lines contemplated by Euclid will meet if produced. (This I have discussed at p. 187.)

Its proposed changes in the sequence of Euclid I have discussed at p. 188.

It has a few other faults, which I have already discussed in Mr. Wilson's own book, and a few peculiar to the Syllabus; but I spare you such minute criticisms.

But what I have now to ask you is simply this. What possible pretext have you left for suggesting that Euclid's Manual, and specially his sequence and numeration, should be abandoned in favour of this far from satisfactory infant?

Nie. There are some new Theorems

Min. Those constitute no reason: you might easily interpolate them.

Nie. I fear there are no other grounds to urge. But I should like to consult the doppelgänger of the Association before I throw up my brief.

Min. By all means.

[''For a minute or two there is heard a rustling and a whispering, as of ghosts. Then  speaks again.'']

Nie. They think that, considering that this book is but just published, and that it is definitely put forward as the Manual to supersede Euclid, it ought to be examined more in detail, with reference to what is new in