Page:Carroll - Euclid and His Modern Rivals.djvu/199

Rh P. 26. Pr. , asserts the equidistance of Parallels. This might be interpolated as Euc. I. 34. B.

Another new Theorem, that angles whose sides are parallel, each to each, are equal (which I observe is a great favourite with the Modern Rivals), seems to me a rather clumsy and uninteresting extension of Euc. I. 29.

I see several Propositions which might well be inserted as exercises on Euclid (e.g. Pr., 'Every point in the bisector of an angle is equally distant from the sides'), but which are hardly of sufficient importance to be included as Propositions: and others (e.g. Pr. , 'The bisectors of the three angles of a Triangle meet in the same point) which seem to belong more properly to Euc. III or IV. I have no other remarks to make on this book, which seems well and clearly written.