Page:Carroll - Euclid and His Modern Rivals.djvu/230

192 which is opposite to the right angle,' where you clearly assume that it cannot have more than one.

P. 12, Def. 32. 'When two of the sides have been mentioned, the remaining side is often called the base.' Well, but how if two of the sides have not been mentioned?

Nos. In that case we do not use the word.

Min. Do you not? Turn to p. 22, Th. 2, Cor. 1, 'Triangles on the same or equal bases and of equal altitude are equal.'

Nos. We abandon the point.

Min. You had better abandon the Definition.

P. 12, Def. 34. Is not 'identically equal' tautology? Things that are 'identical' must surely be 'equal' also. Again, 'every part of one being equal,' &c. What do you mean by 'every part' of a rectilineal figure?

Nos. Its sides and angles, of course.

Min. Then what do you mean by Ax (b) in p. 3. 'The whole is equal to the sum of its parts'? This time, I think I need not 'pause for a reply'!

P. 15, Def. 38. 'When a straight Line intersects two other straight Lines it makes with them eight angles etc.'



Let us count the angles at G. They are, the 'major'