Page:Carroll - Euclid and His Modern Rivals.djvu/138

100 Nie. That would be true, no doubt.

Min. But this extension of limit will require several modifications in Euclid's language: for instance, what is your Definition of an obtuse angle?

P. 8. Def. 13. 'An obtuse angle is one which is greater than a right angle.'

Min. So you tumble headlong into the very first pitfall you come across! Why, that includes such angles as 180° and 360°. You would teach your pupil, I suppose, that one portion of a straight Line makes an obtuse angle with the other, and that every straight Line has an obtuse angle at each end of it!

Nie. It is an oversight—of course we ought to have added 'but less than two right angles.'

Min. A very palpable oversight. I fear we shall find more as we go on. What Axioms have you about angles?

P. 5. Ax. 4. 'An angle may be conceived as transferred to any other position, its magnitude being unaltered.'

Min. Hardly worth stating. Proceed.

P. 5. Ax. 5. 'Angles are equal when they could be placed on one another so that their vertices would coincide in position, and their arms in direction.'

Min. 'Placed on one another'! Did you ever see the child's game, where a pile of four hands is made on the