Page:Carroll - Euclid and His Modern Rivals.djvu/224

186 Now let us regard OA 'as lying between the other two.' Which are 'the angles which it makes with the other two'? For this line OA (which you rightly call 'the mean '—lying is always mean) makes, be pleased to observe, four angles altogether—two with OB and two with OC.

Nos. I cannot answer your question. You confuse me.

Min. I need not have troubled you. I see that I can obtain an answer from the Syllabus itself. It says (at the end of Def. 11) 'when the angle contained by two lines is spoken of without qualification, the minor conjugate angle is to be understood.' Here we have a case in point, as these angles are spoken of 'without qualification.' So that the angles alluded to are both of them 'minor conjugate' angles, and lie on the same side of OA. And these we are told to call 'adjacent' angles!

How do you define a Right Angle?

Nos. As in Euclid.

Min. Let me hear it, if you please. You know Euclid has no major or minor conjugate angles.

P. 9. Def. 14. 'When one straight line stands upon another straight line and makes the adjacent angles equal, each of the angles is called a right angle.'

Min. Allow me to present you with a figure, as I see the Syllabus does not supply one.

Here AB 'stands upon' BC and makes the adjacent angles equal. How do you like these 'right angles'?