Page:Carroll - Euclid and His Modern Rivals.djvu/101

. III.] Min. As many as you like.

Nie. Well, here is our Theorem. 'When two parallel straight Lines AB, CD, are cut by a third straight Line EF, they make with it the alternate angles AGH, GHD, equal; and also the two internal angles at the same side BGH, GHD equal to two right angles.



For AGH and EGB are equal because vertically opposite, and EGB is also equal to GHD (Definition); therefore—'

Min. There I must interrupt you. How do you know that EGB is equal to GHD? I grant you that, by the Definition, AB and CD make equal angles with a certain transversal: but have you any ground for saying that EF is the transversal in question?

Nie. We have not. We surrender at discretion. You will permit us to march out with the honours of war?

Min. We grant it you of our royal grace. March him off the table, and bring on the next Rival.