Perhaps an illustration will make my meaning clearer: when one of those audacious poets affirms that there was once a threeheaded and six-handed man, if you accept that quietly without questioning its possibility, he will proceed to fill in the picture consistently—six eyes and ears, three voices talking at once, three mouths eating, and thirty fingers instead of our poor ten all told; if he has to fight, three of his hands will have a buckler, wicker targe, or shield apiece, while of the other three one swings an axe, another hurls a spear, and the third wields a sword. It is too late to carp at these details, when they come; they are consistent with the beginning; it was about that that the question ought to have been raised whether it was to be accepted and passed as true. Once grant that, and the rest comes flooding in, irresistible, hardly now susceptible of doubt, because it is consistent and accordant with your initial admissions, That is just your case; your love-yearning would not allow you to look into the facts at each entrance, and so you are dragged on by consistency; it never occurs to you that a thing may be self-consistent and yet false; if a man says twice five is seven, and you take his word for it without checking the sum, he will naturally deduce that four times five is fourteen, and so on ad Iibitum. This is the way that weird geometry proceeds: it sets before beginners certain strange assumptions, and insists on their granting the existence of inconceivable things, such as points having no parts, lines without breadth, and so on, builds on these rotten foundations a superstructure equally rotten, and pretends to go on to a demonstration which is true, though it starts from premisses which are false.