Page:Carroll - Euclid and His Modern Rivals.djvu/88

50 Min. No. They adopt the names D and 'E.'

Euc. It is very like making a new Triangle!

Min. It is indeed. I think you have quite disposed of the claims of 'superposition.' The only remaining subject for discussion is the omission of the diagonals in Book II.

§ 7. The omission of diagonals in Euc. II..

Euc. Let us test it on my II. 4. We will go through my proof of it, and then the proof given by some writer who ignores the diagonal, supplying if necessary any of those gaps in argument which my Modern Rivals so often indulge in, and which give to their proofs a delusive air of neatness and brevity.

'If a Line be divided into any two parts, the square of the Line is equal to the squares of the two parts with twice their rectangle.



Let AB be divided at C. It is to be proved that square of AB is equal to squares of AC, CB, with twice rectangle of AC, CB.

On AB describe Square ADEB; join BD; from C