The mistakes of great men leave long shadows in history Euclid’s proofs in the main are elegant and concise, and apart from style of presentation, with slight alterations form the basis for most modern geometrical texts. Exception must be taken, however, to the earlier introductory propositions. These have been found unsuitable for teaching to children. Some have sought to explain this away by saying that Euclid wrote for mature adults, but that children of 11 or 12 cannot comprehend logical proofs. From other eminent authorities, however, come criticisms of the proofs themselves. Thus Russell says that Euclid’s proposition I, 4, is a tissue of nonsense. Undoubtedly Euclid’s earlier proofs fall far short of perfection, but, perversely enough, the criticisms which have been levelled at them are even more mistaken than are Euclid’s proofs.