Page:Carroll - Euclid and His Modern Rivals.djvu/285

Rh words, speaking of the 'invariably syllogistic form of his [Euclid's] reasoning,' and, to show that this is not a mere slip, he afterwards talks of the 'detailed syllogistic form' as a 'source of obscurity to beginners, and damaging to true geometrical freedom and power.'

Euclid a book of syllogistic form! We stared. We never heard of such a book, except the edition of Herlinus and Dasypodius (1566), who, quite ignorant that Euclid was syllogistic already, made him so, and reckoned up the syllogisms. Thus i. 47 has 'syllogismi novem' at the head. They did not get much thanks; the book was never reprinted, and was in oblivion-dust when Hamilton mentioned the zealous but thick-headed logicians, as he called them. Prof. Mansel, in our own day, has reprinted one of their propositions as a curiosity. In 1831, Mr. De Morgan, advocating the reduction of a few propositions to detailed syllogistic form as an exercise for students, gave i. 47 as a specimen, in the Library of Useful Knowledge; this was reprinted, we believe, in the preface to various editions of Lardner's Euclid. A look will show the difference between Euclid and syllogistic form. Had the Elements been syllogistic, it would have been quoted in all time, as a proof of the rapid diffusion of Aristotle's writings, that they had saturated his junior contemporary with their methods: with a controversy, most likely, raised by those who would have contended that Euclid invented syllogistic form for himself. Now it is well known that diffusion of Aristotle's writings commenced after his death, and that it was—not quite correctly—the common belief that evulgation did not take place until two hundred years after his death. Could this belief ever have existed if Euclid had invariably used 'syllogistic form'?

What could have been meant? Craving pardon if wrong, we suspect Mr. Wilson to mean that Euclid did not deal in arguments with suppressed premisses. Euclid was quite right: the first reasonings presented to a beginner should be of full