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THREE:A set of lathe tools should consist of all that are required for every variety of work performed, so that no time will be lost by waiting to prepare tools after they are wanted. An ordinary engine lathe, operating on common work not exceeding [126] twenty inches of diameter, will require from twenty-five to thirty-five tools, which will serve for every purpose if they are kept in order and in place. A workman may get along with ten tools or even less, but not to his own satisfaction, nor in a speedy way. Each tool should be properly tempered and ground, ready for use 'when put away;' if a tool is broken, it should at once be repaired, no matter when it is likely to be again used. A workman who has pride in his tools will always be supplied with as many as he requires, because it takes no computation to prove that fifty pounds of extra cast steel tools, as an investment, is but a small matter compared to the gain in manipulation by having them at hand.The philosophical affinities of the new science were not exhausted by the atomistic analysis of Democritus and the regulative method of Aristotle. Platonism could hardly fail to benefit by the great impulse given to mathematical studies in the latter half of the sixteenth century. The passionate love of its founder for geometry must have recommended him as much to the most advanced minds of the period as his religious mysticism had recommended him to the theologians of the earlier Renaissance. And the increasing ascendency of the heliocentric astronomy, with its splendid defiance of sense and opinion, was indirectly a triumph for the philosophy which, more than any other, had asserted the claims of pure reason against both. We see this distinctly in Galileo. In express adhesion to Platonism, he throws his teaching into a conversational form, endeavouring to extract the truth from his opponents rather than convey it into their minds from without; and the theory of reminiscence as the source of demonstrative knowledge seems to meet with his approval.549 He is always ready with proofs drawn from observation and experiment; but nothing can be more in Plato��s spirit, nothing more unlike Aristotle and Bacon, than his encomium on the sublime genius of Aristarchus and Copernicus for having maintained a rational hypothesis against what seemed to be the evidence of their senses.550 And he elsewhere observes how much less would have been the glory of Copernicus had he known the experimental verification of his theory.551