Arts Quotes - page 26
It would be better, I think, for the man who really seeks the truth not to ask what the poets say; rather, he should first learn the method of finding the scientific premises that I discussed in the second book; then he should train and exercise himself in this method; and when his training is sufficiently advanced, then, as he approaches each particular problem, he should enquire into the premise needed for proving it, which premise he should take from simple sense-perception, which from experience, whether drawn from life or from the arts, which from the truths clearly apprehended by the mind, in order to draw out from them the desired conclusion.
Galen
The ancients considered mechanics in a twofold respect; as rational, which proceeds accurately by demonstration, and practical. To practical mechanics all the manual arts belong, from which mechanics took its name. But as artificers do not work with perfect accuracy, it comes to pass that mechanics is so distinguished from geometry, that what is perfectly accurate is called geometrical; what is less so is called mechanical. But the errors are not in the art, but in the artificers. He that works with less accuracy is an imperfect mechanic: and if any could work with perfect accuracy, he would be the most perfect mechanic of all; for the description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn; for it requires that the learner should first be taught to describe these accurately, before he enters upon geometry; then it shows how by these operations problems may be solved.
Isaac Newton