Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/14

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The Author's Preface

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 ſhews how by theſe operations problems may be ſolved. To deſcribe right lines and circles are problems, but not geometrical problems. The ſolution of theſe problems is required from Mechanics; and by geometry the uſe of them, when ſo ſolved, is ſhewn. And it is the glory of Geometry that from thoſe few principles, fetched from without, it is able to produce ſo many things. Therefore Geometry is founded in mechanical practice, and is nothing but that part of univerſal Mechanics which accurately propoſes and demonſtrates the art of meaſuring. But ſince the manual arts are