Geometry, and especially Algebra, are the Keys of all the Inquiries, that can be made concerning Magnitude. These Sciences which are only conversant about abstruse Relations, and simple Ideas, may seem dry and barren, whilst they keep within the Verge of the Intellectual World; but mixt Mathematicks, which stoop to Matter, and consider the Motion of the Stars, the Augmentation of moving Forces, the different Passages of the Rays of Light through different Mediums; the different Effects of Sound by the Vibration of Things; to conclude all those Sciences, which discover the particular Relations of Sensible Magnitudes go on farther and more securely, when the Art of discovering Relations in General is more perfect. The Universal Instrument cannot be too extensive, too handy, or too easily apply'd: It is useful to all the Sciences, and they cannot be without it: And therefore among the Mathematicians of the Academy, who are design'd to be useful to the Publick, the Geometricians and Algebrists make a Class, as well as the Astronomers and Mechanicks. However, it is certain, that Speculations purely of Geometry, or of Algebra, are not about useful things: But it is certain too, that those that are not, either lead or belong to those that are. It is in it self a very barren thing to know, that in a Parabola a Subtangant is double the corresponding Abscissæ; but yet it is a Degree of Knowledge necessary to the Art of throwing Bombs, so exactly as they can do now. There are not by far so many evident Uses as Propositions or Truths in the Mathematicks: Yet it is enough if the Concourse of several Truths is generally of some use. Farther, a Geometrical Speculation, which was not at first applicable to any use, becomes so afterwards. When the greatest Geometricians in the Seventeenth Century set about to study a new Curve, which they call'd a Cycloide, they only engag'd themselves in a meer Speculation out of Vanity, striving to outdo one another by the Discovery of difficult Theorems. They did not even pretend that this was for the Publick Good; however by diving into the Nature of the Cycloide it was found, that it was destin'd to make Pendulums as perfect as may be, and carry the Measure of Time as far as it can go.