ABSTRACT
THE Disquisition we begun in our first Lecture, concerning the Division of the Mathematical Sciences, we will now assay to pursue more distinctly, as was then proposed, delivering in the first place the Method of the Antients, and afterwards our own Method, n The Pythagoreans who, as Aristotle says, were the first among the Greeks, that meddled with Mathematics, divided them into four Parts, of which, two were Pure and Primary, namely Arithmetic and Geometry; and the other two Mixed and Secondary, as Music and Spheres, i. e. Astronomy. And the Reason which they gave for this Division, according to o Proclus and Boethius was, because since the Species of the general Object are two, to wit, Multitude and Magnitude, each of which may be two Ways considered; viz. Multitude either simply as subsisting in itself, or respectively with reference to the Sounds whose Proportions it expresses; and Magnitude, as it is fixed in a p Place, or is carried about with Motion; hence arise these four Parts of Mathematics. Thus did the Pythagoreans of old divide the Mathematics, I suppose because they had not yet applied themselves to the other Parts, such as Optics Mechanics, &c. which the curious Diligence of after Ages, and Time, the Inventor of all Things, brought forth and devised.
