ABSTRACT
WE have treated in Part concerning the Evidence and Certainty of the Mathematics in the last Lecture; it now remains that we speak of their Dignity, and shew more distinctly that they are really Scientific and Causal, and after what Manner; also, that we answer the principal Objections, that our Adversaries bring against us. As to what pertains to the Manner of casuality we may take notice with x Aristotle that there are three Things to be considered especially in every Demonstrative Science; viz. 1st, The Subject whose necessary Affections or Properties it contemplates, investigates, or demonstrates. 2dly The common Axioms whereby it seeks and demonstrates the Affections concerning the Subject. 3dly, The Affections themselves, which are to be demonstrated of the Subject. There is Nothing that occurs very observable concerning the Subject of Mathematical Demonstrations, unless, as we shall explain by and by, that it is always some Species of Magnitude which is specified, determined and differenced from others by some reciprocal Property; Ex. gr. a Right Line, an Angle, a Triangle, a Circle, a Cube, a Sphere, &c. are Subjects of Mathematical demonstrations.
