An Answer to Borellus's Objections, and of the Insufficiency of the Definitions of Proportional lity which are substituted in the Room of Euclid's.

IN the last Lecture we have endeavoured to repel the Attempts of some principal Adversaries again Euclid’s Definition of Proportionals. Borellus remains, who, in my Opinion is by far his most considerable and powerful Opponent; and the more so, because he has devised of his own Head a new Method of resolving Proportionality in vain attempted by others, which we readly own to be a Work very elegant, laudable, and not unuseful; it being both pleasant and profitable to handle the same Subjects various Ways, and deduce the same Theorems from different Principles; yet, I think, he was more happy in framing his own, than in opposing the common Method, as we shall next attempt to shew.