ABSTRACT
OF the more common Affections and Properties of Magnitudes, which occur to Observation and introduce Mathematical Hypotheses, the last that offered itself was Congruity; from the Supposition of which, we have in Part declared in the preceding Lecture, that the Equality of Magnitudes results and is aptly defined by it. Which Doctrine notwithstanding Proclus and Hobbs’s celebrated Antagonist in his Confutation of the Hobbian Geometry do strenuously oppose, as they thinks with invincible Arguments. It now remains and is incumbent upon us to weigh the Efficacy of the Things objected in the Balance of Reason, and see whether the War be ended, and they have obtained a Victory as compleat as they imagine. Which we undertake to examine the more readily, because there will arise no small Light to these Things from these Conflicts of contrary Sentiments and Reasonings. Certain Sparks of Truth, by no means to be slighted, seem capable of being struck forth; and yet I will not trouble myself very much with removing every little Cavil, but will more diligently examine the Arguments which by a candid Acceptation do seem to approach nearer the Business, and to contain in them something of more weighty Moment, being mindful of Aristotle’s Divine Precept, u That Things will be more credited if the Arguments on both Sides be first heard. For it does not become us to give Sentence without hearing the Cause, or condemn any Side unheard. They who are willing to judge well of the Truth ought not to be Adversaries, but Arbitrators. I will therefore, as far as I am able, propose such Arguments from them as are most nervous.
