ABSTRACT
MOST learned Auditors, I am glad to find you in Health, and wish you a long Continuance of it, and without further Preface apply to my Task, proceeding in my former Method. I suppose you remember we proposed to treat of the General Affections of Magnitudes, and of other Quantities from thence. A few of which having already diligently enquired into, as well as I am able, I have now reached nigh the very Soul of the Mathematics, viz. to Proportionality, on which almost every Thing depends in the Mathematics which is wonderful and abstruse. But since Proportionality consists in the Comparison of Proportions, and Proportion in the Comparison of Quantities, it seems expedient by way of Preparation to consider the Comparability of Quantities, especially that which is requisite to Proportion. For all Quantities cannot be to compared together, as to be said to have a mutual Proportion, but only these that more nearly touch one another in a peculiar Respect, for which Cause they are wont to be called Homogeneous.
