EVery Magnitude is said to be either Finite if it has any bounds or terms of its Quantity; or Infinite if it has none, or at least Indefinite if those bounds are not determined, or at least not considered as so; as Euclid often supposes an Infinite Line, or ra∣ther perhaps, an Indefinite one, i. e. considered without any re∣lation to its bounds or Ends: By a like distinction, and in reality the same with the former, all quantity is either Measurable, or such that some Measure or other repeated some number of Times, either exactly measures and so equals it, (which Euclid and other Geometricians emphatically or particularly call Measur∣ing) or else is greater; or on the other side Immense, whose Amplitude or Extension no Finite Measure whatsoever, or how many times soever repeated, can ever equal: In the first Case, on the one Hand, the Measure (viz. which exactly measures any quantity) is called by Euclid an aliquot Part(a) 1.1 or simply a Part of the thing measured: as e. g. the Length of one Foot is an aliquot Part of a Length or Line of 10 Foot. In the latter Case the Mea∣••ure (which does not exactly measure any Quan∣tity) is called an Aliquant Part, as a line of 3 or 4 Foot is an Aliquant part of a Line of 10 Foot. Now therefore, omitting ••hat perplext Question, whether or not there may be an infinite Magnitude, we shall here, respecting what is to our purpose, deduce the following
EVery Measure, or part strictly so taken, is to the thing Measured, or its whole, as Unity to a whole number, for that (which is one) repeated a certain number of times, is sup∣posed exactly to measure the other.