Qu. whether a M. V. be of any colour? a M. T. of any tangible quality?
If visible extension be the object of geometry, 'tis that which is survey'd by the optique axis.
P.
I may say the pain is in my finger, &c., according to my doctrine[61].
Mem. Nicely to discuss wt is meant when we say a line consists of a certain number of inches or points, &c.; a circle of a certain number of square inches, points, &c. Certainly we may think of a circle, or have its idea in our mind, without thinking of points or square inches, &c.; whereas it should seem the idea of a circle is not made up of the ideas of points, square inches, &c.
Qu. Is any more than this meant by the foregoing expressions, viz. that squares or points may be perceived in or made out of a circle, &c., or that squares, points, &c. are actually in it, i.e. are perceivable in it?
A line in abstract, or Distance, is the number of points between two points. There is also distance between a slave & an emperor, between a peasant & philosopher, between a drachm & a pound, a farthing & a crown, &c.; in all which Distance signifies the number of intermediate ideas.
Halley's doctrine about the proportion between infinitely great quantities vanishes. When men speak of infinite quantities, either they mean finite quantities, or else talk of [that whereof they have[62]] no idea; both which are absurd.
If the disputations of the Schoolmen are blam'd for intricacy, triflingness, & confusion, yet it must be acknowledg'd [pg 012] that in the main they treated of great & important subjects. If we admire the method & acuteness of the Math[ematicians]—the length, the subtilty, the exactness of their demonstrations—we must nevertheless be forced to grant that they are for the most part about trifling subjects, and perhaps mean nothing at all.