One should endeavour to find a progression by trying wth the scale. Newton’s fluxions needless. Anything below an M might serve for Leibnitz’s Differential Calculus. How can they hang together so well, since there are in them (I mean the mathematiques) so many _contradictoriæ argutiæ_. V. Barrow, Lect. A man may read a book of Conics with ease, knowing how to try if they are right. He may take ’em on the credit of the author. Where’s the need of certainty in such trifles? The thing that makes it so much esteem’d in them is that we are thought not capable of getting it elsewhere. But we may in ethiques and metaphysiques. The not leading men into mistakes no argument for the truth of the infinitesimals. They being nothings may perhaps do neither good nor harm, except wn they are taken for something, & then the contradiction begets a contradiction. a + 500 nothings = a + 50 nothings—an innocent silly truth. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ (M417) My doctrine excellently corresponds wth the creation. I suppose no matter, no stars, sun, &c. to have existed before(247). ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ It seems all circles are not similar figures, there not being the same proportion betwixt all circumferences & their diameters. When a small line upon paper represents a mile, the mathematicians do not calculate the 1/10000 of the paper line, they calculate the 1/10000 of the mile. ’Tis to this they have regard, ’tis of this they think; if they think or have any idea at all. The inch perhaps might represent to their imaginations the mile, but ye 1/10000 of the inch cannot be made to represent anything, it not being imaginable. But the 1/10000 of a mile being somewhat, they think the 1/10000 inch is somewhat: wn they think of yt they imagine they think on this. 3 faults occur in the arguments of the mathematicians for divisibility _ad infinitum_— 1. They suppose extension to exist without the mind, or not perceived. 2. They suppose that we have an idea of length without breadth(248), or that length without breadth does exist. 3. That unity is divisible _ad infinitum_. To suppose a M. S. divisible is to say there are distinguishable ideas where there are no distinguishable ideas. The M. S. is not near so inconceivable as the _signum in magnitudine individuum_. Mem. To examine the math, about their _point_—what it is—something or nothing; and how it differs from the M. S. All might be demonstrated by a new method of indivisibles, easier perhaps and juster than that of Cavalierius(249). ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ (M418) Unperceivable perception a contradiction. (M419) Proprietates reales rerum omnium in Deo, tam corporum quum spirituum continentur. Clerici, Log. cap. 8. Let my adversaries answer any one of mine, I’ll yield. If I don’t answer every one of theirs, I’ll yield.