Quantity, containing Quantities, infinitely less than itself, and so on, in infinitum; this is an Edifice so bold and prodigious, that it is too weighty for any pretended Demonstration to support, because it shocks the clearest and most natural Principles of human Reason[1]. But what renders the Matter more extraordinary, is, that these absurd Opinions are supported by a Chain of Reason, the clearest and most natural; nor does it seem possible for us to allow the Premises, without admitting the Consequences. Nothing can be more convincing and satisfactory than all the Conclusions concerning the Properties of Circles and Triangles; and yet, when these are once receiv'd, how can we deny, that the Angle of Contact betwixt a Circle and its Tangent is infinitely less than any rectilineal Angle, that as you may encrease the Diameter of the Circle in infinitum, this Angle of Contact be-
- ↑ Whatever Disputes there may be about mathematical Points, we must allow, that there are physical Points; that is, Parts of Extension, which cannot be divided or lessen'd, either by the Eye or Imagination. These Images, then, which are present to the Fancy or Senses, are absolutely indivisible, and consequently must be allow'd by Mathematicians to be infinitely less than any real Part of Extension; and yet nothing appears more certain to Reason, than that an infinite Number of them composes an infinite Extension. How much more an infinite Number of those infinitely small Parts of Extension, which are still suppos'd infinitely divisible?
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