The mathematicians could not so much as tell wherein truth & certainty consisted, till Locke told ’em(258). I see the best of ’em talk of light and colours as if wthout the mind. By _thing_ I either mean ideas or that wch has ideas(259). Nullum præclarum ingenium unquam fuit magnus mathematicus. Scaliger(260). A great genius cannot stoop to such trifles & minutenesses as they consider. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 1. (261)All significant words stand for ideas(262). 2. All knowledge about our ideas. 3. All ideas come from without or from within. 4. If from without it must be by the senses, & they are call’d sensations(263). 5. If from within they are the operations of the mind, & are called thoughts. 6. No sensation can be in a senseless thing. 7. No thought can be in a thoughtless thing. 8. All our ideas are either sensations or thoughts(264), by 3, 4, 5. 9. None of our ideas can be in a thing wch is both thoughtless & senseless(265), by 6, 7, 8. 10. The bare passive recognition or having of ideas is called perception. 11. Whatever has in it an idea, tho’ it be never so passive, tho’ it exert no manner of act about it, yet it must perceive. 10. 12. All ideas either are simple ideas, or made up of simple ideas. 13. That thing wch is like unto another thing must agree wth it in one or more simple ideas. 14. Whatever is like a simple idea must either be another simple idea of the same sort, or contain a simple idea of the same sort. 13. 15. Nothing like an idea can be in an unperceiving thing. 11, 14. Another demonstration of the same thing. 16. Two things cannot be said to be alike or unlike till they have been compar’d. 17. Comparing is the viewing two ideas together, & marking wt they agree in and wt they disagree in. 18. The mind can compare nothing but its own ideas. 17. 19. Nothing like an idea can be in an unperceiving thing. 11, 16, 18. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ N. B. Other arguments innumerable, both _a priori_ & _a posteriori_, drawn from all the sciences, from the clearest, plainest, most obvious truths, whereby to demonstrate the Principle, i.e. that neither our ideas, nor anything like our ideas, can possibly be in an unperceiving thing(266). N. B. Not one argument of any kind wtsoever, certain or probable, _a priori_ or _a posteriori_, from any art or science, from either sense or reason, against it. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Mathematicians have no right idea of angles. Hence angles of contact wrongly apply’d to prove extension divisible _ad infinitum_. We have got the Algebra of pure intelligences. We can prove Newton’s propositions more accurately, more easily, & upon truer principles than himself(267). Barrow owns the downfall of geometry. However I’ll endeavour to rescue it—so far as it is useful, or real, or imaginable, or intelligible. But for _the nothings_, I’ll leave them to their admirers.