To be inserted in Book I. page 52. line 17. after these words (practicable or imaginable.) beginning a new paragraph.
To whatever side mathematicians turn, this dilemma still meets them. If they judge of equality, or any other proportion, by the accurate and exact standard, viz. the enumeration of the minute indivisible parts, they both employ a standard, which is useless in practice, and actually establish the indivisibility of extension, which they endeavour to explode. Or if they employ, as is usual, the inaccurate standard, deriv'd from a comparison of objects, upon their general appearance, corrected by measuring and juxta position; their first principles, tho' certain and infallible, are too coarse to afford any such subtile inferences as they commonly draw from them. The first principles are founded on the imagination and senses: The conclusion, therefore, can never go beyond, much less contradict these faculties.
A note to Book I. page 64. line 19. to these words (impressions and ideas.)
As long as we confine our speculations to the appearances of objects to our senses, without entering into disquisitions concerning their real nature and operations, we are safe from all difficulties, and can never be embarrass'd by any question. Thus, if it be ask'd, if the invisible and intangible distance, interpos'd betwixt two objects, be something or nothing: 'Tis easy to answer, that it is something, viz. a property of the objects, which affect the senses after such a particular manner. If it be ask'd, whether two objects, having such a distance betwixt them, touch or not: It may be answer'd, that this depends upon the definition of the word, touch. If objects be said to touch, when there is nothing sensible interpos'd betwixt them, these objects touch: If objects be said to touch, when their images strike contiguous parts of the eye,
