Diagonal of particular square commensurable wth its side, they both containing a certain number of m. v. I do not think that surfaces consist of lines, i.e. meer distances. Hence perhaps may be solid that sophism wch would prove the oblique line equal to the perpendicular between 2 parallels. Suppose an inch represent a mile. 1/1000 of an inch is nothing, but 1/1000 of ye mile represented is something: therefore 1/1000 an inch, tho’ nothing, is not to be neglected, because it represents something, i.e. 1/1000 of a mile. Particular determin’d lines are not divisible _ad infinitum_, but lines as us’d by geometers are so, they not being determin’d to any particular finite number of points. Yet a geometer (he knows not why) will very readily say he can demonstrate an inch line is divisible _ad infinitum_. A body moving in the optique axis not perceiv’d to move by sight merely, and without experience. There is (’tis true) a successive change of ideas,—it seems less and less. But, besides this, there is no visible change of place. Mem. To enquire most diligently concerning the incommensurability of diagonale & side—whether it does not go on the supposition of units being divisible _ad infinitum_, i.e. of the extended thing spoken of being divisible _ad infinitum_ (unit being nothing; also v. Barrow, Lect. Geom.), & so the infinite indivisibility deduced therefrom is a _petitio principii_? The diagonal is commensurable with the side. (M392) From Malbranch, Locke, & my first arguings it can’t be prov’d that extension is not in matter. From Locke’s arguings it can’t be proved that colours are not in bodies. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Mem. That I was distrustful at 8 years old; and consequently by nature disposed for these new doctrines(237). ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Qu. How can a line consisting of an unequal number of points be divisible [_ad infinitum_] in two equals? Mem. To discuss copiously how & why we do not see the pictures. (M393) Allowing extensions to exist in matter, we cannot know even their proportions—contrary to Malbranch. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ (M394) I wonder how men cannot see a truth so obvious, as that extension cannot exist without a thinking substance. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ (M395) Species of all sensible things made by the mind. This prov’d either by turning men’s eyes into magnifyers or diminishers. Yr m. v. is, suppose, less than mine. Let a 3rd person have perfect ideas of both our m. vs. His idea of my m. v. contains his idea of yours, & somewhat more. Therefore ’tis made up of parts: therefore his idea of my m. v. is not perfect or just, which diverts the hypothesis. Qu. Whether a m. v. or t. be extended?