Malbranch out in asserting we cannot possibly know whether there are 2 men in the world that see a thing of the same bigness. V. L. 1. c. 6.
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 [pg 079] 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.
M. P.
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.