All ideas come from without. They are all particular. The mind, 'tis true, can consider one thing wthout another; but then, considered asunder, they make not 2 ideas. Both together can make but one, as for instance colour & visible extension(246).
The end of a mathematical line is nothing. Locke's argument that the end of his pen is black or white concludes nothing here.
Mem. Take care how you pretend to define extension, for fear of the geometers.
Qu. Why difficult to imagine a minimum? Ans. Because we are not used to take notice of 'em singly; they not being able singly to pleasure or hurt us, thereby to deserve our regard.
Mem. To prove against Keill yt the infinite divisibility of matter makes the half have an equal number of equal parts with the whole.
Mem. To examine how far the not comprehending infinites may be admitted as a plea.
Qu. Why may not the mathematicians reject all the extensions below the M. as well as the dd, &c., wch are allowed to be something, & consequently may be magnify'd by glasses into inches, feet, &c., as well as the quantities next below the M.?
Big, little, and number are the works of the mind. How therefore can ye extension you suppose in Matter be big or little? How can it consist of any number of points?
(M416) Mem. Strictly to remark L[ocke], b. 2. c. 8. s. 8.
Schoolmen compar'd with the mathematicians.
Extension is blended wth tangible or visible ideas, & by the mind præscinded therefrom.
Mathematiques made easy--the scale does almost all. The scale can tell us the subtangent in ye parabola is double the abscisse.
Wt need of the utmost accuracy wn the mathematicians own _in rerum natura_ they cannot find anything corresponding wth their nice ideas.
One should endeavour to find a progression by trying wth the scale.
Newton's fluxions needless. Anything below an M might serve for Leibnitz's Differential Calculus.
How can they hang together so well, since there are in them (I mean the mathematiques) so many _contradictoriæ argutiæ_. V. Barrow, Lect.
A man may read a book of Conics with ease, knowing how to try if they are right. He may take 'em on the credit of the author.
Where's the need of certainty in such trifles? The thing that makes it so much esteem'd in them is that we are thought not capable of getting it elsewhere. But we may in ethiques and metaphysiques.