I say there are no incommensurables, no surds. I say the side of any square may be assign'd in numbers. Say you assign unto me the side of the square 10. I ask wt 10—10 feet, inches, &c., or 10 points? If the later, I deny there is any such square, 'tis impossible 10 points should compose a square. If the former, resolve yr 10 square inches, feet, &c. into points, & the number of points must necessarily be a square number whose side is easily assignable.
A mean proportional cannot be found betwixt any two given lines. It can onely be found betwixt those the numbers of whose points multiply'd together produce a square number. Thus betwixt a line of 2 inches & a line of 5 inches a mean geometrical cannot be found, except the number of points contained in 2 inches multiply'd by ye number of points contained in 5 inches make a square number.
If the wit and industry of the Nihilarians were employ'd [pg 015] about the usefull & practical mathematiques, what advantage had it brought to mankind!
M. E.
You ask me whether the books are in the study now, when no one is there to see them? I answer, Yes. You ask me, Are we not in the wrong for imagining things to exist when they are not actually perceiv'd by the senses? I answer, No. The existence of our ideas consists in being perceiv'd, imagin'd, thought on. Whenever they are imagin'd or thought on they do exist. Whenever they are mentioned or discours'd of they are imagin'd & thought on. Therefore you can at no time ask me whether they exist or no, but by reason of yt very question they must necessarily exist.
E.
But, say you, then a chimæra does exist? I answer, it doth in one sense, i.e. it is imagin'd. But it must be well noted that existence is vulgarly restrain'd to actuall perception, and that I use the word existence in a larger sense than ordinary.[68]
N. B.—According to my doctrine all things are entia rationis, i.e. solum habent esse in intellectum.
E.