Barrow's arguing against indivisibles, lect. i. p. 16, is a petitio principii, for the Demonstration of Archimedes supposeth the circumference to consist of more than 24 points. Moreover it may perhaps be necessary to suppose the divisibility ad infinitum, in order to demonstrate that the radius is equal to the side of the hexagon.
Shew me an argument against indivisibles that does not go on some false supposition.
A great number of insensibles—or thus, two invisibles, say you, put together become visible; therefore that M. V. contains or is made up of invisibles. I answer, the M. V. does not comprise, is not composed of, invisibles. All the matter amounts to this, viz. whereas I had no idea awhile agoe, I have an idea now. It remains for you to prove that I came by the present idea because there were two invisibles added together. I say the invisibles are nothings, cannot exist, include a contradiction[66].
I am young, I am an upstart, I am a pretender, I am vain. Very well. I shall endeavour patiently to bear up under the most lessening, vilifying appellations the pride & rage of man can devise. But one thing I know I am not guilty of. I do not pin my faith on the sleeve of any great man. I act not out of prejudice or prepossession. I do not adhere to any opinion because it is an old one, a reviv'd one, a fashionable one, or one that I have spent much time in the study and cultivation of.
Sense rather than reason or demonstration ought to be employed about lines and figures, these being things sensible; for as for those you call insensible, we have proved them to be nonsense, nothing[67].
I.
If in some things I differ from a philosopher I profess to admire, 'tis for that very thing on account whereof I admire him, namely, the love of truth. This &c.
I.
Whenever my reader finds me talk very positively, I desire he'd not take it ill. I see no reason why certainty should be confined to the mathematicians.