Quotes About Indivisibles

In other words, if geometry was top-down mathematics, the method of indivisibles was bottom-up mathematics.

The ground-root folly of this piteous philanthropy is thinking to distribute indivisibles, and make equality in things incommensurable: forged under such delusions, all Utopias are castles in the air or counsels of despair.

Torricelli fully realized the advantages and disadvantages of the method of indivisibles; and he suspected that the ancients possessed some such method for discovering difficult theorems, the proofs of which they cast in another form either "to hide the secret of their method or to avoid giving occasion for contradiction to jealous detractors.

There are two famous labyrinths where our reason very often goes astray. One concerns the great question of the free and the necessary, above all in the production and the origin of Evil. The other consists in the discussion of continuity, and of the indivisibles which appear to be the elements thereof, and where the consideration of the infinite must enter in.