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Updated: May 16, 2025
The Italian Cavalleri had, before this, published his "Geometry of Indivisibles," and fully established his theory in the "Exercitationes Mathematicae," which appeared in 1647.
First of all Thales thought that water was the primordial substance of all things. Democritus and his follower Epicurus thought that it was the atoms, termed by our writers "bodies that cannot be cut up," or, by some, "indivisibles." The school of the Pythagoreans added air and the earthy to the water and fire.
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.
With an extraordinary distinguishing Power, by which they can distinguish even Indivisibles, part Unity it self, divide Principles, and distinguish Truth into such and so many minute Particles, till they dwindle it away into a very Nose of Wax, and mould it into any Form they have occasion for, by which means they can distinguish themselves into or out of any Opinion, either in Religion, Politicks or Civil Right, that their present Emergencies may call for.
At this time the notation was in an imperfect state. The publication of the Geometry of Descartes, which contains the application of algebra to the definition and investigation of curve lines , constitutes an epoch in the history of the mathematical sciences. Two years previously, Cavalieri's work on Indivisibles had appeared. This method was improved by Torricelli and others.
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