Pascal’s Indivisibles

Besides a handwritten inscription on a leaf included in the Original Collection of the Pensees, on the back of notes intended for the controversies against the Jesuits, we know nearly nothing of Pascal’s working techniques and of the genesis of his main mathematical writings. Our only recourse concerning indivisibles lays in the published works, to wit mostly the Potestatum numericarum summa included in the Treatise on the Arithmetical Triangle (1654), the Of the Geometrical Spirit opuscule (1655) and the whole of the Lettres de A. Dettonville resulting from the contest launched in 1658 concerning the cycloid. To these we may add a few fragments from the Pensees which testify to Pascal’s reflections on some fundamental issues.