Pascal’s scientific studies may be said to have begun with the remarkable incident of his youth already related, when he elaborated for himself, in a solitary chamber without books, thirty-two propositions of the first book of Euclid. On the other hand, these studies may be said to have extended to his closing years, when (in 1658 and 1659) he reverted to the abstruser mathematics, and made the cycloid a subject of special thought. But his scientific labours were in the main concentrated in the eight or ten years of his life which followed the removal of the family to Rouen. It will be convenient, therefore, to notice these labours and discoveries in a single chapter here, which will, at the same time, carry on the main history of his life during these years. All that can be expected from the present writer is a slight sketch of this part of the subject, which indeed is all that would be interesting to the general reader.
At the age of sixteen Pascal had already acquired a scientific reputation. He is spoken of by the Duchess d’Aiguillon, in the interview with Richelieu in which she pleaded the cause of the exiled father, as “very page 26learned in mathematics;” and when his sister presented him after the dramatic representation on that occasion, the Duchess gave him “great commendation for his scientific attainments.” 1 When allowed by his father to pursue the natural bent of his genius, he made extraordinary progress. He was still only twelve years of age, but Euclid’s Elements, as soon as put into his hands, were mastered by him without any explanation. By-and-by he began to take an active part in the scientific discussions which took place at his father’s house; and his achievement in Conic Sections has been already narrated.