With literature, poetry, love and settling down in life to occupy him, it is hard to think of Ampère as a young man doing great work in science, but he did; and his work deservedly attracted attention even from his very early years. It was in pure mathematics, perhaps, above all other branches, that Ampère attracted the attention of his generation. Ordinary questions he did not care for. Problems which the fruitless efforts of twenty centuries had pronounced insoluble attracted him at once. Even the squaring of the circle claimed his attention for a while, though he got well beyond it even before his boyhood passed away. There is a manuscript note from the Secretary of the Academy of Lyons, which shows that on July 8th, 1788, Ampère, then not quite thirteen years of age, addressed to that learned body a paper on the "Squaring of the Circle." Later, during the same year, he submitted an analogous memoir, entitled, "The Rectification of an Arc of a Circle, less than a Semi-circumference." Arago says that he was tempted to suppress this story of Ampère's coquetting with so dangerous a problem, for Ampère rather flattered himself that he had almost solved it. It was only after Arago recalled how many geniuses in mathematics had occupied themselves with this same problem, that he saw his way clearly not to share the scruples of those who might think this incident a reflection on Ampère's mathematical genius. After all, Anaxagoras, Hippocrates, Archimedes and Apollonius, among the ancients, and among the moderns, Willebrod Snell, Huyghens, Gregory, Wallis, and finally Newton, the mathematician of the heavens, occupied themselves seriously with this very problem. Arago even notes that some men, by their speculations on the squaring of the circle, were led to distinguished discoveries, and mentions the name of Father Grégoire de Saint-Vincent, the distinguished Flemish mathematician of the Society of Jesus, to whom, as a direct result of his studies in attempted circle-squaring, we owe the discovery of the properties of hyperbolic space, limited by the curve and its asymptotes, as well as the expansion of log (1 + _x_) in ascending powers of _x_. Montucla, the historian of mathematics, writing of Père Saint-Vincent, said that, "No one ever squared the circle with so much ability or with so much success." There was, however, a fallacy in his magnificent work which was pointed out by the celebrated Huyghens.