"We find an excellent tract by James Bernoulli concerning the elastic curve, isochronous curves, the path of mean direction in the course of a vessel, the inverse method of tangents, &c. On most of these subjects he had treated already; but here he has given them with additions, corrections, and improvements. His scientific discussions are interspersed with some historical circumstances, which will be read with pleasure. Here for the first time he repels the unjust and repeated attacks of his brother; and exhorts him to moderate his pretensions; to attach less importance to discoveries, which the instrument, with which they were both furnished, rendered easy; and to acknowledge, that, 'as quantities in geometry increase by degrees, so every man, furnished with the same instrument, would find by degrees the same results.' Very modest and remarkable expressions from the pen of one of the greatest geometricians, that ever lived."