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John were staunch friends of Leibniz and worked hand in hand with him. James Bernoulli (1654–1705) was born in Basel. Becoming interested in the calculus, he mastered it without aid from a teacher. From 1687 until his death he occupied the mathematical chair at the University of Basel. He was the first to give a solution to Leibniz's problem of the isochronous curve. In his solution, published in the Acta Eruditorum, 1690, we meet for the first time with the word integral. Leibniz had called the integral calculus calculus summatorius, but in 1696 the term calculus integralis was agreed upon between Leibniz and John Bernoulli. James proposed the problem of the catenary, then proved the correctness of Leibniz's construction of this curve, and solved the more complicated problems, supposing the string to be (1) of variable density, (2) extensible, (3) acted upon at each point by a force directed to a fixed centre. Of these problems he published answers without explanations, while his brother John gave in addition their theory. He determined the shape of the "elastic curve" formed by an elastic plate or rod fixed at one end and bent by a weight applied to the other end; of the "lintearia," a flexible rectangular plate with two sides fixed horizontally at the same height, filled with a liquid; of the "volaria," a rectangular sail filled with wind. He studied the loxodromic and logarithmic spirals, in the last of which he took particular delight from its remarkable property of reproducing itself under a variety of conditions. Following the example of Archimedes, he willed that the curve be engraved upon his tombstone with the inscription "eadem mutata resurgo." In 1696 he proposed the famous problem of isoperimetrical figures, and in 1701 published his own solution. He wrote a work on Ars Conjectandi, which is a development of the calculus of probabilities and contains the investigation now called "Bernoulli's theorem" and the so-called "numbers