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The sea running pretty high at the same time, our hero, who was below in his cabin, began to be squeamish, and, in consequence of the skipper's advice, went upon deck for the comfort of his stomach; while the governor, experienced in these disasters, slipped into bed, where he lay at his ease, amusing himself with a treatise on the cycloid, with algebraical demonstrations, which never failed to engage his imagination in the most agreeable manner.
But, as we have already said, it is well to complete our view of his scientific labours in a single chapter. During an access of severe toothache which, in 1658, deprived him of sleep, his thoughts fastened on certain problems connected with the cycloid. Fermat, Roberval, and Torricelli had all been occupied with the subject, and made some definite progress in ascertaining its properties.
Erud. Lips. an. 1695 to these a lead weight is an eternal balance, and keeps watch as well as a couple of centinels, inasmuch as the construction of them was a curve line approximating to a cycloid if not a cycloid itself.
To account for every new appearance, every deviation from circular perfection, a new cycloid was supposed, till all the simplicity of the original hypothesis was lost in a complication of epicycles: "The sphere, With centric and eccentric scribbled o'er, Cycle and epicycle, orb in orb."
In the first course, there was a shoulder of mutton cut into an equilateral triangle, a piece of beef into a rhomboides, and a pudding into a cycloid. The second course was two ducks trussed up in the form of fiddles; sausages and puddings resembling flutes and hautboys, and a breast of veal in the shape of a harp.
In 1644 he published a tract on the properties of the cycloid in which he suggested a solution of the problem of its quadrature. This led to a long debate, during which Torricelli was seized with a fever, from the effects of which he died, in Florence, October 25, 1647.
Such is the cycloid, first conceived by Galileo, and a stumbling-block and cause of contention among geometers long after he had left it, together with his system of the universe, undetermined. Descartes, Roberval, Pascal, became successively challengers or challenged respecting some new property of this curve.
Many even of the truths of geometry were generalizations from experience before they were deduced from first principles. The quadrature of the cycloid is said to have been first effected by measurement, or rather by weighing a cycloidal card, and comparing its weight with that of a piece of similar card of known dimensions.
It was in the left hand try-pot of the Pequod, with the soapstone diligently circling round me, that I was first indirectly struck by the remarkable fact, that in geometry all bodies gliding along the cycloid, my soapstone for example, will descend from any point in precisely the same time.
Bernouilli's problem was to find out what that curve must be. Newton solved it correctly; he showed that the curve was a part of what is termed a cycloid that is to say, a curve like that which is described by a point on the rim of a carriage-wheel as the wheel runs along the ground.
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