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Updated: May 24, 2025
Now, although artists have not shown any admiration for the cycloid, as they have for the ellipse, yet the mathematicians have gazed upon it with great eagerness, and found it rich in intellectual treasures. Chasles, in his History, says that the cycloid interweaves itself with all the great discoveries of the seventeenth century.
And it should be known that it is none other than that curve which is described by the point E on the circumference of the circle EB, when that circle is made to roll within another whose semi-diameter is ED and whose centre is D. So that it is a kind of Cycloid, of which, however, the points can be found geometrically.
Pascal’s labours on the cycloid may be said to bring to a close his scientific career. There is still one invention, however, of a very practical kind, associated with the very last months of his life. Amongst the letters of Madame Périer, there is one of date March 24, 1662, addressed to M. Arnauld de Pompone —a nephew of the great Arnauld—in which she gives a lively description of the success of an experiment “dans l’affaire des carrosses.” The affair was nothing less than the trial on certain routes in Paris of what is now known as an “omnibus;” and the idea of such conveyances for the public—“carrosses
Now the whole of this variety is the result of subjecting each part of the curve to a law more simple than that of the cycloid. The elastic curve is a curve which bends or curves exactly in proportion to its distance from a given straight line.
There is another curve, generated by a simple law from a circle, which has played an important part at various epochs in the intellectual history of our race. A spot on the tire of a wheel running on a straight, level road, will describe in the air a series of peculiar arches, called the cycloid. The law of its formation is simple; the law of its curvature is also simple.
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