Abstract
The epicycloid is the path of a point on a circle rolling on another circle. Philippe de la Hire (1640–1718) developed mathematical properties of the epicycloid in a 1694 work. Further, according to Bernard de Fontenelle’s Eloge de M. de la Hire, where the shape of gear teeth had earlier been “abandoned to the fantasies of workmen,” M. de la Hire showed “that these teeth, in order to have all the perfection possible, should be in the form of an arc of the epicycloid.” However, despite words praising the utility of mathematics, La Hire’s work itself suggests a mathematician with a solution in search of a problem as much as the reverse motivation. La Hire’s mathematics is examined, together with the views of Fontenelle and de la Hire on the role of science and mathematics.
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