In Newton's Principia Mathematica fundamental theorems, e.g about the motion of planets around the sun, are proven by methods of ancient geometry rather than infinitesimal analysis, as one might expect. There are however problems in the Principia that are treated using techniques from calculus; we present one that in today's terminology belongs to the calculus of variations: to determine the shape of a rotationally symmetric body of prescribed base and height such that its resistance in a uniform fluid flow becomes minimal.

### Abstract or Additional Information

In Newton's Principia Mathematica fundamental theorems, e.g about the motion of planets around the sun, are proven by methods of ancient geometry rather than infinitesimal analysis, as one might expect. There are however problems in the Principia that are treated using techniques from calculus; we present one that in today's terminology belongs to the calculus of variations: to determine the shape of a rotationally symmetric body of prescribed base and height such that its resistance in a uniform fluid flow becomes minimal.