Isaac Newton

“ I shall now add some things relating to the forces of progressive bodies, and to the density and resistance of those mediums in which the motions hitherto treated of, and those akin to them, are performed. ”

“ If a body, in a medium whose density is reciprocally as the distances of places from the centre, revolves in any curve AEB (Figure 3.) about that centre, and cuts the first radius AS in the same angle in B as it did before in A, and that with a velocity, that shall be to its first velocity in A reciprocally in a subduplicate ratio of the distances from the centre (that is, as AS to a mean proportional between AS and BS) that body will continue to describe innumerable similar revolutions BFC, CGD, &c. ”

“ I suppose also the resistance, caeteris paribus, to be proportional to its density. Whence in mediums whose force of resistance is not as the density, the density must be so much augmented or diminished, that either the excess of the resistance may be taken away, or the defect supplied.
Proposition XVII. Problem IV. To find the centripetal force and the resisting force of the medium, by which a body, the law of the velocity being given, shall revolve in a given spiral. ”