Isaac Newton

“ For in those Propositions, instead of the uniform resistance made to an ascending body arising from its gravity, one may substitute the uniform resistance which arises from the tenacity of the medium, when the body moves by its vis insita alone; and when the body ascends in a right line, add this uniform resistance to the force of gravity, and subduct it when the body descends in a right line. One might also go on to the motion of bodies which are resisted in part uniformly, in part in the ratio of the velocity, and in part in the duplicate ratio of the same velocity. ”

“ If a body be resisted partly in the ratio, and partly in the duplicate ratio of its velocity, and moves in a similar medium by its innate force only; and the times be taken in arithmetical progression: then quantities reciprocally proportional to the velocities, increased by a certain given quantity, will be in geometrical progression. ”

“ For the velocity in a non-resisting medium, is proportional to the time, and therefore to this sector; in a resisting medium it is as the triangle; and in both mediums, where it is least, it approaches to the ratio of equality, as the sector and triangle do.
Scholium.
One may demonstrate also that case in the ascent of the body, where the force os gravity is less than can be express'd by DA2 or AB2 + BD2, and greater than can be express'd by AB2 - DB2, and must be express'd by AB2. ”