[T]he Physics delivered in the following Work... was both known and diligently cultivated by the most ancient Philosophers. ...[T]he true System of t… - David Gregory

Although the celestial spaces in which the planets move around are... unresisting, yet media are considered in which the moving body is resisted, and this resistance is considered in conjunction with gravitation or centripetal force. Among others, this problem now presents itself for solution: Given the direction, the law of centripetal force, and the law of resistance, to construct the path of the projectile. In particular, if the law of centripetal force is posited as reciprocally duplicate to the distances and the resistance is in the duplicate ratio of the speed, then indeed the problem of Galileo will be solved, as is fitting.

[U]niversally, the Weights which generate all Tones in Strings, are reciprocally as the Squares of the lengths of Strings of equal Tension, producing the same sound in any Musical Instrument.

[W]ith this one problem... three years ago, after the above was published, Gottfried Leibniz... produced a construction... in terms of his system—not without the blemish of paralogism.