David Gregory

[T]he Physics delivered in the following Work... was both known and diligently cultivated by the most ancient Philosophers. ...[T]he true System of the World, approv'd of Pythagoras, and others among the Ancients...

[T]hose persons seem to apply their thoughts but to a very indifferent purpose in the study of Nature, that overlook this part of Astronomy, from whence the principal and most simple Laws of Nature are to be learn'd.

every Problem in the Terrestrial Physics is very operose and perplex'd, on the contrary, in the Celestial Physics, much more easy and simple

if not accurately done, in vain do we attempt Nature, and make any inquiry into it.

The Celestial Physics, or Physical Astronomy, is not only the first in dignity of all inquiries into Nature... but the first in order, because it is the easiest.

[T]hose who are less vers'd in the more abstruse parts of Geometry, or less concerned about the Physical parts, may pass over, and only read the Astronomy separately and distinct...

[T]he Physics, it is all taken out of the above mention'd Authors; but is here intermix'd with Astronomy, in such places as seem'd proper and convenient; the Geometry to be met with in it, I have either borrowed elsewhere, and quoted... or …

My design in publishing this Book, was, that the Celestial Physics, which the most sagacious Kepler had got the scent of, but the Prince of Geometers Sir Isaac Newton, brought to such a pitch as surprises all the World, might, by my... …

[F]or the further improvement of natural philosophy a more advanced geometry must be found.

[T]he increases of optics, geography and other sciences... are also due to the application of the more intricate geometry to philosophical matters.

The phenomena prove that the tail of a comet is vapour from its head which, when the comet is greatly heated in the neighbourhood of the sun in perihelion, continually rises up and moves away into the regions opposite the sun.

Thus Descartes’s rectilinear cometary trajectory, which he filched from Kepler, collapses, and many things about comets in his fable of the world may be added, which almost two thousand years ago had been shown to be impossible by …

[T]he motion of comets is found to be not at all dissimilar to the motion of the planets

Descartes's cosmic system, which he jokingly called his fable of the world, is shown to be a fable indeed.

the problem of Galileo will be solved, as is fitting.

to construct the path of the projectile.

Newton solved not only the universal problem of determining the trajectory and the motion in it for any given centripetal force, but also its converse.

But... Kepler’s problem was to be resolved, to find the position of a body moved in an elliptical orbit at a given time. As concerns an algebraic resolution... adapted to the construction of tables, we... also have produced a work not... …

[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.

others had long before shown that this was the one and only law that would satisfy the other phenomenon observed by Kepler in the motion of the planets. These results also apply to the hyperbola and the parabola when the centre of forces …

problem when the centre of forces coincides with either focus of the ellipse shows that the law of centripetal force is reciprocally in the duplicate ratio of the distance

be it from a deeper mechanical one or from a law imposed by the supreme creator

of the body borne in that orbit, from whatever cause

Mr Issac Newton in addition to the geometric figure in any orbit of a projectile sought also to find the measure of the