Isaac Newton the Creator
by John Castaño
In Book I of Philosophiae Naturalis Principia Mathematica, Isaac Newton sets out on a journey to describe the motion of bodies. However, in this first book the objective does not seem to be that of describing how the world actually works, but rather of simply giving a description of how bodies would move in worlds without friction or resistance. The word “situations” might be more suitable than “worlds,” yet one cannot help imagine what our world would look like if in the solar system bodies moved in hyperbolic or parabolic orbits. Certainly, some of these situations apply directly to actual phenomena, yet not all of the mathematical descriptions can be given in experience, which does not make them any less true. As of Book I, it appears that from it directly will come The System Of The World (Book III), and that Newton will be able to describe the motion of the heavenly bodies by making use of the terms defined in it (at least from the first three sections of the book). Evidently, those truths which pertain to the system (the solar system) we (Earth) are a part of will be made use of, whereas those that are not, will not. The subject of interest for us here, hence, is almost entirely confined to Book I, and therefore any thoughts we have on real phenomena will be merely speculative, yet nonetheless directly arising out of Newton’s language. Obviously, we must keep in mind that the axioms, laws of motion, and lemmas in section I, are essentially the grounds upon which everything that follows rests. Hence the title of Book I, section I (The method of first and ultimate ratios, for use in demonstrating what follows).
In section II (To find centripetal forces), Newton begins with an all-encompassing proposition, which says that “the areas which bodies made to move in orbits describe by radii drawn to an unmoving center of forces lie in unmoving planes and are proportional to the times.” This...