  The idea of developing a mathematical theory in order to enable experiment and observation to provide theory-mediated answers to questions did not originate with the Principia. In his Horologium Oscillatorium, the work the Principia most emulates, Huygens had developed a mathematical theory of pendulum motion that enabled measurement of the length and period of pendulums to provide a robust precise answer to the question, how far does an object fall in the absence of air resistance in the first second? — the measure then of the strength of surface gravity; and he had developed a mathematical theory of uniform circular motion that enabled measurement of the height and period of conical pendulums to provide a second answer to this question. By the time Newton started on the Principia pendulums had been used for more than a decade to answer questions about how surface gravity varies between Paris and other locations. The special problem Newton saw himself as having to face in using mathematical theory to a comparable end in the Principia stemmed from his realization, expressed in the “Copernican scholium,” that the phenomena of orbital motions are inordinately complicated and hence open to multiple competing descriptions. The problem thus became one of finding a way to use mathematical theory to draw definite robust answers to questions about the physical species and proportions of forces from these phenomena. These answers opened the way to pursing the true motions in a sequence of successive approximations, in the process of which continuing evidence could be brought to bear on the theory, potentially delimiting its exactness and its universal applicability in the manner Newton had noted in his fourth rule of reasoning. Because the “Copernican scholium” was unknown at the time, the subtleties of the new method Newton followed to get around this problem went largely unnoticed.