  The “deduction” of the law of universal gravity from the phenomena in the first eight propositions of Book 3 has provoked a great deal of controversy in the philosophical literature over the last century or  so.[42] At the heart of this controversy is the challenge posed by Pierre Duhem: how can a deduction proceed from premises (the planets sweep out equal areas in equal times and their orbits are stationary) to a conclusion, the law of gravity, that then implies that the premises are false (the planets do not sweep out equal areas in equal times and the orbits are not stationary, but instead  precess)?[43] The answer is simple: Newton's reasoning is approximative. He is using “if, then” statements that have been shown in Book 1 to hold in “if … quam proxime, then … quam proxime” form to infer conclusions from premises that hold at least quam proxime over a restricted period of time. Of course, this means that the deduction shows only that the conclusions, most notably the law of gravity, hold quam proxime over the restricted period of time for which the premises hold. The Rules of Reasoning then license the conclusion to be taken exactly, without restriction of space or time. The conclusions, so taken, do indeed then show that the premises hold only quam proxime, and not exactly. This conclusion in no way contradicts the premises.