3 - The mathematical methods of the Principia
Published online by Cambridge University Press: 29 March 2010
Summary
Purpose of this chapter
In this chapter I will try to give the reader some information about the mathematical methods employed by Newton in the Principia. We will have to consider with some patience a variety of lemmas, propositions, corollaries and scholia. I have found it convenient to postpone a more detailed analysis of some propositions to later chapters.
I have tried to render the structure of Newton's demonstrations without wasting too much space on trivial details. Therefore, I have skipped the lines of demonstration in which appeal is made to simple geometrical properties (e.g. similarity of triangles). We would adopt the same strategy in presenting Laplace's or Poincaré's demonstrations. When dealing with proofs given in a more familiar symbolic language we do not expect that every substitution of variable, or that every elementary integration, should be made explicit and commented on. The Principia has a reputation for being a very difficult, if not tedious, work. This is mainly due to the fact that nowadays we are not used to geometrical techniques. However, when the trivialities are skipped, the structure of most demonstrations emerges as remarkably simple. I hope that the reader will thus be able to follow the essential steps.
In the quotations from the Principia I am using Cohen and Whitman's forthcoming translation. I deemed it necessary not to follow their policy of altering some of Newton's notations and technical terms (see §1.3).
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- Reading the PrincipiaThe Debate on Newton's Mathematical Methods for Natural Philosophy from 1687 to 1736, pp. 39 - 98Publisher: Cambridge University PressPrint publication year: 1999