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Example:

Now, if you picked up the book and looked through it, the first thing you'd notice is that it was presented in the imposing format that the ancient mathematician Euclid had used in his famous book on geometry. You know, the one we all learned in high school. Lots of definitions, propositions, corollaries—that sort of thing. It looked like a book on mathematics. Many of the problems and their proofs were very complicated. Newton had, in fact, invented a new mathematical technique—the calculus—to help him solve the difficult problems he was addressing. But he didn't use calculus in the book. He presented his conclusions in the traditional geometrical form of his day so that he'd be understood.

This is an excerpt from a video course on the history of science. The lecturer first says the calculus and then drops the article and says just calculus. Well, I know that generally you don't place any articles in front of calculus when you use that word when you mean calculus as a branch of mathematics but he did. What gives?

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As @Ben points out in a comment, there is more than one calculus. When considering any given one, you can speak of the calculus, since the one you are speaking of is understood by context.

Without a particular context, the calculus typically refers to what Leibnitz and Newton came up with - which actually is two related things: (the) differential calculus and (the) integral calculus. And without a particular context, calculus refers to the same thing.

(Even within a particular calculus there can be multiple flavors: typed and untyped lambda calculus, for example.)

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