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Sir Isaac Newton, the Enumeration, and the Method of Fluxions

Isaac Newton was born in England on January 4, 1643. Newton made many important scientific discoveries. He studied the law of gravity and showed that white light can be broken into many different colors. He also showed that the problems of finding the tangent to a curve and finding the area under a curve are related, whether the curve is defined as a polynomial or as some other kind of function. Because of this achievement, Newton is known as one of the inventors of calculus. Newton was made a knight in 1705 due to all his accomplishments.

Newton was often slow to publish his discoveries. This reluctance to publish involved him in many quarrels. In particular, Newton spent many years arguing with Leibniz about who had invented calculus first. (The truth is probably that Newton had the idea first, but Leibniz published first. However, all of the English mathematicians took Newton's side, and other European mathematicians took Leibniz's side, so the argument went on for a long time.)

One of the many books Newton delayed publishing was an essay called Enumeratio linearum tertii ordinis, or Enumeration of Curves of Third Degree: Newton had written the essay by 1676, but he didn't publish it until 1704, almost thirty years later. The Enumeration separated third-degree polynomials into seventy-two different categories (Newton still left some out!) and graphed an example polynomial in each category. This was one of the first collections of graphs that consistently used two perpendicular axes. The graphs in the Enumeration also included both positive and negative numbers.

Another book by Newton, The Method of Fluxions, actually listed eight different ways to graph functions, including the method we now know as polar coordinates. Newton obviously understood graphing! But again, he failed to publish his work. Though Newton wrote The Method of Fluxions around 1671, it didn't appear in print until 1736, nine years after his death.


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