HIS 322D November 16, 2011
Today:
Newton on Force and Motion
Between 1664 and 1666, when Newton was in his early twenties, he began to take up
mathematics in several ways. He invented a type of calculus, and began his analysis of motion.
He built on the work of things he’s reading by Galileo and Descartes. He doesn’t get the laws
into crisp form yet (this is during 1680s). By treating forces as motion, you don’t have to look
into the nature, or know this, in order to solve the mathematical problems with what happens
when you have a force against a body.
There are broad comparisons between this and his work on light. You don’t have to know the
inner nature – just know the properties and what laws they follow. He is interested in the nature
of things, but he knows it’s inaccessible to the human mind. His work in mathematics would
have easily qualified him as the top mathematician in Europe at this time, but no one knew that
he was doing this. Until the mid-1680s, when he finally published it, people really discovered the
mathematician that he was.
Newton did important work in the 1660s, but did set this aside to do other things such as
alchemy and theology. In the 1680s, he plunges into his previous work and carries it much
further than he did in the 1660s. But the preliminary work he did during the 1600s did lay a lot of
foundations for his later achievements.
Newton became a great mathematician mostly on his own. He got started on this when he picked
up a book on astronomy at a fair. It had some math he couldn’t understand – so he picked up
other mathematical books to learn how to understand this. Newton didn’t start with basic math –
he started from the top. He had a very solid grasp of very advanced math, but not really with
basic math.
Newton solves all the problems with motion with classical geometry. This would be extremely
difficult if he did this.
By 1665, Newton is pushing on into new areas. He’s not just getting up to speed with
mathematics, but doing new work.
Finding the square feet under a curve was something that had been around for a while. People
knew how to get areas of squares and rectangles, but a circle was more difficult. They did have
means to, but still had some issues.
Newton got very interested in infinite series; The ways you can approximate things by taking a
long series of smaller and smaller things and adding them up.

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