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## Main Question or Discussion Point

Hello all, I was talking to a friend of mine earlier explaining why a force acts as if all the mass is concentrated at the center of mass. I know of no other proof than taking the time derivatives of the center of mass. Seeing as this was long before definitive proof of the atomic structure of matter...

My question is, did Newton assume or imply the system must be divided into atoms?

For one to even be able to consider the internal forces canceling due to Newton's third law, there must be particles with mass accelerating and affecting each other. Historically, I am just wondering if anyone knows, or has read the Principia to find, if Newton took it as an assumption.

If not, what other method did he use to prove it?

I can understand taking arbitrary points with arbitrarily small mass don't necessarily have to be atomic, but the simple assumption that matter can be divided seems like an awfully large assumption due to the split attitudes of scientists at the time on the nature of mass and its divisibility.

My question is, did Newton assume or imply the system must be divided into atoms?

For one to even be able to consider the internal forces canceling due to Newton's third law, there must be particles with mass accelerating and affecting each other. Historically, I am just wondering if anyone knows, or has read the Principia to find, if Newton took it as an assumption.

If not, what other method did he use to prove it?

I can understand taking arbitrary points with arbitrarily small mass don't necessarily have to be atomic, but the simple assumption that matter can be divided seems like an awfully large assumption due to the split attitudes of scientists at the time on the nature of mass and its divisibility.