Wow, that is a real tough one! You can figure out how much air Newton breathed in during his lifetime and convert that to Liters and then to cubic meters. After that you can get the number of L of atmosphere and figure out the fraction of air Newton breathed assuming perfect mixing of his breaths. Once you have that you need to calculate the number molecules per breath of air, so you would factor in the air density and the number of molecules in a Liter (Avogadros numbers). You can then estimate the number molecules we take in per breath.
Kudos if you can figure it out. I'm sure it is a postive value, which is really neat to think about - We are all breathing the same molecules every time we take a breath of one the greatest scientists of all time