As we know,Archimedes in his "The Method" says that surfaces could be considered as made up of an infinity of parallel lines and that the solid revolutions are filled by circles.
In this, I think, he was getting very ,very close to the idea of modern integral calculus.
Of course, I recognise the fact that he says nothing at all about the concept of limit.
But,one is compelled to wonder as to how much things might have changed if he had, or someone, within a century or two of his death, had taken a few more steps in the right direction.
Take care.