The first rigorous solution to the tangent line problem in human history explained.

Link to applet used in demonstration:

https://drive.google.com/open?id=1ON1GQ7b6UNpZSEEsbG14eAFCPv8p03pv

Link to article on Fixing broken mainstream calculus:

https://drive.google.com/open?id=1uIBgJ1ObroIbkt0V2YFQEpPdd8l-xK6y

Link to article describing the historic first rigorous resolution of the tangent line problem:

https://drive.google.com/open?id=1RDulODvgncItTe7qNI1d8KTN5bl0aTXj

Link to my free New Calculus eBook - the first and only rigorous formulation of calculus in human history:

https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view

Note:
You might claim that f1 is being used in the determination of f2, but in geometry this is allowed and it's not circular at all since f(x+h)-f(x) = f1 + f2.

To wit, in geometry we can multiply or divide any magnitude (except for no magnitude of course) EXACTLY. If some magnitude represents pi and another sqrt(2), we can find the exact product pi*sqrt(2) in the form of a magnitude. In algebra this is simply not possible!