Question on gravitation law derivation

[Thiafon]

Hi, guys.
I was wondering on Newton's Gravity Law derivation, and I found this page: http://www.relativitycalculator.com/Newton_Universal_Gravity_Law.shtml
Everything seems clear, but the first step is just killing me, because I can't get it.
Assuming small incremental changes in s; $$\lim_{t\rightarrow 0} {s} \rightarrow 0$$
we have the following ratios
$\frac{\omega}{\nu}$=$\frac{s}{r}$, and $\frac{t}{T}$=$\frac{s}{2πr}$
Could someone help me out? Explain, or just say, which part of math do I have to cover in order to understand that?
(btw, I did pre-calculus, and calculus, so concept of limits is familiar to me)
Thanks in advance.

 

[Drakkith]

It's just telling you the ratios of everything. The vector changes at the same rate that the distance traveled does since v and r are equal. If you double w you double s as well.

In the 2nd ratio, T is the total time of one orbital period and 2*Pi*R is the total distance of the orbit. As t changes, which is the time it takes to transverse the incremental time period s, s changes as well. If you double t you double s. Does that make sense?

 

[Thiafon]

Yes, thank you a lot! I had kind of intuitive feeling about it, but I wasn't sure if it is correct.