Is this a hawk, or an eagle?
The words "hawk" and "eagle" are very confusing and may mean different things in different parts of the world. In fact, the nearly thirty species of raptors (not including owls) native to Taipei apparently include one called a mountain hawk-eagle (Nisaetus nipalensis).

If no one can answer your question, you might narrow the field with a process of elimination. I can't vouch for the accuracy of Wikipedia's list of birds native to Taipei, but it's a start.

There are apparently seven native raptors that are called eagles. If you can eliminate all seven eagles, then it presumably is not an eagle.

Your photographs are helpful insofar as they illustrate the bird's general outline, but it's very hard to distinguish its color pattern. However, the shape of the wings should help narrow the field.

Birds Native to Taiwan

EDIT

I don't know if you're familiar with the terminology, but many raptors are classified as buteos or accipiters. If I remember correctly, species with broader wings are generally buteos. Species commonly called "hawks" include both buteos and accipiters, but I believe most birds called "eagles" are buteos.

Anyway, here's another link...

Buteos