Removing lower section of an old chimney?
Have you the faintest clue what 10 feet of chimney weighs? "reinforce here" to WHAT exactly, that's going to hold up 10 feet of bricks? 

This is a bad, terrible unthinkable idea. Take it down from the top, or hire somone else to take it down from the top, or far enough from the top that you feel comfortable working on it.

Don't kill yourself, or someone else in your house, or do massive expensive damage to your house even if you somehow manage not to kill anyone.

Houses of a certain vintage sometimes have "stub chimneys" that start in the attic, with stovepipes below, but they were structurally supported from below before they were built.