All 4 Uses of

muse
in
Middlemarch

"Why, Trumbull himself is pretty sure of five hundred—that you may depend,—I shouldn't wonder if my brother promised him," said Solomon, musing aloud with his sisters, the evening before the funeral.†
Chpt 4 *

musing = reflecting (thinking) -- perhaps aloud

Rosamond thought that no one could be more in love than she was; and Lydgate thought that after all his wild mistakes and absurd credulity, he had found perfect womanhood—felt as if already breathed upon by exquisite wedded affection such as would be bestowed by an accomplished creature who venerated his high musings and momentous labors and would never interfere with them; who would create order in the home and accounts with still magic, yet keep her fingers ready to touch the lute and transform life into romance at any moment; who was instructed to the true womanly limit and not a hair's-breadth beyond—docile, therefore, and ready to carry out behests which came from that limit.†
Chpt 4

musings = thoughts

Say, goddess, what ensued, when Raphael, The affable archangel ... Eve The story heard attentive, and was filled With admiration, and deep muse, to hear Of things so high and strange.†
Chpt 1 *

Let the high Muse chant loves Olympian: We are but mortals, and must sing of man.†
Chpt 3

Definitions:

(1) (muse as in: her musings)
reflect (think) deeply on a subject -- perhaps aloud
(2) (muse as in: She was his muse)
the source of an artist's inspiration - especially a person or mythological goddess

The 9 muses were the daughters of the Greek gods Zeus & Mnemosyne. Each of the muses was thought to inspire and preside over one of the arts.
(3) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

More rarely, muse is used as a synonym for "poet". In Shakespeare's time, muse could be used in the sense of being astonished or puzzled by something strange or unexpected.