All 4 Uses of

ultimate
in
The Count of Monte Cristo

Still, from an artificial civilization have originated wants, vices, and false tastes, which occasionally become so powerful as to stifle within us all good feelings, and ultimately to lead us into guilt and wickedness.†
Chpt 17-18

ultimately = finally; or in the end

That very day the miners began their labors, with a vigor and alacrity proportionate to their long rest from fatigue and their hopes of ultimate success.†
Chpt 17-18 *

ultimate = most extreme as in final, best, worst, most important, or most fundamental

If it were otherwise—if he treated me diplomatically—that is to say, like a man who wishes, by some means or other, to obtain a footing in the house, so that he may ultimately gain the power of dictating to its occupants—he would, if it had been but once, have honored me with the smile which you extol so loudly; but no, he saw that I was unhappy, he understood that I could be of no use to him, and therefore paid no attention to me whatever.†
Chpt 57-58

ultimately = finally; or in the end

It was then generally reported that Mademoiselle de Villefort, the heiress of the marquis and marchioness of Saint-Meran, had regained the good graces of her grandfather, and that she would ultimately be in possession of an income of 300,000 livres.†
Chpt 77-78

Definition:

most extreme as in final, best, worst, most important, or most fundamental

The exact meaning of ultimate depends upon its context. For example: