In context, “a man of great deserts” means a “man deserving of great things”.¹ The word deserts means “what one deserves”. According to Online Etymology Dictionary, desert in this sense is attested
c.1300, from O.Fr. deserte, noun use of pp. of deservir "be worthy to have," ultimately from L. deservire "serve well"
The term is seen in Shakespeare; for example:
Use every man after his desert, and who should scape whipping?
—Hamlet: Act II, Scene ii
- The man who thinks he deserves great things, but does not, is vain. But the man who thinks he deserves greater things than he does is not in every case vain. The man who thinks he deserves less than he does is small-minded, whether he deserves great things or middling things; indeed even if, though he deserves little, he thinks he deserves even less. But this small-mindedness seems most of all to apply to the man who deserves great things. For what would he do, if he were not deserving of such great things? Well then, the high-minded man represents an extreme in greatness, but a mean in regard to how he ought to judge himself. For he thinks he deserves what in fact he does deserve. Others exceed the mean or fall short of it. [emphasis added] —Aristotle on High-mindedness from Nicomachean Ethics IV.3. http://darkwing.uoregon.edu/~mwilson/Highmindedness.html