How we cite our quotes: (Canto.Stanza)
Quote #4
The favour of the Empress was agreeable;
And though the duty waxed a little hard,
Young people at his time of life should be able
To come off handsomely in that regard. (10.22)
Don Juan becomes a favorite of Catherine the Great because of his youth and beauty. Byron hints here that he receives all kinds of gifts and favors as payment for "pleasing" Catherine in some way that Byron doesn't mention directly (psst: it might be sex).
Quote #5
Newton (that proverb of the mind), alas!
Declared, with all his grand discoveries recent,
That he himself felt only "like a youth
Picking up shells by the great ocean—Truth" (7.5)
Byron admires Isaac Newton for being smart enough to admit his ignorance when it came to science. Byron doesn't like people who think they know everything, so he likes it when Newton compares himself to a young boy picking up shells by the ocean and looking for knowledge.
Quote #6
Suwarrow, who had small regard for tears,
And not much sympathy for blood (7.69)
Compared to the young and innocent Don Juan, Suwarrow is an experienced military man who doesn't have much sympathy left in his body. It's pretty clear that Byron wants us to admire Don Juan's youth and sympathy by comparison.