I know I'm not the only one that was curious about the source of the quotes.
As the manga said they came from Four Books and Five Classics https://en.wikipedia.org/wiki/Four_Books_and_Five_Classics
"To learn and consistently practice something..." comes from Analects - 《學而 - Xue Er》first verse https://ctext.org/analects/xue-er
"When the heavens are about to place a great responsibility on a great man..." comes from Mencius - 《告子下 - Gaozi II》 35th verse https://ctext.org/mengzi/gaozi-ii
"A jade that is never cut..." comes from Book of Rites - 《學記 - Xue Ji》2nd verse https://ctext.org/liji/xue-ji
The translations on that website are quite different obviously.