Would you classify this as cheating? and what would you do?

If you were in a relationship with some one for a few months and later on you found out that a girl he dated a long time ago were sending emails to eachother how would you feel and would you classify it as “cheating” ?

The emails consisted of:

girl: I miss you… can’t stop thinking about you hehe

boy: yeah, me too I’m thinking about you

girl: I wanna hug you so much…. we should catch up

boy: I liked that, haha I’d hug you when I see you

girl: I miss you so much…. still have feelings for you

boy: I do too…. we should catch up some time

things like this go on for a while but if you found out what would you do and say to your partner?
They have stopped but would you get over it? Especially if this girl caused you so much stress and your partner got angry at you and pushed you which might of been the cause of your miscarriage…

Would everything else feel like a like when at the same time he told you he loved you and said sweet things to you.