The word for 'I' has many different forms in the Romance languages, such as French je, Italian io, Portuguese eu and Spanish yo. Yet all these forms stem from one Latin word: egō. Here's how egō step by step changed into a selection of its Romance descendants.
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How did these forms originate?
Latin, Late Latin and Sardinian Around the second century AD, the [g] sound of Latin egō (as in English go) started to weaken. It became a fricative sound similar to the one in Modern Spanish agua 'water'.
In this form, with only minor vowel changes, it survived until this very day in certain Nuorese dialects of Sardinian: ego. These geographically isolated dialects are known for being the most conservative descendants of Latin. Their most notable trait is the conservation of the Latin [k] and [g] sounds before i and e: Latin centum '100' with [k] became kentu, whereas in Italian it became cento with the [tʃ] sound of English check, and in French, Portuguese and many variaties of Spanish it respectively became cent, cento/cem and ciento/cien with [s].
In a Late Latin text from the 6th century, we encounter egō as eo. By this time, the consonant had been dropped. It's this form that's considered Proto-Romance, i.e. the form that gave birth to all descendants except the form in the Nuorese dialects I discussed above. Eo even remained practically intact in a number of other Nuorese dialects.
Portuguese and Romanian In Portuguese and Romanian, the -o of eo became w-like: eu. However, the Romanian spelling hides the diphthongisation of [ɛ] to [jɛ], later [je]. Cfr. ferrum > fier, and pellem > piele.
Italian and Neapolitan In Italian, [ɛ] became [e] and then [i], a sound close to it: io. This sound change didn't only happen in this word: compare mio 'my' (from Old Italian meo) and Dio 'God' (from Deo) with Portuguese meu and Deus. In Neapolitan, the -o weakened and became the schwa sound of English words like roses.
Spanish and French The form io must have also existed in the distant ancestors of Spanish and French, but there, [i] didn't stop changing: it turned into a [j], its consonantal counterpart. In both languages, this [j] eventually underwent fortition: it became a stronger consonant similar to the one in English joke, which eventually weakened again in Modern French je.
In South American Spanish, interesting things are happening. The sound change that yo pronounced as [ʒo] has undergone in the Rioplatense dialects in Uruguay and the southern part of Argentina is called zheísmo, and what's happening in Buenos Aires and spreading through Argentina is called sheísmo: [ʃo].
