I notice that in English (as well as Spanish, and perhaps other European languages), the name of a language is the same word as the adjective form of the country or region name.
In English, this rule seems to be so strong that there doesn't seem to be a single exception.
(This rule works even if the country or language in question doesn't exist. For instance the languages "Indian" and "Israeli" don't exist, but grammatically speaking they would be the English words to refer to hypothetical languages associated with India and Israel. Similarly the word "Hebrew" can be used as an adjective meaning "related to the Hebrew language".)
What is the origin of this practice?
Do most or all European languages (i.e. languages in the SAE sprachbund) have this feature? Is this feature present in any non-European languages?
Addendum: specific further question to those who know Latin: how are languages referred to in Latin? (what about ancient Greek?)