For adjectives of the first and second declension, the corresponding adverb is formed with the ending -e. For example, pulchre (beautifully) comes from pulcher (beautiful). Canonically this -e is viewed as a suffixed used to derive adverbs from adjectives. It is also possible to view it as a case ending, and the adverb as yet another case. The line between declension and deriving adverbs is not always clear1, since many cases of a noun make the word into an adverb of some kind.
Did any ancient or later grammarian hold or consider this view of -e (or the corresponding third declension version -iter) as a case ending? Who was the first to think or propose this? I assume this was never a popular way to see things, but it is not an entirely unreasonable idea to have. I would like to know when this idea came about.
I should add that I have never seen anyone discuss -e or -iter as case endings, but I highly doubt my idea is original.
1 I don't mean only Latin, but all languages that have cases. It could be that such an idea of -e as a case ending was introduced to Latin grammar by analogy to some other language. I also recognize that there are problems in viewing -e as a case ending; see comments below.