Fetching details from the dictionary...

exactly; just; precisely; really; truly; surely; certainly; without doubt
right (when); just (as)
just (about to); on the point of; on the verge of; on the brink of
really (ought to); certainly (should); naturally
正に彼の言う通りの結果になった。
It turned out exactly as he said.
それは正にその通りだと思う。
I think that is exactly right.
正にこれが探していたものだ。
This is exactly what I was looking for.