In scientific articles I often read the phrase:
We assume the reader to have [some basic knowledge in] ...
A simple google search of it reveals tons of examples. But, strictly, it sound a little bit odd, or ungrammatical? Should it not rather be
We assume the reader has some basic knowledge
or
We assume that the reader has some [...]?
Or why is the original form perfectly fine?
It's more formal because it's an older grammatical form. It hasn't completely died out yet—rather, it's been relegated to formal usage. But your suggested alternative we assume the reader has ... can be used in even the most formal writing today (although I'm not sure this was the case in 1850).
Consider this Ngram
In the first half of the 19th century, the most common expression was suppose him to be, but now the most common expression is suppose he is. The Ngram for assume is similar, but is unfortunately complicated by the fact that the use of assume meaning suppose was much less common in the 19th century. See Ngram. But I assume that the grammar of assume and suppose behaved similarly.
