I have seen this method of quoting a source. It is often used in books and research essays, but I am unaware what it called, or if it is legal in the MLA or APA writing format. I have some screenshots to demonstrate it. The first uses text from The Wheel of Fire: Interpretations of Shakespearian Tragedy by George Wilson Knight:
The second quotes material from from Ophelia's End—A document in Madness from The Riddles of Hamlet by Simon Augistine Blackmore. Boston, Stratford & Co.
I have also seen the quotation bolded and indented.