Certainly the petitio principii was a main feature of their logic.
"The Rise of the Dutch Republic, Volume I.(of III) 1555-66" by John Lothrop Motley
The words 'their subject' are 'a petitio principii'.
"Coleridge's Literary Remains, Volume 4." by Samuel Taylor Coleridge
Many more of the arguments of the ancient moralists, and especially of the Stoics, fall within the definition of Petitio Principii.
"A System of Logic: Ratiocinative and Inductive" by John Stuart Mill
The argument based on matter coupling, on the other hand, is a sort of petitio principii .
Are there metric theories of gravity other than General Relativity?
It is clear however from what I have said above that this argument is based on the petitio principii error.
Universality of Einstein's General Relativity