Wallis having meanwhile published other works and especially a comprehensive treatise on the general principles of calculus (Mathesis universalis, 1657), he might take this occasion of exposing afresh the new-fangled methods of mathematical analysis and reasserting his own earlier positions.
By the hypothetical he means the new-fangled analysis from a given proposition to more particular propositions, i.e.
It was rather foggy, I had a new-fangled gadget that I had made out of sheet metal to act as a radar reflector.
He said that ' the men arrived wearing their new fangled black plastic macintosh 's.
Some residents at the time regarded the Pavilion as a ' new fangled upstart of a cinema ' .