Use "being convinced" in a sentence

1. So Martin went on into a thorough study of evolution, mastering more and more the subject himself, and being convinced by the Corroborative testimony of a thousand independent writers

2. In 1979, Russell Noftsker, being convinced that Lisp machines had a bright commercial future due to the strength of the Lisp language and the enabling factor of hardware acceleration, proposed to Greenblatt that they commercialize the technology.