The Taming of the Shrew 1.2 Performance: Hortensio and Petruchio, Lines 172-178

The transcript describes a situation where a gentleman, met by chance, agrees to woo and marry a woman named Catherine, provided her dowry is satisfactory. The speaker introduces the context and the gentleman's willingness to undertake this task.

Who is the gentleman mentioned in the text, and what is his purpose?

What conditions are mentioned regarding the marriage proposal to Catherine?