Senses
何以 why
(literary) why; for what reason; used to ask why something happened or is the case
何以 with what
(literary) by what means; with what; how; used to ask what instrument or method is being used
何以 how
(literary) used in rhetorical questions to suggest there is no difference or no possibility of something happening; often translated as "how can there be..." or "what is the difference..."
何以 whence
(literary) from where; whence