What does the classical construction X 何由 Y mean? I almost never see this construction in classical prose. (In fact, I'll venture I've never seen it.) However, it's in two of my favorite poems. 

In this one, it's from the poem "晨詣超師院讀禪經" by 柳宗元:


  遺言冀可冥， 繕性何由熟？ 


The other one is from a poem, by Li Bai if I recall correctly:


  西飛精衛鳥，東海何由填


What does X何由Y mean?
in classic Chinese, 何由 is the inverse form of 由何, and it should be in the inverse form ,however, you can understand it by understanding 由何.

何 what
由 [preposition] 1. from  2.because of  3.by(method, means,way)

so 由何 could mean, from what, because of what, by what. I guess, you would less commonly(Ok, at least I would) say,&quot;By what, did you arrive at this conclusion?&quot;, instead, you would say,&quot;how did you arrive at this conclusion?&quot; ;furthermore, when you say &quot;how did you arrive at this conclusion?&quot;, you would probably mean &quot;It's impossible to arrive at this conclusion. I don't believe it&quot;, depending on the context. This also happens to 何由.
In your examples,I think 何由 means &quot;how could&quot;.
By the way, I think this word is not rarely used in classic Chinese, I can give you another example from a poem 《茅屋为秋风所破歌》 by the great poet 杜甫, which was picked into the textbook when I was a student.

长夜沾湿何由彻  How could I bear the bad situation(the house is broken and it rains heavily) in the long night , until the dawn comes.