This idiom crossed my mind upon first reading:
http://tinyurl.com/39ujkx3
We have a 'may as well':
http://idioms.thefreedictionary.com/might+as+well
1. You might as well be hung for a sheep as for a lamb.there is no reason you should not do something
2. One might as well not know the thing at all as know it imperfectly.
#1 is said to mean that because the punishment for a bad action and an even worse one will be the same, you have no reason not to do the worse one
By analogy with #1, #2 should mean what?
#2 means if you do not aim for learning something thoroughly, it is better not to bother to crack a book at all, as your teacher will kick your a.s anyway.
I think we have a coordinating conjunction,
http://www.ldoceonline.com/dictionary/as_2
, which links two verb phrases together: not know the thing at all and know it imperfectly.
The coordinator (two words) in bold:
One might as well not know the thing at all as know it imperfectly.
The conjoins in bold:
One might as well not know the thing at all as know it imperfectly.

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