I think your first quotation gives you the answer already.
with a corresponding body
ga: with, together
lik: body, form, like, same
- together same
- with (equal) form
- with (equal) body
ORIGIN Middle English: from Old Norse líkr; related to alike.
Old English gelīc, of Germanic origin; related to Dutch gelijk and German gleich, reinforced in Middle English by Old Norse álíkr (adjective) and álíka (adverb).
álíkr = gleich is not the same as líkr
Alike = the same as or a-like (the same compared to)
however for me alike means more similar to than equal to.
like = same as
In German we distinguish between das Gleiche und dasselbe
Das Gleiche = two identical things
Dasselbe = the same identical thing
You can say: This is just like …
But you would not say: This is just alike …
What you would say is they look alike or kind alike.
In relation to body and form.
If you are comparing two things. What are you comparing? Bodies and their forms? What else could you compare? Immaterial things are hard to compare. I’d say.