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Consequently, Euclid did not just furnish proofs; he furnished them within this axiomatic framework.

I google "furnish", it comes up with 3 meanings.

But seems none of them fit the case. I guess it means "finish" in this case, isn't it?

[Edit] The second definition seems not to fit, because I thought "someone" is the subject, which refers to people, not an object.

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  • What do you think is wrong with the second definition, "supply someone with (something); give (something) to someone."? Why do you think it does not fit this sentence?
    – Andrew
    Commented Dec 14, 2018 at 0:16
  • Because I thought someone is the subject, which refers to people, not an object. Commented Dec 14, 2018 at 0:18
  • Ah, that makes sense. Yes, you can "furnish" things to someone, or just "furnish" them in general. It's the same as "provide".
    – Andrew
    Commented Dec 14, 2018 at 2:45

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(Macmillan Dictionary) Furnish - meaning 2 - to provide someone with something that they need, especially information. For example, Lyall’s evidence may have furnished police with a vital clue.

This is the meaning which "furnish" has in your sentence. In other words, Euclid did not just provide proofs; he provided them within this axiomatic framework.

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