The Collaborative International Dictionary of English v.0.48:

Undertake \Un`der*take"\, v. t. [imp. Undertook; p. p.
   Undertaken; p. pr. & vb. n. Undertaking.] [Under + take.]
   1. To take upon one's self; to engage in; to enter upon; to
      take in hand; to begin to perform; to set about; to
      attempt.
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            To second, or oppose, or undertake
            The perilous attempt.                 --Milton.
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   2. Specifically, to take upon one's self solemnly or
      expressly; to lay one's self under obligation, or to enter
      into stipulations, to perform or to execute; to covenant;
      to contract.
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            I 'll undertake to land them on our coast. --Shak.
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   3. Hence, to guarantee; to promise; to affirm.
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            And he was not right fat, I undertake. --Dryden.
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            And those two counties I will undertake
            Your grace shall well and quietly enjoiy. --Shak.
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            I dare undertake they will not lose their labor.
                                                  --Woodward.
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   4. To assume, as a character. [Obs.] --Shak.
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   5. To engage with; to attack. [Obs.]
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            It is not fit your lordship should undertake every
            companion that you give offense to.   --Shak.
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   6. To have knowledge of; to hear. [Obs.] --Spenser.
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   7. To take or have the charge of. [Obs.] "Who undertakes you
      to your end." --Shak.
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            Keep well those that ye undertake.    --Chaucer.
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The Collaborative International Dictionary of English v.0.48:

Undertook \Un`der*took"\,
   imp. of Undertake.
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Bouvier's Law Dictionary, Revised 6th Ed (1856):

UNDERTOOK. Assumed; promised.
     2. This is a technical word which ought to be inserted in every
declaration of assumpsit, charging that the defendant undertook to perform
the promise which is the foundation of the suit; and this though the promise
be founded on a legal liability, or would be implied in evidence. Bac. Ab
Assumpsit, F; 1 Chit. Pl. 88, note p.