rigorous \rig"orous\, a. f. rigoureux, ll. rigorosus. see
   rigor.
   1. manifesting, exercising, or favoring rigor; allowing no
      abatement or mitigation; scrupulously accurate; exact;
      strict; severe; relentless; as, a rigorous officer of
      justice; a rigorous execution of law; a rigorous
      definition or demonstration.
      1913 webster

            he shall be thrown down the tarpeian rock
            with rigorous hands.                  --shak.
      1913 webster

            we do not connect the scattered phenomena into their
            rigorous unity.                       --de quincey.
      1913 webster

   2. severe; intense; inclement; as, a rigorous winter.
      1913 webster

   3. violent. obs. "rigorous uproar." --spenser.
      1913 webster

   4. mathematics, logic adhering scrupulously and exactly to
      accepted principles; hence, logically valid; as, a
      rigorous proof.
      pjc

   syn: rigid; inflexible; unyielding; stiff; severe; austere;
        stern; harsh; strict; exact.
        1913 webster -- rig"orously, adv. --
        rig"orousness, n.
        1913 webster
see also:
rigor rig"orously rig"orousness 

rigorousness
     n : something hard to endure; "the asperity of northern winters"
         syn: asperity, grimness, hardship, rigor, rigour,
          severity
see also:
asperity grimness hardship rigor rigour severity