rigorous

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"or*ous*ly, adv. -- Rig"or*ous*ness, n. [ 1913 Webster ]