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1. Come up with (an idea, plan, explanation, theory, or principle) after a mental effort
   "excogitate a way to measure the speed of light";
   - invent, contrive, devise, formulate, forge
    
2. Think deeply about a subject or question over a period of time
   "The scientist must stop to observe and start to excogitate";
   - chew over, think over, meditate, ponder, contemplate, muse, reflect, mull, mull over, ruminate, speculate

Derived forms: excogitated, excogitates, excogitating

Type of: cerebrate, cogitate, create by mental act, create mentally, think