Passage 1
Out of all which we may define, (that is to say determine,) what that is, which is meant by this word Reason, when wee reckon it amongst the Faculties of the mind. For Reason, in this sense, is nothing but Reckoning (that is, Adding and Substracting) of the Consequences of generall names agreed upon, for the Marking and Signifying of our thoughts; I say Marking them, when we reckon by our selves; and Signifying, when we demonstrate, or approve our reckonings to other men.
Cognition, attention, and judgmentreasoning is reckoning · advancesLogic, language, and formal reasoningNo judgment offeredIndividualInterpersonalMind and body
Hobbes explicitly defines reasoning as rule-governed addition and subtraction over agreed general names, usable both privately and in demonstration to others.
Chapter V, "Of Reason, and Science"