ratiocination (n.)

1630s, in theological writing, "reason, rationale," from Latin ratio "a reckoning, account, a numbering, calculation," hence also "a business affair; course, conduct, procedure," also in a transferred sense, of mental action, "reason, reasoning, judgment, understanding, that faculty of the mind which forms the basis of computation and calculation." This is from rat-, past-participle stem of reri "to reckon, calculate," also "to think, believe" (from PIE root *re- "to think, reason, count").

Latin ratio often was used to represent or translate Greek logos ("computation, account, esteem, reason") in works of philosophy, though the range of senses in the two do not overlap (ratio lacks the key "speech, word, statement" meaning in the Greek word; see Logos).

The mathematical sense of "relation between two similar magnitudes in respect to quantity," measured by the number of times one contains the other, is attested in English from 1650s (it also was a sense in Greek logos). The general or extended sense of "corresponding relationship between things not precisely measurable" is by 1808.

Middle English deken, "one who reads the Gospel in divine worship, one of a body of assistants to a priest or other clergyman," from Old English deacon, diacon, from Late Latin diaconus, from Greek diakonos "servant of the church, religious official," literally "servant," from dia- here perhaps "thoroughly, from all sides," + PIE *kon-o-, from root *ken- "to hasten, set oneself in motion." Related: Deaconess; deaconship.

"to reason, from two judgments to infer a third," 1640s, from Latin ratiocinatus, past participle of ratiocinari "to reckon, compute, calculate; to deliberate, meditate; to reason, argue, infer" (see ratiocination). "Now rare in serious use" [OED]. Related: Ratiocinant; ratiocinative; ratiocinatory.