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rate [rate 词源字典]: rate: English has two words rate. The commoner, ‘relative quantity’ [15], comes via Old French rate from medieval Latin rata ‘calculated, fixed’, as used in the expression pro rata parte ‘according to a fixed part, proportionally’. This was the feminine form of ratus, the past participle of rērī ‘think, calculate’, from which English also gets ratio, ration, reason, etc.

The other rate, ‘scold’ [14], is now seldom encountered except in its derivative berate [16]. It is not certain where it comes from, although a possible source is Old French reter ‘accuse, blame’, which comes from Latin reputāre (ancestor of English reputation).
=> ratio, ration, reason; berate[rate etymology, rate origin, 英语词源]
proportional (adj.): late 14c. (implied in proportionally), from Late Latin proportionalis "pertaining to proportions," from proportio (see proportion). Related: Proportionally.
prorate (v.): also pro-rate, "divide proportionally," 1860, American English, verb derived from Latin pro rata (parte) (see pro rata). Related: Prorated; prorating.