3

[3.] premium (n.)   c. 1600, "reward given for a specific act,"
[2.] from Latin praemium "reward, profit derived from booty,"
[1.] from prae- "before" (see pre-) + emere "to buy," originally "to take" (see exempt (adj.)). Insurance sense is 1660s, from Italian premio.
Adjectival sense of "superior in quality" is first attested 1925, originally in reference to butter.

[4.] pre-emption, n.   < PRE- prefix + EMPTION n., after French préemption (right to) advance purchase (1569 in Middle French as preemption) and its etymon post-classical Latin praeemption-, praeemptio previous purchase (14th cent. in British and continental sources). Compare classical Latin praeemere to buy beforehand
(recorded in an 8th-cent. epitome of a 2nd-cent. grammarian).

I can conjecture the semantic shift in the etymology for 4. I can imagine some rich compulsive hoarder's excessive buying of some product BEFORE everyone else to anticipate and preclude others from buying the same (this matches the 2016 English definition of 'pre-empt').

5. But how did 3 shift semantically to mean 2? How can the preposition 'prae-' explain the semantic shift from emere's meaning 'to buy', to 'praemium's meaning of 'reward or profit' ?

  1. What underlying semantic notions connect 3 and 4?
5

As you can see in your own quotation, emo originally meant "take", as it still does in demo and adimo.

Praeemo must have originally meant "to take something before others". If you have the right to take something before others, e.g. from a booty or from the possessions of some other party, then that is likely to be a reward for your valour or other virtues.

Praeemptio is a much later invention, based on the sense of emo as "buy". The sense of prae- "before others" is the same as that in praemium.

Lewis & Short say this:

praemĭum, ii, n. [prae-emo, what one has got before or better than others] (class.).

Note that they use has got in its original sense of "has acquired" here.

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