secondary adj.

c. 1300, "next in order, place, time, etc., after the first; an ordinal numeral; being one of two equal parts into which a whole is regarded as divided;" from Old French second, secont, and directly from Latin secundus "following, next in time or order," also "secondary, subordinate, inferior," from PIE *sekw-ondo-, pariticipal form of root *sekw- "to follow."

It replaced native other in this sense because of the ambiguity of the earlier word. From late 14c. as "other, another" (as in "No Second Troy"), also "next in order in rank, quality, or importance."

Second sight is from 1610s; it presumably implies a second way of seeing in addition to the physical sight with the eyes, but it is etymologically perverse as it means the sight of events before, not after, they occur or are revealed. Second-degree in a general sense of "next to lowest on a scale of four" in Arostotelian qualities is from Middle English; in reference to burns, by 1890. Second fiddle is attested by 1809:

A metaphor borrowed from a musical performer who plays the second or counter to one who plays the first or the "air." [Bartlett, "Dictionary of Americanisms," 1848]

Latin secundus, tertius, etc. appended to personal names in English schools (to designate boys having the same surname by order of seniority) is attested by 1826s.

early 15c., primarie, "earliest, most basic, first in time or sequence;" 1560s, "first or highest in rank or importance," from Latin primarius "of the first rank, chief, principal, excellent," from primus "first" (see prime (adj.)).

The meaning "first or lowest in order of growth or development; elementary, preparatory" is from c. 1800, first in education; primary school is attested by 1793 in translations from French, from école primaire.

The Paris journals ... are full of a plan, brought forward by Fourcroy, for the establishment of primary schools, which is not interesting to an English reader. [London Times, April 27, 1802]

Primary color is attested from 1610s (at first the seven of the spectrum, later the three pigments from which the others can be made). Related: Primarily.

Primary and prime mean first in time, and now especially first in order of importance: as, a primary class, definition, consideration, planet; prime mover, importance, idea .... Primitive means belonging to the beginning or origin, original, hence old-fashioned, having an old-fashioned simplicity: as, a primitive word, the primitive church, primitive purity, manners, unconventionality, dress. ... Primeval means of the flrst or earliest ages, and nothing else. [Century Dictionary] 

c. 1300, "main, principal, chief, dominant, largest, greatest, most important;" also "great, large," from Old French principal "main, most important," of persons, "princely, high-ranking" (11c.) and directly from Latin principalis "first in importance; original, primitive," from princeps (genitive principis) "first man, chief leader; ruler, sovereign," noun use of adjective meaning "that takes first," from primus "first" (see prime (adj.)) + root of capere "to take" (from PIE root *kap- "to grasp").