rare (adj.1) Look up rare at Dictionary.com
"unusual," early 15c., originally "few in number and widely separated," from Old French rere "sparse" (14c.), from Latin rarus "thinly sown, having a loose texture," from PIE *er-, *ere- "to loose, split, separate" (cf. Sanskrit rte "besides, except," viralah "distant, tight, rare;" Old Church Slavonic oriti "to dissolve, destroy;" Lithuanian irti "to dissolve;" Old Church Slavonic rediku "rare;" Greek eremos "solitary"). "Few in number," hence, "unusual" (1540s). In chemistry, rare earth is from 1818.
rare (adj.2) Look up rare at Dictionary.com
"undercooked," 1650s, variant of Middle English rere, from Old English hrer "lightly cooked," probably related to hreran "to stir, move." Originally of eggs, not recorded in reference to meat until 1784, and according to OED, in this sense "formerly often regarded as an Americanism, although it was current in many English dialects ...."
rare (v.) Look up rare at Dictionary.com
"rise up," 1833, dialectal variant of rear (v.). Sense of "eager" (in raring to go) first recorded 1909. Related: Rared; raring.