1829, "to recollect," a back-formation from reminiscence. Meaning "indulge in reminiscences" is from 1871. "[S]omewhat colloquial" [OED] and mistrusted by the literary (in the OED's earliest citation for it, reminisce is followed immediately by an aside, "the word shall never enter my vocabulary"). Related: Reminisced. Reminiscing as a verbal noun, "action of remembering," is by 1891.
"short song or poem intended to be sung to a simple melody,"early 14c., from Old French ditie "composition, poem, treatise," from Latin dictatum "thing dictated," neuter past participle of dictare "dictate," frequentative of dicere "to say, speak" (from PIE root *deik- "to show," also "pronounce solemnly"). In Middle English used of any literary composition, including dramas, essays, letters.
mid-15c., review, revewe, reveue, "a formal inspection of military forces" by a higher official or superior in rank, to judge the effectiveness of their training, from Old French reveue "a reviewing, review" (Modern French revue), noun use of fem. past participle of reveeir "to see again, go to see again," from Latin revidere, from re- "again" (see re-) + videre "to see" (from PIE root *weid- "to see").
The sense of "act or process of going over again," especially with a view to correction, is from 1560s. The meaning "general survey of a subject" is from c. 1600; that of "a view of the past, a retrospective survey" is from 1670s. The meaning "general examination or criticism of a recent literary, dramatic, or artistic work" is attested from 1640s. Hence review used as a name for a periodical which publishes mainly articles on current affairs or critical examinations of literary works (1705).
also re-cast, c. 1600, "to throw again," from re- "back, again" + cast (v.). Sense of "to cast or form anew, remodel," especially of literary works and other writing, is from 1790. Meaning "compute anew" is by 1865. Theater sense of "assign an actor or role to another role or actor" is by 1951. Related: Recasting. As a noun, "a fresh molding, arrangement, or modification," by 1840.
late 14c., in reference to Justinian's law codes in ancient Rome, from Late Latin digesta, from neuter plural of Latin digestus, literally "digested thing," noun use of past participle of digerere "to separate, divide, arrange," etymologically "to carry apart," from dis- "apart" (see dis-) + gerere "to carry" (see gest). General sense of "collection of writings (literary, legal, scientific or historical) arranged under different heads" is from 1550s.
"decimal part of a logarithm," 1865, from Latin mantisa "a worthless addition, makeweight," perhaps a Gaulish word introduced into Latin via Etruscan (compare Old Irish meit, Welsh maint "size"). So called as being "additional" to the characteristic or integral part. The Latin word was used in 17c. English in the sense of "an addition of small importance to a literary work, etc."