"in the direction of the length," 1570s, from length + wise (n.). As an adjective by 1871.
Entries linking to lengthwise
length n.
Old English lengðu "property of being long or extended in one direction; distance along a line," from Proto-Germanic *langitho, abstract noun from *langaz "long" (root of Old English lang; see long (adj.)) + *-itho, abstract noun suffix (see -th (2)). Cognate with Old Norse lengd, Old Frisian lengethe, Dutch lengte.
Figurative sense of "the distance one goes, extremity to which something is carried" is from 1690s. Phrase at length "to full extent" is attested from c. 1500. As "the length of a swimming pool," 1903. From the notion of "a piece or portion of the extent of anything" come the theater slang sense "a 42-line portion of an actor's part" (1736) and the sporting sense "the length of a horse, car, etc. in a race" used as a unit of measure (1650s).
wise n.
"way of proceeding, manner," Old English wise "way, fashion, custom, habit, manner; condition, state, circumstance," from Proto-Germanic *wison "appearance, form, manner" (see wise (adj.)). Compare Old Saxon wisa, Old Frisian wis, Danish vis, Middle Dutch wise, Dutch wijs, Old High German wisa, German Weise "way, manner." Most common in English now as a word-forming element (as in likewise, clockwise); the adverbial -wise has been used thus since Old English. For sense evolution from "to see" to "way of proceeding," compare cognate Greek eidos "form, shape, kind," also "course of action." Ground sense is "to see/know the way."