late 14c., artik, "of or pertaining to the north pole of the heavens," from Old French artique and directly from Medieval Latin articus, from Latin arcticus, from Greek arktikos "of the north," literally "of the (constellation) Bear," from arktos "bear;" also "Ursa Major; the region of the north," the Bear being the best-known northern circumpolar constellation.
This is from *rkto-, the usual Indo-European root for "bear" (source also of Avestan aresho, Armenian arj, Albanian ari, Latin ursus, Welsh arth). For speculation on why Germanic lost the word, see bear (n.). The -c- was restored from 1550s.
It is attested from early 15c. as "northern;" from 1660s as "cold, frigid." As a noun, with capital A-, "the northern polar regions," from 1560s.
late 14c., "breadth," from Old French latitude (13c.) and directly from Latin latitudo "breadth, width, extent, size," from lātus (adj.) "wide, broad, extensive" Old Latin stlatus, from PIE *stleto-, suffixed form of root *stele- "to spread, to extend" (source also of Old Church Slavonic steljo "to spread out," Armenian lain "broad").
Geographical and astronomical senses also are from late 14c., literally "breadth" of a map of the known world. Figurative sense of "allowable degree of variation, extent of deviation from a standard" is early 15c. Related: Latitudinal "pertaining to geographic latitude" (1777); latitudinous "having broadness of interpretation" (1829, American English).
The ancients supposed the torrid and the frigid zones to be uninhabitable and even impenetrable by man, but while the earth, as known to them, was bounded westwardly by the Atlantic Ocean, it extended indefinitely towards the east. The dimensions of the habitable world then (and ancient geography embraced only the home of man ....,) were much greater, measured from west to east, than from south to north. Accordingly, early geographers called the greater dimension, or the east and west line, the length, longitudo, of the earth, the shorter dimension, or the north and south line, they denominated its breadth, latitudo. These Latin terms are retained in the modern geography of most European nations, but with a modified meaning. [George P. Marsh, "Lectures on the English Language," 1882]