What's the difference between i.e. and e.g.?
late 13c., "a step in walking; rate of motion," from Old French pas "a step, pace, trace," and directly from Latin passus, passum "a step, pace, stride," noun use of past participle of pandere "to stretch (the leg), spread out," probably from PIE *pat-no-, from root *pete- "to spread" (cf. Greek petannynai "to spread out," petalon "a leaf," patane "plate, dish;" Old Norse faðmr "embrace, bosom," Old English fæðm "embrace, bosom, fathom," Old Saxon fathmos "the outstretched arms"). Also, "a measure of five feet" [Johnson]. Pace-setter in fashion is from 1895.
"with the leave of," 1863, from Latin pace, ablative of pax "peace," as in pace tua "with all deference to you;" from PIE *pak- "to fasten" (see pax). "Used chiefly as a courteous or ironical apology for a contradiction or difference of opinion" [OED].
1510s, "to walk at a steady rate," from pace (n.). Meaning "to measure by pacing" is from 1570s. That of "to set the pace for" (another) is from 1886. Related: Paced; pacing.