MILE.
«Не на суше мили мерить»©
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Элементарный переход – «р» - «L».

mile (n.)
Old English mil, from West Germanic *milja (cf. Middle Dutch mile, Dutch mijl, Old High German mila, German meile), from Latin mila "thousands," plural of mille "a thousand" (neuter plural was mistaken in Germanic as a fem. singular), of unknown origin.

The Latin word also is the source of French mille, Italian miglio, Spanish milla. The Scandinavian words (Old Norse mila, etc.) are from English. An ancient Roman mile was 1,000 double paces (one step with each foot), for about 4,860 feet, but there were many local variants and a modern statute mile is about 400 feet longer. In Germany, Holland, and Scandinavia in the Middle Ages, the Latin word was applied arbitrarily to the ancient Germanic rasta, a measure of from 3.25 to 6 English miles.

Ну, не знают оне, просто с небес спустилось. Мерить чем? Да милями. А то, на мели будем сидеть. Мелко все это. Милые мои.
Словарь 1675:
MILE (meil, Teut. milie, F. and L.) the Distance of 4000 Paces, 5200 English feet or eig’t Furlongs

MILITARY (militaire, F. militaris, L.) belonging to Soldiers or War, warlike
Более позднее – мили + торить
Раннее – мерить + торить.
Чем, собственно, и занимаются солдаты.

Ну, и «дистанция»
TO DISTAIN (destaindre, F.) – to stain, to pollute
DISTANCE (Distantia, L. of “dis” and “stare”) is the Remoteness of one Thing from another, either in Point of Time, Place, or Quantity. F.
Это просто слово «достать», в смысле «до чего-либо». Еще вариант – «без остановки».