aphorism (n.)youdaoicibaDictYouDict
1520s (especially in reference to the "Aphorisms of Hippocrates"), from Middle French aphorisme (14c., aufforisme), from Late Latin aphorismus, from Greek aphorismos "definition, pithy sentence," from aphorizein "to mark off, divide," from apo- "from" (see apo-) + horizein "to bound" (see horizon).

An aphorism is a short, pithy statement containing a truth of general import; an axiom is a statement of self-evident truth; a theorem is a demonstrable proposition in science or mathematics; an epigram is like an aphorism, but lacking in general import. Maxim and saying can be used as synonyms for aphorism.
distinguish (v.)youdaoicibaDictYouDict
1560s, from Middle French distinguiss-, stem of distinguer, or directly from Latin distinguere "to separate between, keep separate, mark off, distinguish," perhaps literally "separate by pricking," from dis- "apart" (see dis-) + -stinguere "to prick" (compare extinguish and Latin instinguere "to incite, impel").

Watkins says "semantic transmission obscure;" the sense might be from "pricking out" as the old way to make punctuation in parchment or some literal image, but de Vaan derives the second element from a different PIE root meaning "to push, thrust."
The meanings of ex- and restinguere 'to extinguish' and distinguere seem quite distinct, but can be understood if the root meant 'to press' or 'push': ex-stinguere 'to put a fire out', re-stinguere 'to push back, suppress', and dis-stinguere 'to push apart [thence] distinguish, mark off ...."
The suffix -ish is due to the influence of many verbs in which it is the equivalent of Old French -iss-, ultimately from Latin inchoative suffix -iscere (this is also the case in extinguish, admonish, and astonish). Related: Distinguishing. The earlier form of the verb was distinguen (mid-14c.).
line (v.2)youdaoicibaDictYouDict
late 14c., "to tie with a cord," from line (n.). Meaning "to mark or mark off with lines" is from mid-15c. Sense of "to arrange in a line" is from 1640s; that of "to join a line" is by 1773. To line up "form a line" is attested by 1889, in U.S. football.
rope (v.)youdaoicibaDictYouDict
c. 1300, "bind with a rope," from rope (n.). Meaning "mark off with rope" is from 1738; to rope (someone or something) in is from 1848. Related: Roped; roping.
scan (v.)youdaoicibaDictYouDict
late 14c., "mark off verse in metric feet," from Late Latin scandere "to scan verse," originally, in classical Latin, "to climb, rise, mount" (the connecting notion is of the rising and falling rhythm of poetry), from PIE *skand- "to spring, leap, climb" (cognates: Sanskrit skandati "hastens, leaps, jumps;" Greek skandalon "stumbling block;" Middle Irish sescaind "he sprang, jumped," sceinm "a bound, jump").

Missing -d in English is probably from confusion with suffix -ed (see lawn (n.1)). Sense of "look at closely, examine minutely (as one does when counting metrical feet in poetry)" first recorded 1540s. The (opposite) sense of "look over quickly, skim" is first attested 1926. Related: Scanned; scanning.
stake (v.1)youdaoicibaDictYouDict
early 14c., "to mark (land) with stakes," from stake (n.1). Hence, to stake a claim (1857). Meaning "to maintain surveilance" (usually stake out) is first recorded 1942, American English colloquial, probably form earlier sense of "mark off territory." Related: Staked; staking. Old English had stacung "piercing of an effigy by a pin or stake" (in witchcraft); staccan "pierce with a stake, spit."
stake (v.2)youdaoicibaDictYouDict
"to risk, wager," 1520s, perhaps from notion of "post on which a gambling wager was placed" (see stake (n.2)), though Weekley suggests "there is a tinge of the burning or baiting metaphor" in this usage. Meaning "to maintain surveillance" (usually stake out) is first recorded 1942, American English colloquial, probably form earlier sense of "mark off territory." Related: Staked; staking.