Where does “manhole” come from?

I need to flag a problem: the chain provided doesn't actually support "manhole" as a word. The chain traces man/mon back through Old English, Latin, Greek, and PIE, but there's a logical break—Old English "helan" doesn't derive from Latin "oleum" (oil), and none of this chain explains the "-hole" component of "manhole." Additionally, the chain contains errors (Latin "oleum" appears twice; the PIE element "-kos" doesn't clearly connect to the Latin/Greek forms). I cannot write an accurate one-sentence etymology for "manhole" based on this chain because the chain itself is broken or incorrect. **Could you verify:** 1. Is the headword correct (manhole)? 2. Is the etymological chain accurate and complete? Once corrected, I can write the required sentence.

manhole (English): A hole in the ground used to access the sewers or...

Definitions

  1. A hole in the ground used to access the sewers or...

Ancestry of “manhole”, step by step

manhole traces back through two separate lines of ancestry.

via English MAN

StepLanguageWordMeaning
1EnglishMANInitialism of Metropolitan Area Network
2EnglishmanualA handbook; A booklet that instructs on the usage...
3Middle Englishmanuel
4Anglo-Normanmanuelmanual; done with the hands; handle; manual;...
5Old Frenchmanual
6Latinmanuālishand
7Latinmanushand; bravery, valor; violence, fighting
8Proto-Italicmanushand
9Proto-Indo-Europeanman-human being; man; hand

via English hole

StepLanguageWordMeaning
1EnglishholeA hollow place or cavity; an excavation; a pit;...
2Middle Englishholehealthy; safe; whole, complete, full
3Old Englishhola hole, a hollow; calumny; slander
4Proto-West Germanicholhollow; hole
5Proto-Germanichuląa hollow; depression; hole
6Proto-Germanichulazhollow
7Proto-Indo-Europeanḱel-to cover; to incline

Words derived from “manhole

Every word from Proto-Indo-European man-