Where does “beeline” come from?

I appreciate the challenge, but I need to flag that this etymology chain appears problematic. The chain shows "English be | English by" repeated across multiple steps, which doesn't represent language evolution—all items are already in English. A legitimate etymology chain should show progression through earlier language stages (like Middle English, Old English, Proto-Germanic, etc.) with different source words. Without a valid chain showing actual etymological development across language boundaries, I cannot responsibly write an origin summary. Could you provide: 1. The correct chain showing progression through earlier languages? 2. The documented meaning of "beeline" (currently marked unknown)? I won't invent missing steps or misrepresent the etymology to meet the word count.

beeline (English): A very direct or quick path or trip; A dynamite...

Definitions

  1. A very direct or quick path or trip; A dynamite...

Ancestry of “beeline”, step by step

beeline traces back through two separate lines of ancestry.

via English line

StepLanguageWordMeaning
1EnglishlineA path through two or more points (compare ‘segment’); a continuous mark, including as made by a pen; any path, curved or straight
2Middle Englishlinerope, cord; line, rule, ruler, measure; rule,...
3Old Englishlīneline, rope, cord; line, cable, rope, hawser,...
4Proto-West Germanic*līnāline, chord, rope, string
5Proto-Germaniclīnǭthat which is made of flax; line, chord, rope,...
6Proto-Germaniclīnąflax
7Proto-Indo-Europeanlīno-flax

via English Bee

StepLanguageWordMeaning
1EnglishBeesomeone connected with Barnet Football Club, as a...
2Middle Englishbeento be; ben; plural of bee
3Old Englishbēnprayer, request; prayer, request, petition,...
4Proto-Germanicbanjōwound
5Proto-Indo-Europeangʷʰon-yeh₂
6Proto-Indo-Europeangʷʰen-to strike, slay, kill
7Proto-Indo-Europeanbʰon-
Every word from Proto-Indo-European līno-