fathomyoudaoicibaDictYouDict[fathom 词源字典]
fathom: [OE] The underlying etymological meaning of fathom appears to be ‘stretching out, spreading’. It probably comes ultimately from the Indo-European base *pot-, *pet-, which also produced Latin patēre ‘be open’ (source of English patent) and Greek pétalos ‘outspread’ (source of English petal). Its Germanic descendant was *fath-, which produced the noun *fathmaz, direct ancestor of Old English fæthm.

Here, the notion of ‘stretching out’ seems to have spread via ‘stretching out the arms’ to, on the one hand ‘embrace’ (and one meaning of Old English fæthm was ‘embrace, bosom’), and on the other ‘length spanned by outstretched arms’ – about six feet.
=> patent, petal[fathom etymology, fathom origin, 英语词源]
fathom (n.)youdaoicibaDictYouDict
Old English fæðm "length of the outstretched arm" (a measure of about six feet), also "arms, grasp, embrace," and, figuratively "power," from Proto-Germanic *fathmaz "embrace" (cognates: Old Norse faðmr "embrace, bosom," Old Saxon fathmos "the outstretched arms," Dutch vadem "a measure of six feet"), from PIE *pot(ə)-mo-, from root *petə- "to spread, stretch out" (see pace (n.)). It has apparent cognates in Old Frisian fethem, German faden "thread," which OED explains by reference to "spreading out." As a unit of measure, in an early gloss it appears for Latin passus, which was about 5 feet.
fathom (v.)youdaoicibaDictYouDict
Old English fæðmian "to embrace, surround, envelop," from a Proto-Germanic verb derived from the source of fathom (n.); cognates: Old High German fademon, Old Norse faþma. The meaning "take soundings" is from c. 1600; its figurative sense of "get to the bottom of, penetrate with the mind, understand" is from 1620s. Related: Fathomed; fathoming.