How did the meaning of "once more, anew" arise in "again"?

Ayto doesn’t expound where the late 14c. meaning of ‘once more, anew’ sprang from? Is "once more, anew" related to "in a direct line with, facing" or "in the opposite direction, back"?

again [OE]

The underlying etymological sense
of again is ‘in a direct line with, facing’, hence
‘opposite’ and ‘in the opposite direction, back’
(its original meaning in Old English). It comes
from a probable Germanic *gagin ‘straight’,
which was the source of many compounds
formed with on or in in various Germanic
languages, such as Old Saxon angegin and Old
Norse íg gegn. The Old English form was
ongēan, which would have produced ayen in
modern English; however, Norse-influenced
forms with a hard g had spread over the whole
country from northern areas by the 16th century.
The meaning ‘once more, anew’ did not develop
until the late 14th century. From Old English
times until the late 16th century a prefix-less
form gain was used in forming compounds. It
carried a range of meanings, from ‘against’ to ‘in
return’, but today survives only in gainsay.
      The notion of ‘opposition’ is carried through
in against, which was formed in the 12th century
from again and what was originally the genitive
suffix -es, as in always and nowadays. The
parasitic -t first appeared in the 14th century.

Word Origins (2005 2e) by John Ayto, p 11 Right column.