II.off [美 ɔf, ɑf, 英 ɒf]副off often appears as the second element of certain verb structures in English (break off, pay off, take off, etc). For translations, see the relevant verb entry (break, pay, take, etc).
I.on [美 ɑn, ɔn, 英 ɒn]介词on often appears as the second element of certain verb structures in English (count on, lay on, sign on, etc). For translations, see the relevant verb entry (count, lay, sign, etc).
But other than that, it should have come before the umbrella and the article have been about a new non-electric device that opens up and keeps the rain off.