The 1837 edition added the before partaking, yet standard English actually prefers no article before the gerund when the gerund is followed by a modifying prepositional phrase. In the original text of the Book of Mormon, such cases of gerunds preceded by the did occur, but some have been eliminated from the current text. For discussion, see under 1 Nephi 17:32; also see the complete discussion under gerundives in volume 3.
Here in Alma 12:22, we have a case where the was added, probably by accident (Joseph Smith did not mark the insertion of the the in the printer’s manuscript). So in accord with standard English as well as the earliest textual sources, the critical text will, in this case, remove the intrusive the.
Summary: Remove the intrusive the before partaking in Alma 12:22, thus restoring the original reading “Adam did fall by partaking of the forbidden fruit”.