[1.] [Etymonline'] from particeps "sharing, partaking" (see participation). In grammatical sense, the Latin translates Greek metokhe "sharer, partaker," and the notion is of a word "partaking"
of the nature of both a noun and an adjective.
Source: p 32, A Student's Introduction to English Grammar (2005) by Huddleston and Pullum
[2.] Traditionally (for example, in the grammar of Latin), ... a participle is
one[a verb-form] that is functionally similar to an adjective.
2 above only states that a gerund resembles an adjective, NOT a noun.
So how do participles partake
of the nature of both a noun and an adjective?
Strangely, 3 below instead mentions only a verb, and NOT a noun.
[3.] [Source:] The OED explains that the Latin term was used to refer to “a non-finite part of a verb” that shares “some characteristics of a verb and some of an adjective.”