Etymology
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Words related to geriatrics

pediatrics (n.)

"medical treatment of children; the branch of medicine dealing with the study of childhood and diseases of children," 1884; from pediatric; see -ics.

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geriatric (adj.)

1909, formed in English from Latinized forms of Greek gēras, gērōs "old age" (from PIE root *gere- (1) "to grow old") + iatrikos "of a physician," from iatros (see -iatric).

-ics 
in the names of sciences or disciplines (acoustics, aerobics, economics, etc.), a 16c. revival of the classical custom of using the neuter plural of adjectives with Greek -ikos "pertaining to" (see -ic) to mean "matters relevant to" and also as the titles of treatises about them. Subject matters that acquired their English names before c. 1500, however, tend to be singular in form (arithmetic, logic, magic, music, rhetoric). The grammatical number of words in -ics (mathematics is/mathematics are) is a confused question.
*gere- (1)
*gerə-, Proto-Indo-European root meaning "to grow old." It forms all or part of: geriatric; geriatrics; gerontocracy; gerontology.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit jara "old age," jarati "makes frail, causes to age;" Avestan zaurvan "old age;" Greek geron "old man;" Ossetic zarond "old man;" Armenian cer "old, old man."