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-a (1) Feminine suffix.
From Latin -a, from Proto-Italic *, from late Proto-Indo-European *-(e)h2, from Proto-Indo-European *-h2, a suffix indicating collective and abstract animate nouns, from Pre-Proto-Indo-European *-h2, a suffix indicating plurale tantum.
In Pre-Proto-Indo-European, a suffix *-h2 was used to form plurale tantum nouns out of collective nouns. (As a somewhat inaccurate analogy to help the reader understand the function of *-h2 to the ancient Pre-Proto-Indo-European speakers, imagine the collective noun "water" becoming plurale tantum "waters" by way of a plural suffix -s (e.g., "the waters of Babylon" of Psalm 173:1 ESV); the role of the -s is akin to the role of Pre-Proto-Indo-European *-h2). This was attached to the vowel stem *-e-, *-i-, *-u- and *-0- to form *-eh2, *-ih2, *-uh2, and *-h2. The four different endings all to express a single idea of plurality would not last. But now we must discuss the historic Proto-Indo-European method for feminizing words.

In Proto-Indo-European *sor "woman" was added as a suffix to animate nouns (retained in Anatolian languages and partially survived as a fossil in a smattering of non-Anatolian words).
Linguists do not agree as to why *-sor, when used as a feminine marker, was slowly supplanted by the *-(e)h2 collective suffix after the Anatolian languages broke off from the rest of the Indo-European community. Recent theories suggest the suffix played an "individualizing" role. Under these lines of thinking, the collective/abstract suffix *-(e)h2 referred to a subset of larger mass nouns (compare in English plurale tantum "glasses," formed from the mass noun "glass"). Gradually, dependence on *-(e)h2 to refer to subsets of broad categories gave the suffix a new sense of individualization - speakers were depending on the suffix to specify individual items out of larger groups. Once an uncommon suffix, by the late Proto-Indo-European period *-(e)h2 enjoyed heavily use to specify individual animate objects, and so speakers contrasted the new animate ending *-(e)h2 against the old animate ending *-s. *-(e)h2 acquired a new meaning, not one of plurale tantum but a meaning of "the other object."

In compelling support of this theory, there is a word a word that looks to be a relic from the transitional period from collective/abstract suffix to a feminine suffix (the familiar -a in Core Indo-European). *h2u̯idhéu̯eh2- "widow," animate in Anatolian but feminine in other Indo-European languages, looks built off of *h2u̯idhéu̯o- "belonging to the one fatally struck." Thus the original meaning of a widow comes from the time when the suffix played an individualizing role: "the one belonging to the fatally struck." Later, the word simplified to "the bereaved." After the Anatolian branch broke from the Indo-European trunk, the suffix was fully feminized as "the female bereaved." See Luraghi (2011), Tichy (1993), and Melchert (2014b) for a broader discussion.
a (Adverb) "at," "in"
A post-Latin development from the 12th cent., deriving from Latin ad "to," "toward." From Proto-Italic *ad 'id.' From Proto-Indo-European *h2ed 'id.'
Indo-European
Romance
Asturian a, Portuguese a, Galician a, Catalan a, French à, Italian a, ad, Romanian a
Italic
Oscan az "by" (< *ad-s)
Celtic
Welsh â
Germanic
Gothic at, Old Icelandic at, Old English æt (English at)
-a (2) Forms masculine nouns.
From Vulgar Latin *-a 'id.' According to Penny (2002), the ending probably survived in Old Spanish only in día as other masculine nouns with this ending were the result of scholastic remodeling under the influence of Classical Latin. From Latin -a, the first declension's nominative singular ending. From Proto-Italic * 'id.' From Proto-Indo-European *-eh2, a nominative singular ending. See also -a (1).
ab- Prefix indicating "off" or "away"
Not a productive prefix in Spanish, and it appears only as a relic in verbs like abrir. From Latin ab 'id.' From Proto-Italic *ap- 'id.' From Proto-Indo-European *h2epo 'id.' As an allative preposition, the word had a full grade *h2epo (preserved in the prefix ab- above) and a zero grade *h2po (preserved in the prefix po-).
Indo-European
Italic
Umbrian ap-, Paelignian af-, Oscan af-
Germanic
Gothic af, aff-, Old Norse af, Old High German aba, Old Saxon af, English of
Albanian
Albanian pa "without"
Balto-Slavic
Lithuanian po-, Latvian ap "beneath," Old Church Slavonic po, Russian po
Hellenic
Ancient Greek ἀπό (apó) "far from"
Messapian
Messapian apa "from"
Indo-Iranian
Sanskrit ápa "away," Avestan apa-
abajo (Adverb) "down," "below"
First attested c. 1300 but was rarely used until the 15th cent. Formed from Latin a(d)- "at," "toward" and bassus "down" (see a- and bajo respectively).
Also the origin of the surname Abajo, given to Moorish families that lived in the lowlands of Spain.
Indo-European
Romance
Asturian (Teberga) abaxu, Portuguese abaixo, Galician abaixo, Catalan abaixo, French à bas
abiertamente (Adverb) "openly"
From abierta and -mente, an adverb-forming suffix.
abierto (Adjective) "open"
12th cent. From Latin apertus 'id.,' from aperire "to open." See abrir.
-able, -ible Prefix indicating ability or inclination.
From Latin -abilis and -ibilis, of identical meanings, both from an a-stem and an i-stem fixed to -bilis "capability." From Proto-Italic *-þli- 'id.' From the Proto-Indo-European instrumental suffix *-dhli-.
ablentar (Verb) "to winnow"
Dialect variant of beldar. From a- and Old Spanish bendlar (a variant bedlar, without the -n-, became the basis for beldar). Formed from 13th cent. Old Spanish bellar via dissimilation. From Latin ventilare "to fan," a verb formed from ventulus "light breeze" (but lit. "little wind"), a diminutive of ventus "wind" (see viento).
Indo-European
Romance
Sardinian bentulai
abogado (Noun) "lawyer," "advocate," "counsel"
13th cent. From Latin advocatus "aide," "advocate," "witness." From advocare "to advocate" (see abogar).
Historically, abogada meant "interceding saint;" the profession of advocate was exclusive to men prior to the 1960s.
Indo-European
Romance
Asturian abogáu, Portuguese advogado, Catalan advocat, Old French avocat, Italian avvocato, Dalmatian abucat, Romanian a(d)vocat