Etymology
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a cappella 

1868, earlier alla capella (1824), from Italian, "in the style of Church music, in the manner of the chapel," literally "according to the chapel," from cappella "chapel" (see chapel). Originally in reference to older church music (pre-1600) which was written for unaccompanied voices; applied 20c. to unaccompanied vocal music generally. Italian a is from Latin ad "to, toward; for; according to" (see ad-); alla is a la "to the." Sometimes in the Latin form a capella.

Also denoting "that instruments are to play in unison with the voices, or that one part is to be played by a number instruments." ["Chambers's Encyclopaedia," 1868]

You are not the first person puzzled by the expression "A Capella," or, at any rate, unable to understand it should signify the exact reverse of what it literally does signify. The chorales in oratorios were invariably accompanied, either by double-bass or the whole band. Hence they were, with perfect correctness, said to be performed "a capella." But, as other chorales, sung as part of the church service, were written in the same and simple style the expression "a capella" came in time to be applied to them also, despite their being sung without any instrumental accompaniment whatever. [The Music World, Sept. 11, 1875]
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a deux 
French, à deux, literally "for two," from à, from Latin ad "to, toward; for" (see ad-) + deux (see deuce). By 1876 as a French term in English.
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a la 
from French à la, literally "to the," hence "in the manner of, according to," from à, from Latin ad "to" (see ad-) + la, fem. of definite article le "the," from Latin ille (fem. illa; see le). Attested in English in French terms from fashion or cookery since late 16c.; since c. 1800 used in native formations with English words or names.
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a la carte 
"ordered by separate items" (itemized on a bill); distinguished from a table d'hôte, indicating a meal served at a fixed, inclusive price; 1826, from French à la carte, literally "by the card" (see a la + card (n.1)).
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a la mode (adv.)
also alamode, 1640s, from French à la mode (15c.), literally "in the (prevailing) fashion" (see a la + mode (n.2)). In 17c., sometimes nativized as all-a-mode. Cookery sense in reference to a dessert served with ice cream is 1903, American English; earlier it was used of a kind of beef stew or soup (1753).
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a posteriori 
17c., in reference to reasoning from a consequent to its antecedent, from an effect to its cause; Latin, literally "from what comes after;" from a "off, away from," usual form of ab before consonants (see ab-) + posteriori, neuter ablative of posterius, comparative of posterus "after, subsequent," from post "after" (see post-). Opposed to a priori. In modern use (from c. 1830, based on Kant) roughly equivalent to "from experience."
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a priori 
1710, "from cause to effect," a Latin term in logic from c. 1300, in reference to reasoning from antecedent to consequent, based on causes and first principles, literally "from what comes first," from priori, ablative of prior "first" (see prior (adj.)). Opposed to a posteriori. Since c. 1840, based on Kant, used more loosely for "cognitions which, though they may come to us in experience, have their origin in the nature of the mind, and are independent of experience" [Century Dictionary]. Related: Apriorist; apriorism; aprioristic. The a is the usual form of Latin ab "off, of, away from" before consonants (see ab-).
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ab initio 
c. 1600, Latin, literally "from the beginning," from ab "from" (see ab-) + ablative of initium "entrance, beginning," which is from or related to the verb inire "to go into, enter upon, begin" (see initial).
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ab ovo 
"from the beginning," Latin, literally "from the egg," from ab "from, away from" (see ab-) + ablative of ovum "egg" (see ovum). The expression is said to refer to the Roman custom of beginning the meal with eggs, as also in the expression ab ovo usque ad mala, "from the egg to the apples" (Horace), hence "from the beginning to the end" (compare early 20c. soup to nuts).
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ab urbe condita 

with year-dates, an occasional Roman method of identifying a given year by reference to the time passed since founding of the city, which in 1c. B.C.E. was calculated to have taken place in what we would call 753 B.C.E. Literally "from the city founded;" the elements are ab "from" (see ab-) + ablative of urbs "city" (see urban) + fem. past participle of condere "put together, store," from assimilated form of com- "together" (see com-) + -dere "put" (from PIE root *dhe- "to put, place").

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