apple-sauce n.

Old English æppel "apple; any kind of fruit; fruit in general," from Proto-Germanic *ap(a)laz (source also of Old Saxon, Old Frisian, Dutch appel, Old Norse eple, Old High German apful, German Apfel), from PIE *ab(e)l- "apple" (source also of Gaulish avallo "fruit;" Old Irish ubull, Lithuanian obuolys, Old Church Slavonic jabloko "apple"), but the exact relation and original sense of these is uncertain (compare melon).

In Middle English and as late as 17c., it was a generic term for all fruit other than berries but including nuts (such as Old English fingeræppla "dates," literally "finger-apples;" Middle English appel of paradis "banana," c. 1400). Hence its grafting onto the unnamed "fruit of the forbidden tree" in Genesis.

As far as the forbidden fruit is concerned, again, the Quran does not mention it explicitly, but according to traditional commentaries it was not an apple, as believed by Christians and Jews, but wheat. [Seyyed Hossein Nasr, "The Heart of Islam: Enduring Values for Humanity," 2002] 

 Cucumbers, in one Old English work, are eorþæppla, literally "earth-apples" (compare French pomme de terre "potato," literally "earth-apple;" see also melon). French pomme is from Latin pomum "apple; fruit" (see Pomona).

Apple of Discord (c. 1400) was thrown into the wedding of Thetis and Peleus by Eris (goddess of chaos and discord), who had not been invited, and inscribed kallisti "To the Prettiest One." Paris, elected to choose which goddess should have it, gave it to Aphrodite, offending Hera and Athene, with consequences of the Trojan War, etc.

Apple of one's eye (Old English), symbol of what is most cherished, was the pupil, supposed to be a globular solid body. Apple-polisher "one who curries favor" first attested 1928 in student slang. The image in the phrase upset the apple cart "spoil the undertaking" is attested from 1788. Road-apple "horse dropping" is from 1942.

A roted eppel amang þe holen, makeþ rotie þe yzounde. ["Ayenbite of Inwit," 1340] 

mid-14c., "condiment for meat, fish, etc.; pickling liquid, brine," from Old French sauce, sausse, from Latin salsa "things salted, salt food," noun use of fem. singular or neuter plural of adjective salsus "salted," from past participle of Old Latin sallere "to salt," from sal (genitive salis) "salt" (from PIE root *sal- "salt").

From late 14c. as "a curative preparation, medicinal salt." Often in 15c.-17. sawce, salse; constant reimportation of the word in French cookery terms might have helped keep the older spelling. Also formerly applied broadly in provincial English and U.S. to condiments of any kind, especially garden vegetables or roots eaten with meat (1620s), also known as garden-sauce.

Figurative meaning "something which adds piquancy to words or actions" is recorded from c. 1500; the sense of "impertinence" is by 1835, but the connection of ideas in it is much older (see saucy, and compare sass). Slang meaning "liquor" is attested by 1940. Figurative phrases suggesting "subject to the same kind of usage" is by 1520s (serued with the same sauce).