Etymology
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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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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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