Etymology
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each other 
reciprocal pronoun, originally in late Old English a phrase, with each as the subject and other inflected (as it were "each to other," "each from other," etc.).
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per annum 

"in each year, annually," c. 1600, Latin, "by the year," from per (see per) + annum, accusative singular of annus "year" (see annual (adj.)).

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American dream 

coined 1931 by James Truslow Adams (1878-1949), U.S. writer and popular historian (unrelated to the Massachusetts Adamses), in "Epic of America."

[The American Dream is] that dream of a land in which life should be better and richer and fuller for everyone, with opportunity for each according to ability or achievement. It is a difficult dream for the European upper classes to interpret adequately, and too many of us ourselves have grown weary and mistrustful of it. It is not a dream of motor cars and high wages merely, but a dream of social order in which each man and each woman shall be able to attain to the fullest stature of which they are innately capable, and be recognized by others for what they are, regardless of the fortuitous circumstances of birth or position. [Adams]

Others have used the term as they will.

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per diem 

1510s, "by the day, in each day," Latin, "by the day," from per (see per) + diem, accusative singular of dies "day" (from PIE root *dyeu- "to shine"). As a noun from 1809, "amount or allowance of so much every day."

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attention deficit disorder (n.)
(abbreviated ADD), introduced as a diagnosis in the third edition of the "Diagnostic and Statistical Manual of Mental Disorders" (1980), from attention in the "power of mental concentration" sense. Expanded to attention deficit hyperactivity disorder ("the co-existence of attentional problems and hyperactivity, with each behavior occurring infrequently alone;" ADHD) in DSM-III (1987).
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round robin (n.)
"petition or complaint signed in a circle to disguise the order in which names were affixed and prevent ringleaders from being identified," 1730, originally in reference to sailors and frequently identified as a nautical term. As a kind of tournament in which each player plays the others, it is recorded from 1895.
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Cadmean victory (n.)

c. 1600, "victory involving one's own ruin," translating Greek Kadmeia nikē, from Cadmus (Greek Kadmos), legendary hero-founder of Thebes in Boeotia and bringer of the original sixteen-letter alphabet to Greece. Probably a reference to the story of Cadmus and the "Sown-Men," who fought each other till only a handful were left alive. Compare Pyrrhic (adj.1).

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contra-dance (n.)

"dance by four couples placed opposite to each other and making the same steps and figures," 1803, from French contre-danse, altered from English country dance by folk etymology from French contra "against," suggested by the arrangement of the partners in the dance. The dances and the name were taken up in France c. 1720s and from there passed to Spain and Italy (Spanish, Italian contra danza) then back to English.

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per stirpes 

1680s, Latin, "by families, by stocks;" in legal use, for inheritances, etc., opposed to per capita. See per- + stirpes.

[A]pplied to succession when divided so as to give the representatives belonging to one branch the share only that their head or ancestor would have taken had he survived. Thus, in a gift to A and the children of B, if they are to take per capita, each child will have a share equal to that of A; but if they are to take per stirpes, A will take one half and the other half will be divided among the children of B. [Century Dictionary]
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hay fever (n.)

also hay-fever, 1825, from hay + fever. Also called summer catarrh (1828); not much noted before the 1820s, when it was sometimes derided as a "fashion" in disease.

People are apt to sneeze, in hot weather for example; and people do not die of sneezing now-a-days, as they did in days that no one knows any thing about. We cannot give six draughts a-day, at one and nine pence each, for sneezing: call it the hay-fever. What a wonderful man! what a clever man! he understands the hay-fever: call him in! Thus is the hay-fever among the last in the list of fashionables. ["On Fashions in Physic," London Magazine, October 1825]
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