Etymology
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vice versa 

"the order being changed," c. 1600, Latin, from vice, ablative of vicis "a change, alternation, alternate order" (from PIE root *weik- (2) "to bend, to wind") + versa, feminine ablative singular of versus, past participle of vertere "to turn, turn about" (from PIE root *wer- (2) "to turn, bend"). "The phrase has the complete force of a proposition, being as much as to say that upon a transposition of antecedents the consequents are also transposed" [Century Dictionary].

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bully pulpit (n.)
1904, coined by U.S. president Theodore Roosevelt, in reference to the White House.
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brain trust (n.)
"group of experts assembled to give advice on some matter," occasionally used since early 1900s, it became current in 1933, in reference to the intellectuals gathered by U.S. President Franklin D. Roosevelt as advisers; from brain (n.) + trust (n.).
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teddy bear (n.)

1906, named for U.S. president Theodore "Teddy" Roosevelt (1858-1919), a noted big-game hunter, whose conservationist fervor inspired a comic illustrated poem in the New York Times of Jan. 7, 1906, about two bears named Teddy, whose names were transferred to two bears presented to the Bronx Zoo that year. The name was picked up by toy dealers in 1907 for a line of "Roosevelt bears" imported from Germany. Meaning "big, lovable person" first attested 1957, from the song popularized by Elvis Presley.

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Monroe 

the surname (also Munroe, etc.) is said to be ultimately from the River Roe in Derry, Ireland. James Monroe (1758-1831), the fifth U.S. president, was in office from 1817 to 1825. The Monroe Doctrine (so called from 1848) is a reference to the principles of policy contained in his message to Congress on Dec. 2, 1823. Monrovia, the capital of Liberia, also was named for him at its founding in 1822 by the American Colonization Society.

In terms of national psychology, the Monroe Doctrine marked the moment when Americans no longer faced eastward across the Atlantic and turned to face westward across the continent. [Daniel Walker Howe, "What Hath God Wrought"]
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lame duck (n.)

1761, "any disabled person or thing;" especially Stock Exchange slang for "defaulter."

A lame duck is a man who cannot pay his differences, and is said to waddle off. [Thomas Love Peacock, "Gryll Grange," 1861]

Sometimes also in naval use for "an old, slow ship." Modern sense of "public official serving out term after an election" is recorded by 1863, American English. The quote attributed to President Lincoln ("[A] senator or representative out of business is a sort of lame duck. He has to be provided for") is from an anecdote of 1878.

It is well known to everybody who knows anything of its history, that this court [Court of Claims] was made a sort of retreat for lame duck politicians that got wounded and had to retreat before the face of popular condemnation. That is just exactly what it was for, a safe retreat for lame ducks; and it was so filled up; (etc.) [Sen. John P. Hale, New Hampshire, Congressional Globe, Jan. 12, 1863, p.271]
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