# reciprocally

## Definitions

• WordNet 3.6
• adv reciprocally in an inverse or contrary manner "inversely related","wavelength and frequency are, of course, related reciprocally"- F.A.Geldard"
• adv reciprocally in a mutual or shared manner "the agreement was mutually satisfactory","the goals of the negotiators were not reciprocally exclusive"
• adv reciprocally (often followed by `for') in exchange or in reciprocation "gave up our seats on the plane and in return received several hundred dollars and seats on the next plane out","we get many benefits in return for our taxes"
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Webster's Revised Unabridged Dictionary
• Reciprocally In a reciprocal manner; so that each affects the other, and is equally affected by it; interchangeably; mutually. "These two particles do reciprocally affect each other with the same force."
• Reciprocally (Math) In the manner of reciprocals.
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Century Dictionary and Cyclopedia
• reciprocally In a reciprocal manner; with reciprocating action or effect; alternatingly; interchangeably; correspondingly.
• reciprocally In a reciprocal ratio or proportion; inversely. Thus, in bodies of the same weight the density is reciprocally as the magnitude—that is, the greater the magnitude the less in the same proportion the density, and the less the magnitude the greater in the same proportion the density. In geometry two magnitudes are said to be reciprocally proportional to two others when one of the first pair is to one of the second as the remaining one of the second is to the remaining one of the first.
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Chambers's Twentieth Century Dictionary
• adv Reciprocally mutually: interchangeably: inversely
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## Quotations

• Samuel Johnson
“Life cannot subsist in society but by reciprocal concessions.”
• Washington Irving
“Love is never lost. If not reciprocated, it will flow back and soften and purify the heart.”
• Louis K. Anspacher
“Marriage is that relation between man and woman in which the independence is equal, the dependence mutual, and the obligation reciprocal.”

## Etymology

Chambers's Twentieth Century Dictionary
L. reciprocus.

## Usage

### In literature:

Two years was the limited time of his absence, and, on his departure, the sorrow of my parents was reciprocal.
"Beaux and Belles of England" by Mary Robinson
Surely, I may say so; since all duties are reciprocal.
"Clarissa, Volume 3 (of 9)" by Samuel Richardson
The feeling then was reciprocal, and he was proposed for the vacant seat.
"The Grand Old Man" by Richard B. Cook
Reciprocal complaints are not easily adjusted, but by reciprocal compliance.
"The Works of Samuel Johnson, Vol. 6" by Samuel Johnson
And how can there be conjunction with God by love and wisdom, unless a man have some reciprocity of conjunction?
"The Delights of Wisdom Pertaining to Conjugial Love" by Emanuel Swedenborg
Perhaps they are absorbed in the calculation of their reciprocal interests, which are not yet perfectly amalgamated.
"The Adventures of a Special Correspondent" by Jules Verne
The rights and duties of master and apprentice are correlative and reciprocal.
"The Anti-Slavery Examiner, Omnibus" by American Anti-Slavery Society
The other is the reciprocity treaty of 1903.
"Cuba, Old and New" by Albert Gardner Robinson
It is the sum total of rules and laws resulting from the reciprocal action of mind and body.
"Delsarte System of Oratory" by Various
This treaty is unilateral, not reciprocal.
"A Compilation of the Messages and Papers of the Presidents" by James D. Richardson
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### In poetry:

Urit spes animi credula mutui.—Hor.
Imitation.
Fond hope of a reciprocal desire
Inflames the breast.
"Ode, written 1739" by William Shenstone
"I doubt it not," said John, "and I
Reciprocate the feeling,
And here, with one despairing cry,
I kneel, and love you, kneeling."
"John And Jane" by Thomas Frederick Young
Reciprocal visits were often,
He slept with me, I slept with him,
Talked till near dawn of daylight,
With fluent and scholarly Tim.
"Tim" by Jared Barhite
OUR hero felt a thousand times more blessed
Than when he first the beauteous fair caressed;
For when a flame reciprocal is raised,
The bliss redoubles, and by all is praised.
"Richard Minutolo" by Jean de La Fontaine
Who seek a friend should come dispos’d
To exhibit, in full bloom disclos’d,
The graces and the beauties
That form the character he seeks,
For ‘tis a union that bespeaks
Reciprocated duties.
"Friendship" by William Cowper
The worthy priest, he up and drew his cowl upon his crown,
And started off in haste to tell the news to ROBBER BROWN -
To tell him how his daughter, who was now for marriage fit,
Had winked upon a sorter, who reciprocated it.
"Gentle Alice Brown" by William Schwenck Gilbert

### In news:

But unlike some other conversions in which the entire slide reciprocates, Nighthawk 's unit is composed of two parts.
He posits that there are 6 triggers that influence us to act, to believe, to be persuaded : reciprocity, commitment, social proof, liking, authority, and scarcity.
Kansas scraps reciprocal tuition agreement with Missouri.
NITL files petition with Surface Transportation Board, calling for new reciprocal switching rules.
Dewalt Reciprocal Saw Product Review.
Interested in the Dewalt Reciprocal Saw.
CHAMPAIGN-URBANA, IL — The American Meat Science Association's (AMSA) 62nd Annual Reciprocal Meat Conference was held in Rogers, Arkansas.
Reciprocity is a key determinant of human behavior and has been well documented in the psychological and behavioral economics literature.
Michigan Becomes First State to Achieve Maximum Reciprocity for Concealed Carry Across the Nation.
Owens votes in favor of gun-control ' reciprocity '.
Reciprocity News & Trends.
Schneiderman urges Senate against reciprocity .
Louisiana State Police and the Ohio attorney general have signed an agreement allowing reciprocity between the states for residents with valid concealed weapons permits.
Minnesota and Wisconsin students who live in one state and want to attend school in the other can again pay the resident rates at colleges in either state after a new reciprocity agreement was reached.
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### In science:

When G is nonbipartite, we deﬁne the reciprocal polynomial of G, denoted RG (x), by RG (z) = znχG (z + 1/z) .
Salem numbers, Pisot numbers, Mahler measure and graphs
When G is bipartite, the reciprocal polynomial RG (x) is deﬁned by RG (z) = zn/2χG (√z + 1/√z ) .
Salem numbers, Pisot numbers, Mahler measure and graphs
We can construct its reciprocal polynomial, RG , and τ = τ (G) is a root of this.
Salem numbers, Pisot numbers, Mahler measure and graphs
Were λ (respectively λ2 ) to be a rational integer—cases excluded in the deﬁnition—then these would be the only roots of mτ , and τ would be a reciprocal quadratic Pisot number.
Salem numbers, Pisot numbers, Mahler measure and graphs
Throughout this section, reciprocal polynomials will be written as functions of a variable z , and we conveniently treat the bipartite and nonbipartite cases together by writing y = √z if the graph is bipartite, and y = z otherwise.
Salem numbers, Pisot numbers, Mahler measure and graphs
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