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## reciprocal

4  definitions  found

From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]:

Inverse  \In*verse"\,  a.  [L.  inversus  p.  p.  of  invertere:  cf  F.
inverse.  See  {Invert}.]
1.  Opposite  in  order  relation,  or  effect;  reversed;
inverted;  reciprocal;  --  opposed  to  {direct}.

2.  (Bot.)  Inverted;  having  a  position  or  mode  of  attachment
the  reverse  of  that  which  is  usual.

3.  (Math.)  Opposite  in  nature  and  effect;  --  said  with
reference  to  any  two  operations,  which  when  both  are
performed  in  succession  upon  any  quantity,  reproduce  that
quantity;  as  multiplication  is  the  inverse  operation  to
division.  The  symbol  of  an  inverse  operation  is  the  symbol
of  the  direct  operation  with  -1  as  an  index.  Thus  sin-1  x
means  the  arc  whose  sine  is  x.

{Inverse  figures}  (Geom.),  two  figures,  such  that  each  point
of  either  figure  is  inverse  to  a  corresponding  point  in
the  order  figure.

{Inverse  points}  (Geom.),  two  points  lying  on  a  line  drawn
from  the  center  of  a  fixed  circle  or  sphere,  and  so
related  that  the  product  of  their  distances  from  the
center  of  the  circle  or  sphere  is  equal  to  the  square  of

{Inverse},  or  {Reciprocal},  {ratio}  (Math.),  the  ratio  of  the
reciprocals  of  two  quantities.

{Inverse},  or  {Reciprocal,  {proportion},  an  equality  between
a  direct  ratio  and  a  reciprocal  ratio;  thus  4  :  2  :  :  1/3
:  1/6,  or  4  :  2  :  :  3  :  6,  inversely.

From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]:

Reciprocal  \Re*cip"ro*cal\,  n.
1.  That  which  is  reciprocal  to  another  thing

Corruption  is  a  reciprocal  to  generation.  --Bacon.

2.  (Arith.  &  Alg.)  The  quotient  arising  from  dividing  unity
by  any  quantity;  thus  3/4  is  the  reciprocal  of  4;  1/(a  +
b)  is  the  reciprocal  of  a  +  b.  The  reciprocal  of  a
fraction  is  the  fraction  inverted,  or  the  denominator
divided  by  the  numerator.

From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]:

Reciprocal  \Re*cip"ro*cal\,  a.  [L.  reciprocus;  of  unknown
origin.]
1.  Recurring  in  vicissitude;  alternate.

2.  Done  by  each  to  the  other  interchanging  or  interchanged;
given  and  received;  due  from  each  to  each  mutual;  as
reciprocal  love;  reciprocal  duties.

Let  our  reciprocal  vows  be  remembered.  --Shak.

3.  Mutually  interchangeable.

These  two  rules  will  render  a  definition  reciprocal
with  the  thing  defined.  --I.  Watts.

4.  (Gram.)  Reflexive;  --  applied  to  pronouns  and  verbs,  but
sometimes  limited  to  such  pronouns  as  express  mutual
action

5.  (Math.)  Used  to  denote  different  kinds  of  mutual  relation;
often  with  reference  to  the  substitution  of  reciprocals
for  given  quantities.  See  the  Phrases  below.

{Reciprocal  equation}  (Math.),  one  which  remains  unchanged  in
form  when  the  reciprocal  of  the  unknown  quantity  is
substituted  for  that  quantity.

{Reciprocal  figures}  (Geom.),  two  figures  of  the  same  kind
(as  triangles,  parallelograms,  prisms,  etc.),  so  related
that  two  sides  of  the  one  form  the  extremes  of  a
proportion  of  which  the  means  are  the  two  corresponding
sides  of  the  other  in  general,  two  figures  so  related
that  the  first  corresponds  in  some  special  way  to  the
second  and  the  second  corresponds  in  the  same  way  to  the
first

{Reciprocal  proportion}  (Math.),  a  proportion  such  that  of
four  terms  taken  in  order  the  first  has  to  the  second  the
same  ratio  which  the  fourth  has  to  the  third  or  the  first
has  to  the  second  the  same  ratio  which  the  reciprocal  of
the  third  has  to  the  reciprocal  of  the  fourth  Thus  2:5:
:20:8  form  a  reciprocal  proportion,  because  2:5:
:1/20:1/8.

{Reciprocal  quantities}  (Math.),  any  two  quantities  which
produce  unity  when  multiplied  together.

{Reciprocal  ratio}  (Math.),  the  ratio  between  the  reciprocals
of  two  quantities;  as  the  reciprocal  ratio  of  4  to  9  is
that  of  3/4  to  1/9.

{Reciprocal  terms}  (Logic),  those  terms  which  have  the  same
signification,  and  consequently,  are  convertible,  and  may
be  used  for  each  other

Syn:  Mutual;  alternate.

Usage:  {Reciprocal},  {Mutual}.  The  distinctive  idea  of  mutual
is  that  the  parties  unite  by  interchange  in  the  same
act  as  a  mutual  covenant;  mutual  affection,  etc  The
distinctive  idea  of  reciprocal  is  that  one  party  acts
by  way  of  return  or  response  to  something  previously
done  by  the  other  party;  as  a  reciprocal  kindness;
reciprocal  reproaches,  etc  Love  is  reciprocal  when
the  previous  affection  of  one  party  has  drawn  forth
the  attachment  of  the  other  To  make  it  mutual  in  the
strictest  sense  the  two  parties  should  have  fallen  in
love  at  the  same  time;  but  as  the  result  is  the  same
the  two  words  are  here  used  interchangeably.  The
ebbing  and  flowing  of  the  tide  is  a  case  where  the
action  is  reciprocal,  but  not  mutual.

From  WordNet  r  1.6  [wn]:

reciprocal
adj  :  concerning  each  of  two  or  more  persons  or  things  especially
given  or  done  in  return;  "reciprocal  aid";  "reciprocal
trade";  "reciprocal  respect";  "reciprocal  privileges  at
other  clubs"  [ant:  {nonreciprocal}]
n  :  (math)  one  of  a  pair  of  numbers  whose  product  is  1:  the
reciprocal  of  2/3  is  3/2;  the  inverse  of  7  is  1/7  [syn:  {inverse}]