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reciprocalmore about 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 
  the  radius. 
  {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 
  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 
  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 
  {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: 
  {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]: 
  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}] 

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