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proportionmore about proportion

proportion


  5  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]: 
 
  Proportion  \Pro*por"tion\,  n.  [F.,  fr  L.  proportio;  pro  before 
  +  portio  part  or  share.  See  {Portion}.] 
  1.  The  relation  or  adaptation  of  one  portion  to  another,  or 
  to  the  whole,  as  respect  magnitude,  quantity,  or  degree; 
  comparative  relation;  ratio;  as  the  proportion  of  the 
  parts  of  a  building,  or  of  the  body. 
 
  The  image  of  Christ,  made  after  his  own  proportion. 
  --Ridley. 
 
  Formed  in  the  best  proportions  of  her  sex.  --Sir  W. 
  Scott. 
 
  Documents  are  authentic  and  facts  are  true  precisely 
  in  proportion  to  the  support  which  they  afford  to 
  his  theory.  --Macaulay. 
 
  2.  Harmonic  relation  between  parts  or  between  different 
  things  of  the  same  kind  symmetrical  arrangement  or 
  adjustment;  symmetry;  as  to  be  out  of  proportion.  ``Let 
  us  prophesy  according  to  the  proportion  of  faith.''  --Rom. 
  xii.  6. 
 
  3.  The  portion  one  receives  when  a  whole  is  distributed  by  a 
  rule  or  principle;  equal  or  proper  share;  lot 
 
  Let  the  women  .  .  .  do  the  same  things  in  their 
  proportions  and  capacities.  --Jer.  Taylor. 
 
  4.  A  part  considered  comparatively;  a  share. 
 
  5.  (Math.) 
  a  The  equality  or  similarity  of  ratios,  especially  of 
  geometrical  ratios;  or  a  relation  among  quantities 
  such  that  the  quotient  of  the  first  divided  by  the 
  second  is  equal  to  that  of  the  third  divided  by  the 
  fourth  --  called  also  {geometrical  proportion},  in 
  distinction  from  arithmetical  proportion,  or  that  in 
  which  the  difference  of  the  first  and  second  is  equal 
  to  the  difference  of  the  third  and  fourth 
 
  Note:  Proportion  in  the  mathematical  sense  differs  from 
  ratio.  Ratio  is  the  relation  of  two  quantities  of  the 
  same  kind  as  the  ratio  of  5  to  10,  or  the  ratio  of  8 
  to  16.  Proportion  is  the  sameness  or  likeness  of  two 
  such  relations.  Thus  5  to  10  as  8  to  16;  that  is  5 
  bears  the  same  relation  to  10  as  8  does  to  16.  Hence 
  such  numbers  are  said  to  be  in  proportion.  Proportion 
  is  expressed  by  symbols  thus:  a:b::c:d,  or  a:b  =  c:d, 
  or  a/b  =  c/d. 
  b  The  rule  of  three  in  arithmetic,  in  which  the  three 
  given  terms,  together  with  the  one  sought,  are 
  proportional. 
 
  {Continued  proportion},  {Inverse  proportion},  etc  See  under 
  {Continued},  {Inverse},  etc 
 
  {Harmonical,  or  Musical},  {proportion},  a  relation  of  three 
  or  four  quantities,  such  that  the  first  is  to  the  last  as 
  the  difference  between  the  first  two  is  to  the  difference 
  between  the  last  two  thus  2,  3,  6,  are  in  harmonical 
  proportion;  for  2  is  to  6  as  1  to  3.  Thus  24,  16,  12,  9, 
  are  harmonical,  for  24:9::8:3. 
 
  {In  proportion},  according  as  to  the  degree  that  ``In 
  proportion  as  they  are  metaphysically  true,  they  are 
  morally  and  politically  false.''  --Burke. 
 
  From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]: 
 
  Proportion  \Pro*por"tion\,  v.  t.  [imp.  &  p.  p.  {Proportioned}; 
  p.  pr  &  vb  n.  {Proportioning}.]  [Cf.  F.  proportionner  Cf 
  {Proportionate},  v.] 
  1.  To  adjust  in  a  suitable  proportion,  as  one  thing  or  one 
  part  to  another;  as  to  proportion  the  size  of  a  building 
  to  its  height;  to  proportion  our  expenditures  to  our 
  income. 
 
  In  the  loss  of  an  object  we  do  not  proportion  our 
  grief  to  the  real  value  .  .  .  but  to  the  value  our 
  fancies  set  upon  it  --Addison. 
 
  2.  To  form  with  symmetry  or  suitableness,  as  the  parts  of  the 
  body. 
 
  Nature  had  proportioned  her  without  any  fault.  --Sir 
  P.  Sidney. 
 
  3.  To  divide  into  equal  or  just  shares;  to  apportion. 
 
  From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]: 
 
  Geometric  \Ge`o*met"ric\,  Geometrical  \Ge`o*met"ric*al\,  a.  [L. 
  geometricus  Gr  ?:  cf  F.  g['e]om['e]trique.] 
  Pertaining  to  or  according  to  the  rules  or  principles  of 
  geometry;  determined  by  geometry;  as  a  geometrical  solution 
  of  a  problem. 
 
  Note:  Geometric  is  often  used  as  opposed  to  algebraic,  to 
  include  processes  or  solutions  in  which  the 
  propositions  or  principles  of  geometry  are  made  use  of 
  rather  than  those  of  algebra. 
 
  Note:  Geometrical  is  often  used  in  a  limited  or  strictly 
  technical  sense  as  opposed  to  mechanical;  thus  a 
  construction  or  solution  is  geometrical  which  can  be 
  made  by  ruler  and  compasses,  i.  e.,  by  means  of  right 
  lines  and  circles.  Every  construction  or  solution  which 
  requires  any  other  curve,  or  such  motion  of  a  line  or 
  circle  as  would  generate  any  other  curve,  is  not 
  geometrical,  but  mechanical.  By  another  distinction,  a 
  geometrical  solution  is  one  obtained  by  the  rules  of 
  geometry,  or  processes  of  analysis,  and  hence  is  exact; 
  while  a  mechanical  solution  is  one  obtained  by  trial, 
  by  actual  measurements,  with  instruments,  etc.,  and  is 
  only  approximate  and  empirical. 
 
  {Geometrical  curve}.  Same  as  {Algebraic  curve};  --  so  called 
  because  their  different  points  may  be  constructed  by  the 
  operations  of  elementary  geometry. 
 
  {Geometric  lathe},  an  instrument  for  engraving  bank  notes, 
  etc.,  with  complicated  patterns  of  interlacing  lines;  -- 
  called  also  {cycloidal  engine}. 
 
  {Geometrical  pace},  a  measure  of  five  feet. 
 
  {Geometric  pen},  an  instrument  for  drawing  geometric  curves, 
  in  which  the  movements  of  a  pen  or  pencil  attached  to  a 
  revolving  arm  of  adjustable  length  may  be  indefinitely 
  varied  by  changing  the  toothed  wheels  which  give  motion  to 
  the  arm. 
 
  {Geometrical  plane}  (Persp.),  the  same  as  {Ground  plane}  . 
 
  {Geometrical  progression},  {proportion},  {ratio}.  See  under 
  {Progression},  {Proportion}  and  {Ratio}. 
 
  {Geometrical  radius},  in  gearing,  the  radius  of  the  pitch 
  circle  of  a  cogwheel.  --Knight. 
 
  {Geometric  spider}  (Zo["o]l.),  one  of  many  species  of 
  spiders,  which  spin  a  geometrical  web.  They  mostly  belong 
  to  {Epeira}  and  allied  genera,  as  the  garden  spider.  See 
  {Garden  spider}. 
 
  {Geometric  square},  a  portable  instrument  in  the  form  of  a 
  square  frame  for  ascertaining  distances  and  heights  by 
  measuring  angles. 
 
  {Geometrical  staircase},  one  in  which  the  stairs  are 
  supported  by  the  wall  at  one  end  only. 
 
  {Geometrical  tracery},  in  architecture  and  decoration, 
  tracery  arranged  in  geometrical  figures. 
 
  From  WordNet  r  1.6  [wn]: 
 
  proportion 
  n  1:  the  quotient  obtained  when  the  magnitude  of  a  part  is 
  divided  by  the  magnitude  of  the  whole  [syn:  {proportionality}] 
  2:  magnitude  or  extent;  "a  building  of  vast  proportions"  [syn: 
  {dimension}] 
  3:  balance  among  the  parts  of  something  [syn:  {symmetry}]  [ant: 
  {disproportion}] 
  4:  harmonious  arrangement  or  relation  of  parts  or  elements 
  within  a  whole  (as  in  a  design):  "in  all  perfectly 
  beautiful  objects  there  is  found  the  opposition  of  one 
  part  to  another  and  a  reciprocal  balance"-  John  Ruskin 
  [syn:  {balance}] 
  v  1:  give  pleasant  proportions  to  "harmonzie  a  building  with 
  those  surrounding  it" 
  2:  adjust  in  size  relative  to  other  things 




more about proportion