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## ratio

```  6  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]:

Ratio  \Ra"ti*o\,  n.  [L.,  fr  reri,  ratus,  to  reckon,  believe,
think,  judge.  See  {Reason}.]
1.  (Math.)  The  relation  which  one  quantity  or  magnitude  has
to  another  of  the  same  kind  It  is  expressed  by  the
quotient  of  the  division  of  the  first  by  the  second  thus
the  ratio  of  3  to  6  is  expressed  by  3/6  or  1/2;  of  a  to  b
by  a/b;  or  (less  commonly)  the  second  is  made  the
dividend;  as  a:b  =  b/a.

Note:  Some  writers  consider  ratio  as  the  quotient  itself
making  ratio  equivalent  to  a  number.  The  term  ratio  is
also  sometimes  applied  to  the  difference  of  two
quantities  as  well  as  to  their  quotient,  in  which  case
the  former  is  called  arithmetical  ratio,  the  latter,
geometrical  ratio.  The  name  ratio  is  sometimes  given  to
the  rule  of  three  in  arithmetic.  See  under  {Rule}.

2.  Hence  fixed  relation  of  number,  quantity,  or  degree;
rate;  proportion;  as  the  ratio  of  representation  in
Congress.

{Compound  ratio},  {Duplicate  ratio},  {Inverse  ratio},  etc
See  under  {Compound},  {Duplicate},  etc

{Ratio  of  a  geometrical  progression},  the  constant  quantity
by  which  each  term  is  multiplied  to  produce  the  succeeding
one

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

Anharmonic  \An`har*mon"ic\,  a.  [F.  anharmonique  fr  Gr  'an
priv.  +  ?  harmonic.]  (Math.)
Not  harmonic.

{The  anharmonic  function}  or  {ratio}  of  four  points  abcd  on  a
straight  line  is  the  quantity  (ac/ad):(bc/bd),  where  the
segments  are  to  be  regarded  as  plus  or  minus,  according  to
the  order  of  the  letters.

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

Duplicate  \Du"pli*cate\,  a.  [L.  duplicatus  p.  p.  of  duplicare
to  double,  fr  duplex  double,  twofold.  See  {Duplex}.]
Double;  twofold.

{Duplicate  proportion}  or  {ratio}  (Math.),  the  proportion  or
ratio  of  squares.  Thus  in  geometrical  proportion,  the
first  term  to  the  third  is  said  to  be  in  a  duplicate  ratio
of  the  first  to  the  second  or  as  its  square  is  to  the
square  of  the  second  Thus  in  2,  4,  8,  16,  the  ratio  of  2
to  8  is  a  duplicate  of  that  of  2  to  4,  or  as  the  square  of
2  is  to  the  square  of  4.

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}.

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]:

ratio
n  :  the  relative  magnitudes  of  two  quantities  (usually  expressed
as  a  quotient)
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