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Encyclopedia Britannica



LOCUS (Lat. for " place "; in Gr. rinros)

This article appears in Volume V16, Page 857 of the Encyclopedia Britannica.

Encyclopedia Britannica - Main :: LOB-LUP
LOCUS (Lat. for " place "; in Gr. rinros) , a geometrical
term
 , the invention of the notion of which is attributed to Plato. It occurs in such statements as these: the locus of the points which are at the same distance from a fixed point, or of a point which moves so as to be always at the same distance from a fixed point, is a circle; conversely a circle is the locus of the points at the same distance from a fixed point, or of a point moving so as to be always at the same distance from a fixed point; and so in
general
  a
curve
  of any given
kind
  is the locus of the points which satisfy, or of a point moving so as always to satisfy, a given
condition
 . The theory of loci is thus identical with that of curves (see
CURVE
  and
GEOMETRY
 :
Analytical
 ). The notion of a locus applies also to solid
geometry
 . Here the locus of the points satisfying 'a single (or onefold)
condition
  is a surface; the locus of the points satisfying two conditions (or a twofold condition) is a curve in space, which is in
general
  a
twisted
  curve or curve of
double
  curvature.


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