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Durchgangspunkt

Durchgangspunkt (literally through-point) is a term used in German-language mathematics and technical literature to denote a point that lies on or is common to a geometric object. The precise meaning depends on context, and there is no single formal definition universally used in all fields.

In geometry, the term is often used in two senses: (1) as the common point of a

Examples: If a family of lines all passes through a single point P, then P is the

Interpretation and usage vary by author; in English-language texts the concept is usually described with phrases

Etymology: from durch (through) + Gang (path) + Punkt (point). See also: Schnittpunkt, Punkt, Gerade, Kurve.

pencil
of
lines,
i.e.,
a
fixed
point
through
which
every
line
of
the
family
passes;
(2)
as
a
designated
point
through
which
a
curve,
path,
or
locus
is
constrained
to
pass.
In
construction
or
surveying
problems,
a
Durchgangspunkt
may
be
a
specified
point
that
must
be
contained
in
a
solution,
such
as
the
path
of
a
ray
or
the
trajectory
of
a
line
being
designed.
Durchgangspunkt
of
the
pencil.
If
a
curve
is
required
to
go
through
the
origin,
the
origin
serves
as
the
Durchgangspunkt
for
that
problem.
like
“the
point
through
which
all
lines
pass”
or
“the
through-point
of
the
curve”
rather
than
using
a
dedicated
term.