Meyer Franz. A Handbook of Ornament
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GEOMETRICAL
ELEMENTS.
11
Diaper Platterns.
Plate
6.
12
GEOMETRICAL
ELEMENTS.
r
N
\
Diaper
ratterns.
—
The
Sector,
Polygon,
and
Star.
13
11.
Mural
painting,
Assisi,
(Vorbilder fiir
Fabrikanten
und
Hand-
werker).
12.
Old
Italian
mural
painting, San
Francesco,
Assisi,
(Hessemer).
Plate
7.
Diaper
Patterns,
with
Mixed
lin-es.
10.
Old
Italian
mural
painting
San Francesco,
Assisi,
(Hessemer).
The
Sector,
The
Polygon,
and
the
Star.
Polygons
and
Stars are
of
frequent
occurrence
in
ornamental
design.
The
Sector
is
the
foundation of
Rosettes.
The
Polygon
and
the
Star
are
often
used as
Frames to
Ornaments.
They
also
servo
as
compartments
in
coffer
Ceilings
and
composite
ornamental
designs.
In
this
case,
they
are
frequently divided
into
smaller
figures, as
will
be
seen
in
the
following
plates.
Plate
8
gives
the
shape,
and
construction
of
those
which most
frequently occur;
followed by
some
examples of
their
application.
Plate
8.
Radiating
Figures, &c.
1
—
4.
The Sector,
produced by
the
regular
division of
circles.
5.
The
Square,
described
obliquely in a
circle,
6.
The
Square
formed by
the juxtaposition
of
right angles and
cutting-off
the
lengths
for
the sides.
7.
The
regular
Octagon,
described
obliquely
in
a
circle.
8.
The
regular
Octagon,
described
in
the square by
measuring
half diagonals
from its
angles.
9.
The
regular
Triangle
and
Hexagon,
formed by
measuring the
radius,
as
chords, six
times
round the
circumference.
10.
The
regular
Duodecagon,
formed by
applying the radius
to
the circle
from the
ends of
two
diameters at
right angles
to
each
other.
11
—
12.
The
regular Pentagon
and
Decagon,
formed by a
construc-
tion
based on
tho
theorem of
the
"Golden Mean",
as shown
in the
figures.
13.
The
regular
five-pointed
Star,
formed by
joining
the
alter-
nate
points
of
five points placed
at
equal
distances
in the
circumference of a
circle.
Known
in
the history
of
magic
and
witchcraft
as the
Peiitagram or
'Tentacle
".
14.
The
regular six-pointed
Star,
formed by
joining alternate
points placed at
equal distances
in
the
circumference of
a
circle.
14 The Sector, Polygon,
and Star.
—
The
Square,
and
its Subdivisions.
15
—16.
Eegular
eight-pointed
Star, formed
by
combining
every
second or
third
of
eight points
placed at
equal
distances
in
the circumference
of a circle.
17
—18.
Regular
ten-pointed
Stars, formed
by joining
every
second
or third of ten
points
placed at equal
distances in
the
circumference
of a circle.
The
pointed Stars may
also
be
formed
by producing
to
a sufficient distance
the sides of ordinary
regular
polygons;
and, conversely,
each star contains
a simpler
star,
as
well
as
the regular
polygon of
the same
number
of sides.
19.
Star,
formed by a
suitable
combination
of
corresponding
i:>oints
regularly
placed on
the circumferences
of
two
con-
centric circles.
20.
Uraniscus, the star-like
decoration
.of a Greek coffer
ceiling.
From the Propylaea
in
Athens. Gold on
a blue ground.
21.
Back of
a
modem
chair, carved
in basrelief.
22.
Ornamentation
of a semi
-regular
pointed star. Arabic,
16th century,
(Prisse d'Avenues).
The
Square,
and its Subdivisions.
(Plates 9
and
10.)
The regular
four-sided figure
or Square, with
its
equal sides
and
angles, is a
fundamental form
of frequent occurence.
It
may
be
divided
into compartments in various ways; the principal auxiliary
lines
for
this purpose being the Diagonals
(or
oblique lines
con-
necting
the angles), and the Diameters (or lines connecting the
centre
of
each side).
Where the
square is
divided for
a ceiling, floor or
similar
object: a
border
is made round the enclosed space. In most
cases, a
large central compartment
is
retained; and this may be a
square,
either parallel or oblique
to the
other; or may be a circle,
an
octagon, &c.
The Subdivisions of Plate 9
follow the
richer divisions
of
Plate 10.
Plate
9. The Square.
1
—
15.
The simple Subdivisions.
Plate 10.
The Square.
1—8. Richer and more
complicated
Subdivisions.
6.
Panelling of Ceiling,
inn,
Nuremberg,
Modern.
8.
Panelling of ceiling,
Massimi
Palace,
Rome, by Baldassare
Peruzzi, Italian Renascence, (Letarouilly).
GEOMETRICAL
MOTIVES.
The
Sector,
the
Polygon,
and the
Star.
Plate
8.
16
GEOMETRICAf. MOTIVES.
Plate
9.
The
Square,
and its
Subdivisiou.
GEOMETRICAL
MOTIVES.
17
The
Square,
and
its
Subdivieion.
Heyer,
Handbook
of
Ornament.
Plate
10.
2
1 8
The
Subdivisious of the
Octagou,
Triangle, aud Hexagon.
—
The Oblong,
&c.
The
Suddivision
of
the Octagon,
Triangle,
and
Hexagon. (Plates 11
and
12.)
Next
to
tbe
square:
the regular
polygons most frequently occur-
ring
in ornamentation
are
the Octagon
and the Hexagon. The Triangle,
Pentagon, Decagon
and
Duodccagon are,
for obvious reasons, less
common; ^vhile the
other
regular polygons are
scarcely used
at
all.
Sometimes the
semi-regular
polygons
also appear.
These are formed
by
cutting-off
equal
triangles from
the angles of a
regular polygon
in
such
a
manner
that the
resulting
figare has long and
short sides
alternately, and
the
angles all lie
on
the circumference of a
circle.
Diagonals
and
Diameters
wth series of
lines in the
manner
of
pointed
stars,
are the
readiest
auxiliaries for
dividing regular
and
semi-regular
Polygons.
Plate
11.
The Octagon.
1
—
8.
Tbe
best-known
Subdivisions.
Plate 12.
The Tkiangle,
the
Hexagon,
&c.
1
—
5.
Simple
Subdivisions
of the
Equilateral triangle.
6
—
13.
The
best-known
Subdivisions of
the
regular
Hexagon.
14.
Subdivisions of a
regular
Pentagon.
The
Oblong, and its
Subdivision. (Plates
13
—
IG)
The
right-angled
plane figure
with
unequal
pairs of sides,
known as
an Oblong, is the most
usual
of all fundamental
forms.
Ceilings,
floors, walls, doors, wainscoting,
panels
of
furnitme,
table-
tops,
book-covers, and numbers of
other objects,
have an
oblong
shape.
The difference
in
the
lengths
of
the sides
adapts itself to
all
possible
conditions:
the Oblong
approaching
the
square on
the one
hand
and the Band
or Border on the
other;
so
that the
divisions are
very
various; as will be
seen by a
glance at
the
examples.
As
a
rule,
the
diagonal
is not used
as an
auxiliaiy line,
but is
replaced
by
the
mitral-line of the angle, as this
latter
alone
gives
equal
breadths
of the
Border. When
the Oblong
appVoaches
the
Square,
a
distorted square subdivision
is sometimes
resorted-to,
(Compare
PL
16,
lig.
2).
Plate
13. The Oblong.
1
—
6.
The usual subdivisions.
Mosaic, flooring, Italian, 16th century,
(Stored).
GEOMETRICAL MOTIVES. 19
F
~/^
GEOMETRICAL
MOTIVES
Plate 12. The
Triangle,
HexagoD,
&c.,
and
their
Subdivision.