American telegraph. [volume] (Washington [D.C.]) 1851-1851, 1851-06-02


Two cquilateral triangles combined form q
rhombus, commonly called diamond. 1t is n
| quadrilateral figure, with all the sides and the
opposite angles equal. Another equilateral tri-
angle added to the rhombus forms trapezoid /;
also four-sided figure, with two of its opposite
sides parallel, but not the other two. The
fourth triangle added to the trapezoid on one
side forms a rhomboid, four sided figure, with
its opposite sides and angles equal, but not all
the sides or angles If the triangle is added to
another side Of the trapezoid, the result is an
other equilateral triangle. Four equilatera
triangles when combined into rhomboid or
another triangle, can be folded into "A tetra-
edron, the most simple of the 9 five regular
solids" enclosed, of course, in four equilateral
triangles. The tetraedron, though the mos
simple-and because the most simple of all fig
ures with length, breadth, and thickness-has
properties exceedingly interesting and curious
When made of pasteboard, in considerable mum.
bers il can be combined into forms literally
numberless and namcless, illustrating the works
of nature and of art.
| SIX equilateral triangles, combined around
| one point as n centre, form n regular hexagon ::
plane fiat surface with six equal sides and
angles This figure has very peculiar proper
ties, exhibited in thousands of forms in the
mechanism Of creation, as it is in works of art
As two triangles combined form the rhombus,
three of the latter figure, like six of the former
make hexagon. The triangular hexagon, as
formed of trianglcs and the rhombc hexagon,
as formed Of rhombuses, together are capable
of combinations uniting economy. strength, and
beauty, sufficient for the employment of whole
| life, becoming more interesting. rich and beau
tful at every step of progress in the work. The
simplicity OF such combinations fits them at
miraby for young hands, in which they work
with an assiduity which never tires, because
producing forms constantly new and increas-
ingly beautiful
Eight equilnteral triangles combined in sew
eral different forms, can be folded into an oc-
taedron, one Of the FIVE regular solids. This is
the primary crystal Of very many crystalline
forms, as exhibited in nature, and as formed by
art. The alum crystal is regular octaedron,
as may be shown by dissolving half pound Of
alum in pint of water. heated till the whole is
dissolved, and then suffered to stand perfectly
still, with some form of wire or other material
immersed, till the water cools, when the octae-
dral crystals of alum will appear in regular
forms and in great numbers. The tetraedron,
just described, combined with the octaedron
here mentioned, may produce new and greatly
varied forms, illustrating mechanism, both Of
divine and human origin, of illimitable exten-
sion, and indescribably beautiful. Twenty equi-
lateral triangles folded may form an icosaedron,
one Of the five regular solids
ExPER1MENT.-The few short articles on
Agricultural Geology" recently given to the
public, by being widely copied in public jour
nails, both in this and other countries, have
been made very extensively reading lessons IN
schools. If the same should be done with
Mechanism, now in progress, and various
other subjects of practical science, newspapers
would become "school books and schools be
constantly enlivened and enriched by something
new, instructive, and entertaining, and thus
relieved from their present dull monotony, which