American telegraph. [volume] (Washington [D.C.]) 1851-1851, 1851-06-05
MECHANISM, No. lV-gY JOSIAH HoLDRooK.

Irlgonometry is the science Of triangles, and
more an art than science. The term is de-
rived from three Greek words: ri, three; gonia,
corner and metron measure. 1t hence literally
means the measure of triangles; really and
practically measuring by triangles. SO curious,
useful, and wonderful are the properties of tri-
angles, as to constitute instruments and furnish
modes for measuring any body, however irregu-
lar, and whether of one, two, or three dimen-
sions-length, or length and breadth, or length,
breadth, and thickness. They also furnish in
strumentS for measuring bodies, however distant
ut least within the distance of the sun, and ex-
tend much beyond it. The heights of mountains,
the distances of bodies across rivers, and the
dimensions of them, or other intervening objects
ut distance, as well as those accessible or near
at hand, by the wonderful powers of triangles
can be determined with great accuracy and by
very simple modes. Surveying, navigation,
astronomy, engineering architecture, and even
the squaring of every building erected, have
trigonometry, or some one or more properties
of triangles, at their foundation.
Every three-sde figure is called a triangle
or trigon, angulus being the Latin, and gonia
the Greek, of the word angle, or corner. Three
sided figures of plain surfaces and bounded by
straight lines, are called plain triangles when
| of curved surfaces and bounded by curved lines
they are called curved trianglcs; when bounded
by three great circles of sphere, as the equa-
tor, ecliptic, and a meridian of the earth, a
three-sided figure is called a spherical triangle,
and the science relating to that class of trian-
| giles is called spherical trigonometry, as that
TO plain triangles is called plain trigonometry
The properties of these two classes of three
sided figures are SO different and distinct, and
each so important, both to science and art as
to constitute two separate sciences and each
important if not essential to the other
Of plain triangles there are six different kinds;
three differing in their sides and three in their
angles. When all the sides are equal, or Of the
same length any three-sided figure is called an
equilateral triangle When two sides are equal
and either longer or shorter than the third il is
called an isosceles triangle. When all the sides
are unequal, or of different lengths, it is called
a scalene triangle. Every plain triangle, hav-
ing one right angle, as no one can have two, is
called n right-angle triangle. If one angle is
obtuse or larger than n right angle, it is called
an obtuse-angle triangle. If all the angles are
acute, or smaller (sharper) than right angle,
it is called an acute angle triangle. III tri-
angle have one right angle and two equal sides,
IT Is right-angled isosceles triangle, combining
the properties both of triangles and squares
The whole secret of the " ChiR,se Puzzles" is in
the rght-anged isosceles triagle. Fifty, or
even smaller number of pieces Of wood, paper.
ivory porcelain, glass, or other material, in the
shape of a right-angled isoscees triangle say
one inch for each of the two equal sides, can be
combined into forms literally without number,
illustrating natural and artificial mechanism in
forms exceedingly beautiful and curious, and
applicable, both in scientific and business opera
tions, to an extent without limits
Experiments. any teacher or parent give
to his pupils or children, as n forenoon exer-
else, an excursion for examining and collecting
minerals or other objects of nature coming
under their observation. AS an afternoon ex
ercise let them draw and describe upon their
states, or upon paper, or both, the various
objects thus coming under their observation If
they should find one mineral and draw a three
sided figure, they would "make a Jegisning, as
the work of one day, in a Cabinet of Nature
and Art" illustrating agriculture and mechan-
ism, and take the first step towards preparing
specimens for Agricultural Fairs" for which
premiums are offered by the Maryland Society,
as they doubtless will be awarded by any SO
ciety thus favored by the work Of young hanos
and generous minds.