American telegraph. [volume] (Washington [D.C.]) 1851-1851, 1851-06-19
MECHANISM, No. Why JOSIAH HoLBnook


About five hundred years before Christ a
hundred oxen were sacrificed to commemorate
the discovery OF a principle combining the pro-
pertles OF the triangle and square The sacri-
flee OF a hundred oxen is called a hecatomb
The proposition presenting this principle is
hence called the q Hecatomb Problem" 1t is
also called the Carpenters Theorem," from
the fact that carpenters make special use of it
in squaring their buildings, and determining
many other points about their work. 1t is con-
stantly brought into by architects engi-
neers, surveyors, nayigators, and numerous
other classes of business men. In colleges this
principle is known by the title ''Asses' Bridge"
grounded on the supposition that the student
who gets well over it by satisfactory demon
stration has proved himself to be not quite the
most stupid animal in the world. 1t is also
known among students by the somewhat more
genteel title ''Old Forty y-seventh; :" being the
forty seventh proposition of the first book of
Euclid.
If the principle referred to warranted a hec-
atomb for its commemoration at the time OF its
discovery, it must at this age of the world at
least deserve place as subject of instruction
in course of practical business education.
If squares be drawn on the sides of any right
angled triangle, the square upon the longest
side is i'll all cases precisely equal in surface to
the sum Of the squares on the other two sides.
This presents the proposition, and embraces the
principle referred to- The longest side is, in
all cases, opposite the right angle. The two
sides containing the right angle may be equal;
or, they may vary infinitely. The variation
does not affect the principle, always with the
proviso that the figure contain one right angle
To illustrate by particular case. Suppose
the side opposite the right angle is ten inches
those containing the right angle are eight and
six inches. The square of the first will of course
contain one hundred square inches squares of
the latter will contain sixty-four and thirty six
square inches; the sum also one hundred. This
case shows precisely the plan of carpenters in
squaring their buildings By measuring from
u corner on one sill eight feet, and on the other
six feet, the distance between the extreme points
of the two lines will be made precisely ten feet
no more, no less, if the building be exactly
square The length of braces, rafters, and other
parts of buildings required by the general plan
may also be determined with perfect exactness
by the sold Forty
AS great as is the Importance of this princi-
pie to various departments of science, and to
almost every useful art in college course a
single mode only of demonstrating it is fire.
quently adopted, and that an abstraction. In
a school in Washington the same principle is
shown by eight different illustrations, all prac-
| tical; prepared by the hands of the pupils, and
capable of being seen by the whole at all times
when in their seats.
Erpeyiments.-A boy in New York got pas
sion for running with fire engines apparently
beyond all restraint, greatly affecting his mother
and alarming her for his safety. A friend of
the boy suggested to the mother her aiding him
in practical illustrations of mechanism-the
hecatomb problem, and many others. She
availed herself Of the suggestion, and in few
days, TO her great pleasure, she found her son
al Iuta IN to- kp no of
engines on their rafting by their door. Some
Of the work made by him and others was sent,
at the request Of agent Of the British and
Foreign Bible Society, to the city Of Mexico,
which the reverend gentleman soon after visited.
These specimens broughtin in return several pack
ages, containing variety Of the work Of the
young Mexican Indians,