Wheeling Sunday register. [volume] (Wheeling, W. Va.) 1882-1934, 1899-04-09


and nye the Offspring. S.
III 4 square be erected on each side
OF IKE triangle and t'hese squares be
which is one part in length. there will
be as many of these squares in the by
potenuse as in the other two together,
25-9 and is make rs.
Ptolemy Softer. founded the tower
of Fharoah. or. as some call it. the
Obelisk of Queen Semer-Amis. 1t was
tower Is feet square at the base and
$50 feet high, and when completed, was
considered the sixth wonder of the
world and had some symbolic meaning
of which we shall not treat. it being a
dangerous and difficult subject to those
who have not made it deep and care
full study.
Carpenters, builders and operative
masons make use of the 4lth problem
of Euclid when laying a foundation
ynereon to erect their building. Even
those who have never heard of Pyth-
ogorus or his problem and may be as
ignorant of Eaclid or mathematics as
q poodle dog, will draw line, put in
a peg thus, attach a line ten feet long,
measure off six feet, drive in peg
and attach line eight feet long, draw
ing them together thus, he makes a
perfect triangle whose sides are equal
to 6, and 10, throwing away the ten
foot line or hypotenuse he has per-
feet square and base upon which to
square his building, this is sometimes
called the carpenters theorum.
| have just referred to a dogs igno-
rance of arithmetic; l want TO modify
that remark; a dog may be said to
understand something of arithmetic,
for if you throw stone striking him
on one leg, he will put down three and
carry one. He may also be made TO
demonstrate the problem of Euclid, for
if YOU throw a bone striking dog on
one leg he will grab that bone, limp off,
carrying two and putting down three,
and demonstrates the 47th problem be-
cause three represents the perpendic-
ular. two being squared will represent
the base, and the product of two and
three will make five, the hypotenuse,
completing the triangle of the problem
of Euclid.
The Egyptians made a still more i'm
portant use of this Triangle: it VS. the
standard of all their measure 81 ex-
tent and was applied to the building OF
the Pyramids.
If we inscribe within a circle a tri-
angle whose perpendicular will be ooo
parts and base 400 parts, the hypotenuse
will be 500 parts, which, of course, bear
the same proportion as 8, 4 and 8. linen
if we let a perpendicular fall from the
angle OF the perpendicular and base
of the triangle and extend 1t through
the hypotenuse to the circumference OF
this circle, this chord or line Will be
equal to 4S0 parts, and the two seq
ments of the hypOtenuse on each SIDE
of it will be found equal respectively to
1870 and 800 From the point where
this cord intersects the hypothenuse let
another line fall perpendicular to the
shortest side of the triangle and this
line will equal to IA parts, While the
shorter segment formed by its juno
ton will be equal to 10S parts. Hence
we may derive 500, $50, 400, $40, 300,
$50, 144 and 108, and all these without
the slightest fraction.
Surprising the 500 then to be cubits
we have the measurements of base of
the great pyramid of Memphis. In the
400 cubits we have the exact measure
ments of the Egyptian stadium, the
800 cubits give us the exact number
contained in the Hebrew and Babylon
ian stadium. The stadium of Ptolemy
is represented by the 4S0 cubits, the
1870 being doubled will be the stadium
of Cleomedus. Doubling the 144 gives
the stadium of Archimedes, and doub-
ling 108 gives us the precise value OF
the lesser Egyptian stadium.
In this way we obtain from the tri-
angle all the measures of length that
were in use among the Egyptians, and
the triangle whose sides are equal to
8, and 5, was used by Pythagorus in
demonstrating the 47th problem of
Euclid. By these three sides the Egyp-
tians symbolized Osiris, Isis and Horus
the two products, and then produced
the very principle expressed in SYM
bolic language as already explained.
DR.. Lardner says: Whether we
consider the 47th proposition with ref
erence to the peculiar and beautiful re-
lationship established in it or its num-
cradle uses in every department OF
mathematical science or to its fertility
in the consequences derived from 1t,
it must certainly be esteemed the most
celebrated and important in the whole
of the elements if not in the whole
range of mathematical science. 1t is
by the influence of this proposition and
that which establishes the similitude
of equiangular triangles that geometry
has been brought under the domination
of algebra, and it is upon the same
principle that the whole science OF
trigonometry is founded"
In our lectures we have been told
that the forty-seventh problem was an
invention of our ancient friend and
brother Pythagorus, that he drew out
many problems, etc, and among
the most distinguished he originated
this, when in the joy of his heart he
exclaimed Eureka meaning l have
found it," and upon the discovery he
sacrificed a hectacomb, or, in other
words, one hundred oxen.