The spirit of democracy. [volume] (Woodsfield, Ohio) 1844-1994, 1853-07-06

triangle-the square of the hypothenuse is
tequal to the sum Of the squares of the two
remaining sides.
About the second century, A. D., sys-
tenn of notation was invented, called the
Sexigesimal. supposed to have been invent
ed by Ptolemy. Some traces of it are still
to be found in the division of an hour, min
ute, circle, &c. Sixty units Of the first or.
der was equal to one of the next higher.
| The notation of this system of Arithmetic
was founded nearly upon the same princi-
pies as that of the Arabian, and differed
only in the division Of the unit-the Ptole-
maic by sixty. and the Arabic by ten. Not
withstanding the sexigesimal Arithmetic is
ascribed to Ptolemy, yet it has the proba-
bility of eastern origin, as the Indians reck-
on time by this method. They divide the
day into sixty parts-each of these into
sixty, and again by sixty. They reckon
periods Of sixty years, as we do centuries.
| The science of Arithmetic was improv-
ed in the fourth century. by Diophantus,
of the Alexandrian school, who was also
the supposed inventor Of Algebra. The
Diophantine Arithmetic was very much
neglected from that period until the time
Of the celebrated Euler, who was born at
Basil, 1907.
The Romans paid little attention TO
Ari,hmetic-their war-like habits being op-
lposed to the 7milder arts Of peace. BG-
THUS, who hourished in the sixth century,
/ was perhaps the only distinguished mathe
matician among them. Hetranslated the
Geometry Of Euclid, and the Arithmetic
/ Of Nichomacus.
About the middle Of the seventh centu-
ry, the Arabs who were at this time fierce
and uncivilized race, overran Egypt and
Persia, and. consigned the Alexandrian
library to flames, and thus destroyed the
accumulated labors OF ages. The man.
1ners of this people soon changed. They
began to cultivate the very sciences they
had endeavored to exterminate from the
4 y 2
/ earth.
About the beginning of the eighth CEN
tury. the Arabians invaded Spain, and in
1troduced into Europe their admirable sys-
/ tenn of Arithmetic, which is now used by
every civilized nation. The celebrated
Gerbert went to Spain, and acquired a
knowledge of the Arabian Arithmetic, and
returned to France, about go A. d. Ii
was soon introduced into Britain. Not
withstanding we are indebted to the Ara
bians for our present sy stem of Arithmetic,
tthey do not pretend TO have been the in
ventors, but acknowledge that they receiy
ed ii from India.
France, Germany and England have, in
modern times, made great improvements
in Mathematics. During the latter par
of the 18th century. the rival mathemati
cians of Europe were engaged in theil
1s.War of Problems" Many importan
discoveries were made in their efforts fol
success. Amongst these were the Ber
noullis, Leibnitz, Huygens, Gregory, .Sil
Isaac Newton and others.
| h the last century, Germany and Swift
zerland made investigations into the bes
. methods of imparting sound learning
Il There were four schools--the IIumanists
Philanthropists, Pestalozzian and Produc
tive. The Hlmanists had, until the mid
die Of the last century,sthe entire sway o
the learned world. They believed that w
were entirely indebted to the Greeks AMI
Romans for all sound learning-that th'
classics embraced all that was valuable il
human knowledge. The Philanthropist
discarded this idea, and maintained tha
practical and physical education was ne
cessary to the development of the mind
that the -Humanists paid too much atten
ton to the formation of mere scholars. with
out the development of real men. Pesta
iozzi, in noticing the errors of the Philan
thropists, perceived that they had too mucl
neglected the -sdepcfopnaent Of the mint
! itself; and consequently regarded Mathe
lmaties as the foundation Of all-real learn
ling. In the investigation Of this science
he discarded all rules and traced ever!
principle to its first cause,
+ From the Pestalozzian system, original
; ed the Productive School, which is ais.
) termed the Eclectic. It aims at embrac
!, ing all the valuable principles of othe
! systems, without adhering to their errors
5 Our school books are now based upon tn
r Productive system. embracing the reason
5 forevery proposition. and leading the pupi
, by gradual progression. from the most in
/ Ecipient steps. to the highest range of hu
man knowledge.
5 In 1920, Warren Colburn of Massachu
3 sets, published treatise entitled an SIN
8 PRODUCTION to Arithmetic on the Inductiv
J. For Intellectual sy stem." This may be re
III 0ardads tho hou;nu;uu of tho Analvtic a