Evening star. [volume] (Washington, D.C.) 1854-1972, 1891-08-19

After the war; returning to his home and pur-
suing his studies. he fitted himself for college
and in 1869 entered Cornell University. Three
years later he graduated with the degree of
b. c. E., and two years later, in 1874, he
took postgraduate degree of c. E.
Meanwhile he had, in 1871, been APP
pointed instructor in engineering at Cornell,
and he held this place for two years. when he
resigned to become professor of mathematics
in Chester Military Academy, where he re-
manned .Year. In April, 1875, Prof HYDE was
elected professor of mathematics by the Uni
versity of Cincinnati. and he has been in that
position ever since. Besides large number of
papers he has contributed to the engineering
and mathematical engineering Journals Prot.
Hyde is the author OF a work on ''Directonal
Calculus" founded on the methods of Herman
Grassmann's "Ausdehmungslehre."
The first business of the mathematics and
astronomy section today was to elect a secre-
tary, Prof Z. d. Preston of this city the Sec
rotary elected at indianapolis, being away.
PRESIDENT HYDE's ADDRESS.
At o'clock section assembled again to
hear Vice President Hydes annual address,
The professors subject was ''The Evolution
of algebra" He talked rapidly and vet dis
tinctly, and his address was a concise presenta-
ton of Algebra's history, extending from be-
fore the Christian era to the present time, and
even projecting the future of the science
The earlies. traces of algebraic knowledge we
can find, he said, are in ancient Egyptian
manuscripts. Records of an early almost pre-
historic, Egyptian mathematician named
Ahmes, who lived and figured and died some
hundred Years before Christ as nearly as can
be found out. were referred to as showing that
this pioneer in algebra had left behind him
documentary evidence that he had performed
a few geometrical and some algebraical prob
lens. Scarcely anything was known to mod
erns Of the mathematics of ancient Epypt
Among the early Greeks, long before the
dawn of the Christian era. geometry was cuIti-
waited extensively, but very little in the wov of
algebra was done till about 400 A. D. Then the
foundation of the algehraic science was laid by
Diophantus of Alexandria. He wrote in Greek
though little is known either of the man or his
methods. Algebra has been classified by Nes-
selmann as rhetorical. syncophated and SYM
bolical. In the first stage algebraic work was
purely by reasoning in words. In the svnco-
phatic method authorizations were introduced
and used instead of words The symbolical
stage is the stage CT the present. Arbitrary
characters represent what was once represented
by spoken words and later by authorizations of
written words Most of the work of
the early algebraists was in the rhetorical
stage. Diophantus made use, to a certain
exten OF appropriated methods. He used
particular characters for unknown guam
titles, a character for '.minus," and
represented addition by juxtaposition
The square and cube of the unknown quantity
were represented by contractiOns of the words
| power" and cube" Here the speaker Illus
trated by writing on the blackboard an algebraic
equason as Diophantus would have written il.
He went on to say that Diophantus was greatly
hampered by having but one character to
| represent the unknown quantity, though he
accomplished trueiy remarkable results by his
ingenuity and the skill with which he made the
necessary combinations Diophantus had no
successor among the Greeks as an algebraist.
Algebra was cultivated at a very early period in
India. The first Indian methods Of which
moderns know were those of Arya Bhatta, who
lived six centuries before Christ. He wrote
works on arithmetic. algebra, geometry. trig-
onometry and astronomy, stating his rules
and propositions in verse. All his work
was purely Of the rhetorical style. The
only other ancient Indian mathematician OF
whom moderns know was Brahma Gupta,
whose period was about A. d. 700. He also
| figured i'll verse, the name of his work, En-
| glished, being THE System of Brahma in
Astronomy" Prof. Hyde said that these
Indian writings were interesting as being the
source from which the Arabs derived Their
first knowledge Of algebra. They absorbed
| from the Greeks through the translations Of
Euclid and others q knowledge of geometry
| mechanics aud astronomy, but there seems to
have been no translation of the works Of
Diophantos till after they themselves had
already made considerable progress 1t was
from the Arabs that western Europe derived