New-York tribune. [volume] (New York [N.Y.]) 1866-1924, 1900-11-11
A MATHEMATICAL GENIUS.
HE HAS DISCOVERED ENTIRELY NEW
PRINCIPLES IN EQUATIONS
From The Kansas city star.

From The Kansas City Star.
When William q Hovner OF Bath. England
an obscure school teacher, IN INt9 >Iuade
known 10 the world his method of solving nR-
mericaI equations IF any deElre the discovery
was viewed with suspicion by nearly all the
algebraists of Great Britain The Royal Society
of Great Britain had the luck, so Professor
Augustus De Morgan says in mis- budget OF
Paradoxcs,' to accept HOrn@r'S celebrated paper
containing the method which - FAR ON the way
to become universal, but they r. use the paper
IN which HOrner developed MS views 81 TINS
and other subjects. 1T to"h more IMAM t"Sn,y
years for H"rne:'S method 10 S"s q I"n'r'u IN
the University Cambridge. The professors
and tutors in that stronghold of mathematical
learning used it till students coming N
from the most progressive preparatory schools
employed it in their solutions Of cubic equations,
and at first they Wer" criticised because il
was out of the. usual line of wCrk, although il
was ten times SIM ia as The methods OF
approximation then in vogue.
All attempts - sCIVe general equation ~ the
fifth degree have proved Intellectual. and
noted analyst, Abel. has demonstrated 70 his
own satisfaction. at least. that the solution IS
impossible Equations are divided INTO two
classes. numerical and literal, and general
equation OF Whatever degree II an EQUATION
whose coefiicients dis we'll as the absolute term
are literal
In the history OF mathematics it took long
time to obtain a general solution of an equation
of the third degree. ard after repeated efforts
and many failures the general solution Of an
equation of the fourth degree was eff,cted by
several different mathematician. an here
general soluti have been at a standsjIH more
than two hundred years. Hurncr's method was
that as il became known i cook high
rank and it is the simplest Yet discovered.
Recently diSCoVcrer has aPps7~nd, and
he handles numerical equations ..igh case and
precision that rrlcga;e Horner's method 20 the
department Of ancient history. This author is
| Professor NJ A. Mctiinnis. of Neosho. Mo. In
a book Of 1873 pages Professor Mctluris pre-
sents his system. Tn E"y 70 the discovery
consists in certain definite relations that the
coefficents of thu unknown quantity bear 20 all
| the roots of thu EQUATION Analysts hd'! DIS
covered certain laws governing the CoCtii .@ntS
| when the cOeffiCi, of the highest power ~ the
| unknown quantity is unity BY working with
| the sum of the squares of the roots Professor
McGinniS shows that certain relations SunslSs
| when the sum of the squares of the products
! of thu roots taken two ana two. and 50 on
| for higher degrees. The author lays dow z FIVE
| fundamental th-oromS which H. discovered,
and by the application 0f these and some other
1 PRINCIPLES he has succeeded in solving uU-neri-
cal equations in the hrefest manner ever pre-
! scented. Abel demonstrated that the general
| solution of equation of the fifth dySr,",
] cOrdinR to the methods employed in the solution
| of lower equations, " as impossible, which means
| that thu modes ~ attack hitherto resort-d 10
| would not work Tho complications We're so
! great that they could not he unraVellvd Prof.
! fcSSOr MCtiinniS docs not work al equations
/ C"rding To- tn usual methods presented by
! from another point OF attack altogether. Ry
! discovering new laws. not hitherto suspected.
| that enter into the structure of equations. and
| that the COcfiCirntS bear constant relation
! to all the roots of the equation. he deduevs
! principles that Wtr' unknown. These being
| admitted he then proceeds To solve general
! equations both 80 the fifth and sixth de-rcvs.
/ all numrri, al equations 10y proc ess,s almost
/ ayithfn.tj,al-