The Seattle post-intelligencer. [volume] (Seattle, Wash. Terr. [Wash.]) 1888-1914, 1900-12-17
A MATHEMATICAL GENIUS.
He Has Discovered Entirely New
Principles in Equations.

When William @. Horner, of Bath. Eng
land. an obscure school teachers in 1919
made known to the world his method of
solving numerical equations of any degree
the discovery was viewed with suspicion
by nearly all the alRebraists OF Great
Britain. The Royal Society of Great
Britain had the luck" so Prof. Augustus
De Morgan says In his budget OF Para
doxes." TO accept Horner's celebrated
paper containing the method which Is far
on the way to become universal. but they
refused the paper In which Horner devel-
oped his Views In this and other subjects.
II took more than twenty years for
Horner's method to get a foothold In the
University OF Cambridge, The professors
and tutors In that stronghold Of mathe-
NAUTICAL learning never used IL till students
coming in from the most progressive
preparatory schools employed 1t in their
solutions of cubic equations, and at first
they were criticised because 1t was out
OF the usual line of work, although II was
ten times simple as the methods of
approximation then In vogue.
All attempts to solve a general equation
OF the Nth degree have proved Intellectual
and one noted analyst. Abel. has demon
strated to 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 is an equation whose
coefficients as well as the absolute term
are literal
In the history Of mathematics II took
long time to obtain a general solution
of an equation Of the third degree. and
after repeated efforts and many failures
the general solution of an equation %
the fourth degree was effected by several
different mathematician. and here gem
eral solutions have been at a standstili
more than 200 years. Horner's method
was such an Improvement over all former
methods that as soon as II became known
il took high rank. and II Is the simplest
yet discovered
Recently new discoverer has appeared
and he handles numerical equations with
an ease and precision that relegate Hor-
ner's method to the department 81 an
Client history. This author is Prof. NJ. A.
Mcoinnis Of Neosha, Mo. In book 81
1ss pages Prof McGinns presents his sys-
tenn. The key to the discovery consists
In certain definite relations that the CO.
eficients of the unknown quantity bear
10 all the roots Of the equation Analysts
had discovered certain laws governing the
coefncients when the coefiicient Of the
highest power OF the unknown quantity
is unity. BY working with the sum %
the squares OF the roots Prof McGinnis
shows that certain relations suhslst when
the sum OF the squares OF the products OF
the roots are taken two and two. and so
on for higher degrees The author lays
down Ave fundamental theortms which
he discovered. and by the application on
these and some other principles ne has
succeeded in solving numerical equations
IN the briefest manner ever presented.
Abel demonstrated that the general soiu-
tion Of an equation Of the hfth degree. ac-
corsiing to the methods employed IN the
solution OF lower equations was iuapossi-
BILE. which means that the modes 0f al.
tack hitherto resortei to would not work.
The complications were 50 great that they
could not be nRravelied. Prof. McGinnls
does not work at equations acccrd4Rg 10
the usual methods presented By mathe-
matlcianS bat he goes AZ the subject
from another point OF attack aitogethcT.
by discovering new laws, not hitherto
suspected. that enter into the structure
Of equation and that the eoeff1ciente
bear a constant relation 10 ala ihe roots
of the equation. he dedtoes principles that
were unknown. These being admitted. he
then proceeds 10 solve general equations
both Of the hfth and sixth degrees. and
The beauty OF the method Is thai IL solves
all numerical equations by processes al
most arit knnsse city star.