Show A MATHEMATICAL GENIUS He Has Discovered Entirely Now Principles in Equations When William G Iforner of Bath England an obscure school teacher in 1S10 made known to the world his method of solving numerical equations of any degree the discovery was viewed with suspicion by nearly all the algebraists alge-braists of Great Britain The Royal Society of Great Britain had the luck so Prof Augustus De Morgan says In his Budget of Paradoxes to accept Homers celebrated paper containing con-taining the method which is far on the way to become universal but they refused re-fused the paper in which Homer developed de-veloped his views of this and other subjects It took moie than twenty years for Homers method to get a foothold in the University of Cam bildge The professors and tutors in that stronghold of mathematical learning learn-ing never used it till students coming m from me most progressive preparatory prepara-tory schools employed it in their solutions solu-tions of cubic equations and at first thev were criticised because Lt was out of the usual line of work although it was ten limes as simple as the methods of approximation then in ogue All attempts to solve a general equation equa-tion of the fifth degree have proved ineffectual in-effectual and one noted analyst Abel has demonstrated to his own satisfaction satisfac-tion at least that the solution Is impossible im-possible Equations are divided into two classes numerical and literal and a general equation of whatever degree Is an equation whose cocfllclents Jis well as the absolute term are literal In the history of mathematlc It took a long time to obtain a general solution solu-tion of an equation of the third degree and after repealed efforts and many failures the general solution of an equation of the fourth degree was effected ef-fected by several different mathematicians mathemati-cians and here general solutions have been at a standstill more than 2rtX years llorners method was such an improvement over all former methods that as soon as it became known St took high rank and It Is the simplest yet discovered j Recently a new discoverer has appeared ap-peared and he handles numerical equations with an case and precision that relegate Homers method to the department of ancient history This author is Prof M A McGinnls of Nco sho Mo In a book of 135 pages Prof McGinnls presents his system The key lo the discovery consists in certain definite relations that the coefficients of the unknown quantity bear to all the roots of the equation Analysts had discovered certain laws governing the coefficients when the coefficient of the highest power of the unknown quantity Is unity By working with the sum of the squares of the roots Prof McGInnis shows that certain relations rela-tions subsist when the sum of the squares of the products of the roots aro taken two and two and so on for higher degrees The author lays iown live fundamental theorems which he discovered and by the application of these and some other principles he has succeeded in solving numerical equations equa-tions in the briefest manner ever presented pre-sented Abel demonstrated that the general solution of an equation of the fifth degree according to the methods employed in the solution of lower equations equa-tions was Impossible which means that the modes of attack hitherto resorted re-sorted to would not work The compll callons were so great that they could not be unravelled Prof McGInnis does not work at equations according to the usual methods presented by mathematicians mathema-ticians but he goes at the subject from another point of attack altogether By discovering nov laws not hitherto suspected sus-pected that enter Into the structure of equations and that the coefficients bear a constant relation to all the roots of the equation he deduces principles that were unknown These being admitted ad-mitted he then proceeds to solve general gen-eral equations both of the fifth and sixth degrees and the beauty of the method Is that it solves all numerical equations by processes almost arithmetical arith-metical Kansas City Star |