Prof. Young on Algebraic Equations. 403 
mathematical knowledge, but of taste for mathematical pursuits in 
the younger branches of the community, to claim the gratitude of 
every sincere friend of science and of man. How many have turned 
away in disgust from the illogical statements (for arguments they 
deserve not to be called, nor, scarcely, even sophisms,) of the general 
mass of writers on analysis, under the impression, justly entertained 
so far as any impression could result from such works, that it was com- 
posed of a mere set of hocus pocus triflings ! or in despair of ever ac- 
quiring even a glimpse of the promised land that lay beyond the ele- 
mental mountain-range, darkened as it was by the symbolical mists 
in which ignorant or injudicious compilers had involved them! Not 
on by easy steps, generalizing the particulars, one after another, in 
a way that not only commands our assent, but interests the attention 
too deeply to allow of our being turned aside from the further pursuit 
of science. His algebraical reasonings are not less convincing than 
those of the Euclidian logic; and the hold which the elegant formule 
and elegant results he derives take upon the fancy, is not less strong 
than that which his compact and unsophisticated reasoning takes upon 
the understanding. So much may be said of all Professor Young’s 
writings: but his present work, in addition to this, has many and pe- 
culiar claims upon the attention of the mathematical world, as well as 
upon the young and aspiring class of mathematical students. 
From the time that our distinguished countryman Harriot trans- 
posed the “ absolute term” to the same side of the equation with the 
other terms, algebra has taken a new aspect,—a totally new cha- 
racter. He wasthus enabled to show that an equation of the nth 
degree may be compounded, from n simple equations having n roots, 
which may be any numbers whatever ; and he inferred (not so illogi- 
cally as has been ofter represented by foreign historians of algebra*, 
and too implicitly admitted by our own,) that every equation of the 
mth degree has also n roots. From that time the great problem of 
algebra became the determination of those roots by a practicable pro- 
cess. Certain cases of it had been already solved, so far as the fourth 
degree inclusive, by more than one person ; the simple and the quadra- 
tic equation at a very early period, the cubic by Tartaglia and Cardan, 
and the biquadratic by Ferrari. All these were solved by exhibiting 
a general formula in terms of the 2nd and 3rd roots of certain as- 
signed functions of the coefficients ; and the ambition of the earlier 
inquirers was to find analogous expressions for the roots of the fifth 
and higher degrees. The inquiry undet this form has been altogether 
unsuccessful ; and the most signal mistakes, and, in many cases, the 
most ludicrous ones, have been made in the progress of such attempts. 
* A lithographic specimen of a manuscript page of Harriot’s work, pub- 
lished by that eminent mathematical antiquary Professor Rigaud of Oxford, in 
his Supplement to the works of Dr. Bradley, sets this question quite at rest. 
He distinctly understood the nature both of negative and imaginary roots. 
The“ Ars Praxis Analytic,” we would add, is rather to be taken as a specimen 
of Warner's power to comprehend Harriot s views, than as a standard of those 
views themselves. 
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