"On the Expression of Unknown Quantities." By Prof. Muddelwitz.
A method of expressing unknown quantities by known formulæ has long been a desideratum in mathematical science. This process the author stated he had discovered; for that the fractions of coefficient indices, when used to express the powers of differential equations, are always capable of being solved into pure algebraic roots. Thus, if in an infinitesimal series, in which p, o, o2—t—t2 are unknown given quantities, a, a2, and e, known, and the value to be limited, the equation stands as follows:—
1. a x — a2 × p o t2 = t, o, e.
2. a x = t o e + a — p o t2
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3. x = 2 √(a - p o t2 + a2 — t o e)
Thus the generalization of the equation of x, to the nth degree, gives its fraction in the form of an algebraic root.
[To some readers the above demonstrations may seem rather obscure; but as the late Dr. Dundertop, in his treatise on the Perspicuous, clearly explains—"Ephpnxmqzomubh grudcnkrl, hqmpt on kronswt.">[
We were all thrown into a state of such intense dumbness, such complete torpor, by the profundity of these scientific researches, that everybody tacitly admitted the appropriateness of the next subject; it was a case of still-life which met our startled eye the other evening, in the form of a pair of