If there has been a feeble initial current, this oscillatory after-current, by algebraical summation, will cause the current in the circuit to be alternately weaker and stronger than the initial current.
The want of a good algorithm was doubtless a great impediment, but it was not quite so deficient as from reading modern histories of algebraical discovery, without reference to the original writers, we might be led to suppose.
The following may be stated as the general problem of the algebraical calculus: F being a certain function of a given number, to find what function F will be of any function of that number.
Algebra extends the generalization still farther: every number represents that particular number of all things without distinction, but every algebraical symbol does more, it represents all numbers without distinction.
As soon as we conceive a thing divided into equal parts, without knowing into what number of parts, we may call it a or x, and apply to it, without danger of error, everyalgebraical formula in the books.
The system of general language calledalgebraical notation does this.
Since then algebraical truths are true of all things whatever, and not, like those of geometry, true of lines only or of angles only, it is no wonder that the symbols should not excite in our minds ideas of any things in particular.
Hence the symbols can be separated from the functions on which the operations are performed, and treated as if they were algebraical quantities.
At the same time, every thinking man must at least dimly have felt that this conception is void of all positive content, because, like analgebraical symbol, it denotes a mere relation in abstracto.
Their integration is made to depend on the resolution of an algebraical equation.
It includes the properties of numbers; extraction of roots of arithmetical andalgebraical quantities, solutions of simple and quadratic equations, and a fairly complete account of surds.
The first difficulty to be overcome was the algebraical solution of cubic equations, the pons asinorum of the earlier mathematicians.
The ancients are in fact the true inventors of the present trigonometry, spherical as well as rectilinear; it being only much less perfect in their hands, on account of the extreme inferiority of their algebraical knowledge.
We can only say that we shall have so many more resources in this matter as we shall know more of true analytical geometry, that is, as we shall know the algebraical expression of a greater number of different algebraical phenomena.
Under the first point of view, the theory of negative quantities can be established in a complete manner by a single algebraical consideration.
Since then algebraical truths are true of all things whatever, and not, like those of geometry, true of lines only or angles only, it is no wonder that the symbols should not excite in our minds ideas of any things in particular.
To a missing member of a family group of terms in an algebraical formula.
Diderot was informed that a learned mathematician was in possession of an algebraical demonstration of the existence of God, and would give it him before all the Court, if he desired to hear it.
It is an algebra upon algebra; a calculus which enables us to combine and foretell the results of algebraical operations, in the same way as algebra itself enables us to dispense with the performance of the special operations of arithmetic.
Mr. Dodgson then wrote to him, "taking leave of the subject, until he should be willing to enlarge his field of knowledge to the elements of Algebraical Geometry.
To which is prefixed a summary of all the necessary algebraical operations, arranged in order of difficulty.
This algebraical reading of the Bible subdues all idea of contradiction to any science, geology for instance, chemistry or any other science, as well as of the apparent language of the book in letter to letter.
In 1873 Charles Hermite proved that the base [eta] of the Napierian logarithms cannot be a root of a rational algebraical equation of any degree.
We have in the above an algebraical summation of the effects of direct and indirect stimulations.
In such a case the effect of an external stimulus, say of light, is one of algebraical summation.
It will be shown that the curvature of an organ is determined by the algebraical summation of effects induced at the proximal and distal sides of the responding organ.
The effects of direct and indirect stimulus are independent of each other; the final effect is determined by their algebraical summation.
The individual effects of direct and indirect stimulus are practically independent of each other; hence their joint effects exhibit algebraical summation.
The phenomenon of algebraical summation is demonstrated in a very striking and convincing manner in the following experiment, which I have been successful in devising.
If the periodicity of the autonomous movements coincides with the periodicity of the external stimulus, the resulting movement will be determined byalgebraical summation; it will be very pronounced when the two effects are concordant.
Euler that he could convert arithmetical addition into algebraical multiplication, and in the paper referred to he gives the complete formal solution of the main problems of the partition of numbers.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "algebraical" in a variety of sentences. We hope that you will now be able to make sentences using this word.