# Mathematically Sentence Examples

It was

**mathematically**treated by Louis Carre in 1705 and Koersma in 1741.He also made important contributions to the mathematical theory of electrodynamics, and in papers published in 1845 and 1847 established

**mathematically**the laws of the induction of electric currents.Oliver Heaviside showed

**mathematically**that uniformly-distributed inductance in a telephone line would diminish both attenuation and distortion, and that if the inductance were great enough and the insulation resistance not too high the circuit would be distortionless, while currents of all frequencies would be equally attenuated.Amongst the earliest mechanical contrivances of Fraunhofer was a machine for polishing

**mathematically**uniform spherical surfaces.This equation, which is

**mathematically**deducible from the kinetic theory of gases, expresses the behaviour of gases, the phenomena of the critical state, and the behaviour of liquids; solids are not accounted for.AdvertisementWhen the interval is very small the discrepancy, though

**mathematically**existent, produces no practical effect, and the illumination at B due to P is as important as that due to A, the intensities of the two luminous sources being supposed equal.The choice between various methods of resolution, all

**mathematically**admissible, would be guided by physical considerations respecting the mode of action of obstacles.**Mathematically**we have thus in all cases to compute present value on the basis of a deferred as well as a limited annuity.Most of the writers already noticed worked out the problems connected with the projection of images in the camera obscura more by actual practice than by calculation, but William Molyneux, of Dublin, seems to have been the first to treat them

**mathematically**in his Dioptrica Nova (1692), which was also the first work in English on the subject, and is otherwise an interesting book.This capacity is then a function of the geometrical dimensions of the conductor, and can be

**mathematically**determined in certain cases.AdvertisementThis is

**mathematically**expressed by the statement that dE is an exact differential of a function of the co-ordinates defining the state of the body, which can be integrated between limits without reference to the relation representing the path along which the variations are taken.It can be shown

**mathematically**that the velocity of propagation will be greatly increased if the frequency of the light-wave is slightly greater, and greatly diminished if it is slightly less than the natural frequency of the molecules; also that these effects become less and less marked as the difference in the two frequencies increases.The combination of ductility, which lessens the tendency to break when overstrained or distorted, with a very high limit of elasticity, gives it great value for shafting, the merit of which is measured by its endurance of the repeated stresses to which its rotation exposes it whenever its alignment is not

**mathematically**straight.In treating

**mathematically**the propagation of other kinds of waves, it is necessary to analyse them into their simple-harmonic components, which may be treated as being propagated independently.In astronomy he depreciates the merits of Newton and elevates Kepler, accusing Newton particularly, a propos of the distinction of centrifugal and centripetal forces, of leading to a confusion between what is

**mathematically**to be distinguished and what is physically separate.AdvertisementFor long periods he was

**mathematically**unproductive, but then sudden inspiration would come upon him and his ideas and theories poured forth far more quickly than he could record them.It has now been firmly established, both experimentally and

**mathematically**, that coronae are due to diffraction by the minute particles of moisture and dust suspended in the atmosphere, and the radii of the rings depend on the size of the diffracting particles.Any scheme of abstract dynamics constructed in this way, provided it be self-consistent, is

**mathematically**legitimate; but from the physical point of view we require that it should help us to picture the sequence of phenomena as they aCtually occur.We may briefly notice the case of resistance varying as the square of the velocity, which is

**mathematically**simple.Unfortunately, the return of age is amongst the less satisfactory results of a general enumeration, though its inaccuracy, when spread over millions of persons, is susceptible of correction

**mathematically**, to an extent to make it serve its purpose in the directions above indicated.AdvertisementWeber at the same time deduced the mathematical laws of induction from his elementary law of electrical action, and with his improved instruments arrived at accurate verifications of the law of induction which by this time had been developed

**mathematically**by Neumann and himself.In this assertion we think he was

**mathematically**wrong, though in his own hypothesis that the density does actually vary, he was probably right.The limiting conditions of the stability of these figures have been studied both

**mathematically**and experimentally.Stefan's law of radiation according to the fourth power of the temperature is too difficult to pursue, but if we are content with cognate results we can follow them out

**mathematically**in a hypothetical law of the first power.With this conception of the infinite as absolutely unconditioned should be compared what may be described roughly as lesser infinities which can be philosophically conceived and

**mathematically**demonstrated.AdvertisementSuch are the evangelical principle of " doing as you would be done by the principle of justice, or " giving every man his own, and letting him enjoy it without interference "; and especially what More states as the abstract formula of benevolence, that " if it be good that one man should be supplied with the means of living well and happily, it is

**mathematically**certain that it is doubly good that two should be so supplied, and so on."The declination, or deviation between the magnetic pole and the rotation pole, should theoretically be a simple,

**mathematically**calculable figure.Show that you're

**mathematically**inclined with number conundrums.Fantastic tho it seems, time dilatation has been proved

**mathematically**.The first dances are very symmetrical within the spirit of Bach's

**mathematically**precise manner.The course will be explanatory rather than

**mathematically**rigorous.It is straightforward to show students that the only

**mathematically**tractable way forward is to minimize the squared error or the mean squared error.Then the quantity E cos OdS is the product of the normal component of the force and an element of the surface, and if this is summed up all over the surface we have the total electric flux or induction through the surface, or the surface integral of the normal force

**mathematically**expressed by JE cos OdS, provided that the dielectric constant of the medium is unity.Young (see Brande's Quarterly Journal, 1820) investigated

**mathematically**the magnetism of ships.In other words, a force is

**mathematically**of the nature of a vector (see VECTOR ANALYSIS, QIJATERNIONS).For the

**mathematically**challenged who find it hard to figure out how many bags of soil or mulch to buy, this calculator comes in handy.One neat way to do this without being

**mathematically**inclined is to mark the area you want to create the opening for.You evaluate Golden Ratio beauty by measuring the proportions of an object or person and determining

**mathematically**how close the ratio is to the Golden Ratio.Depending on the results, you can

**mathematically**evaluate just how beautiful the object or human being truly is.If you have, you are wondering about something that is

**mathematically**explained and found all around you in the arts and sciences, nature and life itself.An infinite number, the Golden Ratio is generally expressed

**mathematically**as 1.618.**Mathematically**known as Phi, the Golden Ratio is a constant number that stands for the ratio of two quantities and how those quantities relate to each other.Moreover, some students skate by

**mathematically**merely by memorizing the formulae required for problem solving.**Mathematically**speaking, a conjunction is formed when two planets are approximately at the same degree within one sign.Using this signal, the receiver can calculate the distance from itself to the satellite and

**mathematically**creates a "sphere" representing a radius within which your position exists.The receiver retrieves a signal from the second satellite and, based on the distance from that satellite,

**mathematically**creates a second sphere.It is simply not

**mathematically**possible.The basis of the novels is the theory that large groups of people can be

**mathematically**modelled and their actions predicted, assuming you know everything about conditions under which they live.**Mathematically**, this makes it easy to come up with colors that will show up the same regardless of browser.