Such a mass of imaginary matter as we are now considering may be compared to a collection of heavy particles held in position relatively to one another by a system of light spiral springs, one spring being supposed to connect each pair of adjacent particles.
He paused at the door and mimed a jump shot at an imaginary hoop.
Brinkley's imaginary star-parallaxes (Phil.
I can get into enough trouble without people squeezing imaginary insults out of my words.
Would give negative, surd or imaginary values; Diophantus then traces how each element of the equation has arisen, and formulates the auxiliary problem of determining how the assumptions must be corrected so as to lead to an equation (in place of the "impossible" one) which can be solved rationally.
It's queer how ready people always are with advice in any real or imaginary emergency, and no matter how many times experience has shown them to be wrong, they continue to set forth their opinions, as if they had received them from the Almighty!
It is an imaginary history of the patriarchs and their descendants.
After he had gone Pierre continued pacing up and down the room for a long time, no longer piercing an imaginary foe with his imaginary sword, but smiling at the remembrance of that pleasant, intelligent, and resolute young man.
Kant's point is ignored, that deductions from these " imaginary " figures apply to the " real " world of experience.
Its provisions, real and imaginary, formed the standard towards which Englishmen must strive.
Nor were these precautions by any means superfluous, for not a few princes died on the journey or were condemned to death and executed for real or imaginary offences.
The whole story was an imaginary embroidery of the facts that barnacles attach themselves to submerged timber and that a species of goose is known as the bernicle goose.
As a typical instance we may take the chapter on the ant-lion - not the insect, but an imaginary creature suggested by Job.
It concludes with an imaginary vision of a beautiful world of spirits who have stripped off the fetters of earthly cares and sorrows and revel in the pure light of divine wisdom and love.
Maps of the 16th and 17th centuries often show Cambaluc in an imaginary region to the north of China, a part of the misconception that has prevailed regarding Cathay.
Expressions of the form b1,1 - I and a-}-b A l - I, where a and b are real numbers, are then described as imaginary and complex numbers respectively; the former being a particular case of the latter.
At other parts of the field the effect is the same, in accordance with the principle known as Babinet's, whether the imaginary screen in front of the object-glass is generally transparent but studded with a number of opaque circular disks, or is generally opaque but perforated with corresponding apertures.
In the following year Webster delivered his oration in commemoration of the second and third presidents of the United States - John Adams and Thomas Jefferson - who died on the 4th of July 1826; it is particularly remarkable for Adams's imaginary reply in the Continental 'Congress to the arguments against a Declaration of Independence, beginning with the familiar quotation: "Sink or swim, live or die, survive or perish, I gave my hand and my heart to this vote."
The settlements were called respectively Oster Bygd (or eastern settlement) and Vester (western) Bygd, both being now known to be on the south and west coast (in the districts of Julianehaab and Godthaab respectively), though for long the view was persistently held that the first was on the east coast, and numerous expeditions have been sent in search of these " lost colonies " and their imaginary survivors.
They added "that the public at large have only to know that their rights are imaginary to induce them also to be content with the extant system under which permission is very freely granted by owners of fisheries to the public for angling on the more frequented parts of the Thames."
The progress of analytical geometry led to a geometrical interpretation both of negative and also of imaginary quantities; and when a " meaning " or, more properly, an interpretation, had thus been found for the symbols in question, a reconsideration of the old algebraic problem became inevitable, and the true solution, now so obvious, was eventually obtained.
See also D'Ohsson's imaginary Voyage d'Abul Cassim, based on these sources.
If we consider any short length of the stream bounded by two imaginary cross-sections A and B on either side of the plug, unit mass of the fluid in passing A has work, p'v', done on it by the fluid behind and carries its energy, E'+ U', with it into the space AB, where U' is the kinetic energy of flow.
This telegram might have exercised the most prejudicial influence on the course of the battle had not Ladmirault (4th Corps), nearer to the seat of the imaginary danger, taken upon himself to disregard the warning transmitted to him by headquarters.
To endow the universal substance with moral attributes, to maintain that it is more than the metaphysical ground of everything, to say it is the perfect realization of the holy, the beautiful and the good, can only have a meaning for him who feels within himself what real not imaginary values are clothed in those expressions.
He sees insoluble contradictions in every mode of conceiving God as real, yet he advocates religious belief, though the object of that belief have but an abstract or imaginary existence.
THE] were practically powerless, the more so as their political activity consisted mainly in " building theories for an imaginary world."
Thenceforward, while never possessing or abusing the insolence of health, he could say " few persons have been more exempt from real or imaginary ills."
A line of force may be defined as an imaginary line so drawn that its direction at every point of its course coincides with the direction of the magnetic force at that point.
The treatment of equations of the second and higher degrees introduces imaginary and complex numbers, the theory of which is a special subject.
This led to a prolonged controversy on the nature of negative and imaginary quantities, which was ultimately settled in a very curious way.
Clearer ideas of imaginary quantities and the " irreducible case " were subsequently published by Bombelli, in a work of which the dedication is dated 1572, though the book was not published until 1579.
The battle of Langensalza (June 27th) showed that the risks Moltke deliberately accepted when he transferred so many of the western troops to the Bohemian frontier were by no means imaginary, for v.
(6) The least admissible value of p is that which makes the roots equal of this quadratic in µ, and then ICI s ec 0,, u= z - p (7) the roots would be imaginary for a value of p smaller than given by Cip 2 - 4(c 2 -c i)c2C 2 u 2 =o, (8) p2 = 4(c 2 -c l)cl C2.
There also he wrote the life of St Paul of Thebes, probably an imaginary tale embodying the facts of the monkish life around him.
Its adoption by the languages of Europe cannot apparently be traced farther back than the 4th century of our era, at which date it was employed to designate an imaginary animal living on the banks of the Euphrates.
In the case of plane figures, the congruence is tested by an imaginary superposition of one figure on the other; but this may more simply be regarded as the superposition, on either figure, of the image of the other figure on a contiguous plane.
The lower end of the jet tube, being open, is a loop, and the node may be regarded as in an imaginary prolongation of the jet tube above the nozzle.
ZODIAC (o ituKAos, from 'Cv&cov, " a little animal "), in astronomy and astrology, an imaginary zone of the heavens within which lie the paths of the sun, moon and principal planets.
In this review of the inhabitants of the Pacific islands an imaginary ethnological line has been drawn round it so as to include none but the-branches of the two great divisions.
And he fell back into that artificial realm of imaginary greatness, and again--as a horse walking a treadmill thinks it is doing something for itself--he submissively fulfilled the cruel, sad, gloomy, and inhuman role predestined for him.
By separation of real and imaginary parts, C =M cos 27rv 2 +N sin 27rv2 1 S =M sin 27rv 2 - N cos 27rv2 where 35+357.9 N _ 7rv 3 7r 3 v 7 + 1.3 22.214.171.124 126.96.36.199.9.11 These series are convergent for all values of v, but are practically useful only when v is small .
The geometrical interpretation of imaginary quantities had a far-reaching influence on the development of symbolic algebras.
A-, privative, and ywvia, an angle), the term given to the imaginary lines on the earth's surface connecting points at which the magnetic needle points to the geographical north and south.
The De algebra tractatus contains (chapters lxvi.-lxix.) the idea of the interpretation of imaginary quantities in geometry.
In this work, which is one of the most valuable contributions to the literature of algebra, Cardan shows that he was familiar with both real positive and negative roots of equations whether rational or irrational, but of imaginary roots he was quite ignorant, and he admits his inability to resolve the so-called lation of Arabic manuscripts.
Mosheim's " Servede " is an imaginary form.
The width of the gap may be diminished until it is no greater than the distance between two neighbouring molecules, when it will cease to be distinguishable, but, assuming the molecular theory of magnetism to be true, the above statement will still hold good for the intermolecular gap. The same pressure P will be exerted across any imaginary section of a magnetized rod, the stress being sustained by the intermolecular springs, whatever their physical nature may be, to which the elasticity of the metal is due.
Modern scholars have sometimes found in the name the expression of the aseity 14 of God; sometimes of his reality, in contrast to the imaginary gods of the heathen.
His triumphs, whether real or imaginary, to the reverso Campaiza sustained by the armies of the French directory, wa~
The purport, then, of ablutions is to remove, not dust and dirt, but the - to us imaginary - stains contracted by contact with the dead, with childbirth, with menstruous women, with murder whether wilful or involuntary, with almost any form of bloodshed, with persons of inferior caste, with dead animal refuse, e.g.
The development of the theory of equations leads to the amplification of real numbers, rational and irrational, positive and negative, by imaginary and complex numbers.