The above construction for Z is a corollary of the general theorem given in 127.
On the whole serfdom appears as a characteristic corollary of feudalism.
Whether he subsequently regarded the victory of the monarchy and its corollary, the admittance of the middle classes to all offices and dignities, as a satisfactory equivalent for his original demands; or whether he was so overcome by royal favour as to sacrifice cheerfully the political liberties of his country, can only be a matter for conjecture.
§ 99a (3rd ed., 1892), where the expression in question is deduced as a corollary of Green's theorem.
Europe had sinned in the face of God; otherwise Jerusalem would never have fallen; and the idea of a spiritual reform from within, as the necessary corollary and accompaniment of the expedition of Christianity without, breathes in some of the papal letters, just as, during the conciliar movement, the causa reformationis was blended with the causa unionis.
The fact that a question of which Smith had given the solution in 1867, as a corollary from general formulae governing the whole class of investigations to which it belonged, should have been set by the Academie as the subject of their great prize shows how far in advance of his contemporaries his early researches had carried him.
With grammatical precision, antiquarian learning and critical discernment Origen combines the allegorical method of interpretation - the logical corollary of his conception of the inspiration of the Scriptures.
Our concern lies with the first kind of Crusade, and with the other three only so far as they bear on the first, and as they illustrate the immense widening which the term "Crusade" now underwent - a widening accompanied by its inevitable corollary of shallowness of motive and degradation of impulse.
(iv.) The procedure is sometimes stated differently, the transposition being regarded as a corollary from a general theorem that the roots of an equation are not altered if the same expression is added to or subtracted from both members of the equation.
The hour of Bestuzhev's triumph coincided with the peace congress of Aixla-Chapelle, which altered the whole situation of European politics and introduced fresh combinations, the breaking away of Prussia from France and a rapprochement between England and Prussia, with the inevitable corollary of an alliance between France and the enemies of Prussia.
As a corollary of this he founded in 1875 the "Hebrew Union College" in the same city, and this institution has since trained a large number of the rabbis of America.
Constructing a square of twice the area of a given square (which follows as a corollary to the Pythagorean property of a right-angled triangle, viz.
Now this doctrine of material atoms is an almost necessary corollary to the doctrine of a universal aether.
The corollary, that the electric resistance of a metal can be determined in absolute units by experiments on the reflexion of heat-rays from its surface, is a striking illustration of the unification of the various branches of physical science, which has come in the train of the development of the theory of the aether.
But at the end of his Metaphysik, from the conclusion that everything beyond phenomena is divine interaction, he drew the consistent corollary that individual souls are simply actions of the one genuine being.
He infers the corollary that universal experience contains the same duality of subjective and objective factors without dualism.
As a human person, I am body and soul; and the idealistic identification of the Ego with soul or mind, involving the corollary that my body belongs to the non-Ego and is no part of myself, is the reductio ad absurdum of idealism.
Thus, in the third, fourth and fifth general sessions it was enacted, with characteristic precipitation, that an ecumenical council could not be dissolved or set aside by the pope, without its consent: the corollary to which was, that the present council, notwithstanding the flight of John XXIII., continued to exist in the full possession of its powers, and that, in matters pertaining to belief and the eradication of schism, all men - even the pope - were bound to obey the general council, whose authority extended over all Christians, including the pope himself.
A corollary to this system was the much needed reform of the Polish constitution, without which nothing beneficial was to be expected from any political combination.
One corollary was the famous doctrine of " hero worship " first expounded in his lectures.
But Kant's criticism and Sigwart's corollary only derive plausibility from a false definition of truth.
As the way of salvation was modified, so too was the idea of salvation: the dream of a Messianic kingdom on earth, with its corollary the resurrection of the physical body, faded away, especially after the Roman empire ado pd y?
With the approval of Antiochus Epiphanes, the Sadducean section embraced the outward forms of Hellenism, and out of the persecution of the orthodox which followed was born the hope of a future life which was in the circumstances the necessary corollary of God's righteousness and was discovered to be latent in Scripture.
If, on the contrary, we must hold that man is essentially related to what the same writer calls "a common nature," then it is a legitimate corollary that in man as intelligence we ought to find the key of the whole fabric. At all events, this method of approach must be truer than any which, by restricting itself to the external aspect of phenomena as presented in space, leaves no scope for inwardness and life and all that, in Lotze's language, gives "value" to the world.
This relation was soon by the canonists identified with the blood-tie which connects real parents with their offspring, and the corollary drawn that children, who in baptism had the same god-parent, were real brothers and sisters, who might not marry either each the other or real children of the said god-parent.
This hedonism has perplexed Plato's readers needlessly (as we have said in speaking of the Cyrenaics), inasmuch as hedonism is the most obvious corollary of the Socratic doctrine that the different common notions of good - the beautiful, the pleasant and the useful - were to be somehow interpreted by each other.
Another corollary is that in the case of a body moving in a parabolic orbit the velocity at any moment is that which would be acquired by the body in falling from an infinite distance to the place it occupies at the moment.
And I think that helps explain why no one quite foresaw the rise of the Internet: because it doesn't have an offline corollary of its own.
This has no offline corollary and is economically empowering to so many people. 5. eBay and reallocating existing goods. eBay is actually a little like direct trade.
The caucus, which is the natural corollary of the detachment, determines by majority the vote of the whole of the members of the party, independence of action being allowed on minor questions only.
Another corollary of the fact that there is no electric force in the interior of a charged conductor is that the potential in the interior is constant and equal to that at the surface.
The existence of a prophet is shown to be a corollary from a belief in God as a moral governor, and the phenomena of miracles are required to evidence the genuineness of the prophetic mission.
This bold attempt is entirely factitious and verbal, and it is only his employment of various terms not generally used in such a connexion (axiom, theorem, corollary, etc.) that gives his treatise' its apparent originality.
Maha-vira treated ethics as corollary and subordinate to his metaphysics, with which he was chiefly concerned."
The equation of energy for a rigid body has already been stated (in effect) as a corollary from fundamental assumptions.
Razin proclaimed that his object was to root out the boyars and all officials, to level all ranks and dignities, and establish Cossackdom, with its corollary of absolute equality, throughout Muscovy.
The liberum veto was based on the assumption of the absolute political equality of every Polish gentleman, with the inevitable corollary that every measure introduced into the Polish diet must be adopted unanimously.