Congruence means a close match between what you feel and how you think and act.
A perfect congruence of morphological relationships could only take place if transformations resulted from an internal power instead of external influences.
Conclusions as to the causes of change will then be drawn, and these will corroborate from another side a subsequent inquiry as to the presence or absence of complete congruence in the two morphological systems.
This lack of congruence between the mental picture and the object itself is necessary for obvious reasons.
Mathematicians, notably non-Euclideans, have sought to extend the comparatively small sphere of limits of congruence between mathematic and perceptual space to such an extent as to cause it to encroach upon forbidden territory.
How then could it be expected that a system of space-measurement so far removed from this primary congruence as the non-Euclidean system is should exhibit more obvious signs of correspondence?
And although there is no hesitancy in admitting the basic agreement of the most primary facts of mathematical knowledge with the essential character of the intellect the existence of well-defined limits for such congruence cannot be gainsaid.
Adaptation succeeds adaptation and with each there is a change in the form and this process continues until there is a more or less perfect congruence between form and juxtaposed environmental conditions.
But in thus admitting the natural congruence between the intellectuality and the phenomenal or sensuous we do not thereby unite with those who already believe that this kosmic agreement is the ne plus ultra of psychogenesis.
Moreover, it is certain that no sane mind cherishes the hope that there shall ever be found in the universe of life and form a congruence for all of the possibilities held out by the purely formal.
The natural course of all waters is downward, wherefore of congruence they fall that way where they find the earth most low and deep: in respect whereof, it was erst said, the seas do strike from the northern lands southerly.
Space and time are now interconnected; and this peculiar factor of time which is so immediately distinguished among the deliverances of our sense-awareness, relates itself to one particular congruence relation in space.
Such measurement does not follow from the mere serial property of time; it requires a theory of congruence which will be considered in a later lecture.
Uniformity in change is directly perceived, and it follows that mankind perceives in nature factors from which a theory of temporal congruence can be formed.
So in appealing to familiar phenomena it allows that there is some factor in nature which we can intellectually construct as a congruence theory.
Poincaré asks for information as to the factor in nature which might lead any particular congruence relation to play a preeminent rôle among the factors posited in sense-awareness.
We then enquire about congruenceand lay down the set of conditions--or axioms as they are called--which this relation satisfies.
We shall find that this discovery of definite unique properties defining perpendicularity is of critical importance in the theory of congruence which is the topic for the next lecture.
It was noted at the close of the previous lecture that the question of congruence had not been considered, nor had the construction of a timeless space which should correlate the successive momentary spaces of a given time-system.
It selects one definite system of congruence embracing both space and time, and thus explains the concordance as to measurement which is in practice attained.
The new theory provides a definition of the congruence of periods of time.
On the other hand Russell is in an equally strong position when he asserts that, as a fact of observation, we do find it, and what is more agree in finding the same congruence relation.
He in effect challenges anyone to point out any factor in nature which gives a preeminent status to the congruence relation which mankind has actually adopted.
Congruence is extended in any space beyond parallel rects to all rects by two axioms depending on perpendicularity.
Finally the sixth axiom of congruence is that the relation of congruence is transitive.
This is the reason for placing it by itself, followed by the congruence theorems.
He now introduces a theorem, which might equally well have been his first proposition, namely, the case of the congruence of two triangles, having given two sides and the included angle.
For example, the nine propositions on congruence in a plane are followed by nine on congruence in space.
In speaking of two congruent triangles it is somewhat easier to follow the congruence if the two are read in the same order, even though the relatively unimportant counterclockwise reading is neglected.
In particular, Professor Hilbert has given a system[45] of congruence postulates, but they are rather for the scientist than for the student of elementary geometry.
A double infinite number of lines, that is, all lines which satisfy two conditions, or which are common to two complexes, are said to form a congruence of lines; e.
It has, however, been proved by Sophus Lie[46] thatcongruence is capable of definition without recourse to a new fundamental idea.
The distinctive property of the points A is that two of the congruence lines through them coincide, and in like manner the planes a each contain two coincident lines.
As regards the analytical treatment, the difficulty is of the same nature as that arising in the theory of curves in space, for a congruence is not in general the complete intersection of two complexes.
Each of these lines is a bitangent of the singular surface, which is therefore completely determined as being the focal surface of the (2, 2) congruence above.
By means of formulae connecting the number of singular points and their orders with the class m of quadratic congruence Kummer proved that the class cannot exceed seven.
There will therefore be one line of the congruencepassing through Q, and only one.
If the above four conditions are satisfied by a group throughout the whole of projective space, the congruence group is the continuous group for which some imaginary quadric (with a real equation) is latent.
But in addition to the difficulties of the theory of algebraic surfaces, a subject still in its infancy, the theory of congruences has other difficulties in that a congruence is seldom completely represented, even by two equations.
In the light of these considerations it seems feasible to indicate both the congruence and the distinction between the two categories of assets a little more narrowly than was done above.
But the great truths or laws of the science remain hypothetical laws; and the test of scientific reality is congruence with the hypothetical laws, not coincidence with matter-of-fact events.
The stress laid on this axiom by Bolyai is probably due to the influence of Gauss, whose work on the curvature of surfaces laid the foundation for the use made of congruence by Helmholtz.
Nevertheless, he maintains that Congruence is proved by experience.
In spite of this fact, he defines space as an extent, and then regards Congruence as empirical, and as possibly false in the infinitesimal.
Is wholly false if it means that the axiom of Congruence actually asserts the existence of rigid bodies, 75 71.
Congruence was to refer to geometrical bodies, with none of the properties of ordinary bodies except impenetrability (Erdmann, Axiome der Geometrie, p.
In the first place, there is no necessity to make the axiom of Congruence apply to actual rigid bodies--on this subject I have enlarged in Chapter II.
Persons are encouraged to bring forth who they are so there is congruence between actions and feelings.
Personhood implies living out who we are, demonstrating congruence between beliefs and behaviors, and living the meaning of one's life.
Smith (1999) analyzed concepts from the literature on caring in nursing in an effort to uncover points of congruence between that literature and the theoretical perspective of the Science of Unitary Human Beings.
Our ideals of action must be self-made or self-begotten, but yet they must be congruent with known fact; but the manner of such congruence is hard to see, hard to express.
The naturall course of all waters is downeward, wherefore of congruence they fall that way where they finde the earth most lowe and deepe: in respect whereof, it was erst sayd, the seas doe strike from the Northern landes Southerly.
As in the Rhopalocera most of the families show a complete congruence in the form-relationship of the caterpillars and perfect insects, so a similar congruence is also found in the majority of the families belonging to other groups.
The number of the changes would here alone determine whether congruence or incongruence occurred between the two stages.
Is there a complete congruenceof form-relationship between larvæ on the one hand and imagines on the other?
Now when we see that two species which differ in their imaginal characters present correspondingly small differences in their larvæ, this exact systematic congruence indicates a completely parallel phyletic development.
In the butterflies, therefore, a perfect congruence of form-relationship does not exist, inasmuch as the imagines constitute one large group of higher order whilst the larvæ can only be formed into families.
I believe that the phenomena can be quite well understood without any such assumption--both the phenomena of congruence and incongruence, in their two forms of unequal divergence and unequal group-formation.
Therefore of a congruence From hence thou must have my heart and obedience.
On the whole, therefore, as we turn to more and more comprehensive groups, the incongruence diminishes whilst the congruence increases, until finally the latter becomes the rule.
All these cases show a complete congruence in the two kinds of form-relationship; but exceptions are not wanting.
The morphological congruence between larvæ and imagines declares itself most sharply in genera, where it is the rule almost without exception.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "congruence" in a variety of sentences. We hope that you will now be able to make sentences using this word.
