They paid a fixed proportion of the produce (pars agraria) to the owner of the estate, and gave a determinate amount of labour (operae) on the portion of the domain which he kept in his own hands (mansus dominicus).
Yet the problem of the individual is really contained in this prior question; for determinate matter already involves particularity or this-ness.
To complete the experiment, the graduated tube containing the expelled air is brought to a constant and determinate temperature and pressure, and this volume is the volume which the given weight of the substance would occupy if it were a gas under the same temperature and pressure.
But 8 they are not congenitally present in the individual in a determinate shape.
Bare or indeterminate being, for instance, the first of the determinations of Hegel's logic, as the being of that which is not anything determinate, of Kant's thing-in-itself, for example, positively understood, implicated at once the notion of not-being, which negates it, and is one with it, yet with a difference, so that we have the transition to determinate being, the transition being baptized as becoming.
The position of a lamina movable in its own plane is determinate when we know the positions of any two points A, B of it.
It follows that the single resultant to which the system in general reduces is uniquely determinate, i.e.
9 is balanced by three determinate tensions (or thrusts) in the three links, provided the directions of the latter are not concurrent.
It is often a question of importance to determine the number of teeth in a train of wheels best suited for giving a determinate velocity ratio to two axes.
The active principle makes the matter a given determinate thing, characterizing and qualifying it, whence it is termed quality (7roLOrns).
The notions of distance and of lines at right angles are connected with the circular points; and almost every construction of a curve by means of lines of a determinate length, or at right angles to each other, and (as such) mechanical constructions by means of linkwork, give rise to curves passing the same definite number of times through the two circular points respectively, or say to circular curves, and in which the fixed centres of the construction present themselves as ordinary, or as singular, foci.
The office of reason is to give a true and distinct appreciation of the values of goods and evils; or firm and determinate judgments touching the knowledge of good and evil are our proper arms against the influence of the passions.3 We are free, therefore, through knowledge: ex magna lute in intellectu sequitur magna propensio in voluntate, and omnis peccans est ignorans.
In connexion with the problem of universals, he held that the diversity of individuals depends on the quantitative division of matter (materia signata), and in this way he attracted the criticism of the Scotists, who pointed out that this very matter is individual and determinate, and, therefore, itself requires explanation.
Hence " negative theology," which ascends from the creature to God by dropping one after another every determinate predicate, leads us nearest to the: truth.
Among the great variety of problems solved are problems leading to determinate equations of the first degree in one, two, three or four variables, to determinate quadratic equations, and to indeterminate equations of the first degree in one or more variables, which are, however, transformed into determinate equations by arbitrarily assuming a value for one of the required numbers, Diophantus being always satisfied with a rational, even if fractional, result and not requiring a solution in integers.
They are an extension of the principle on which gongs and cymbals and all instruments without notes of determinate pitch are employed in otherwise polyphonic music.
They teach further the solution of problems leading to equations of the first and second degree, to determinate and indeterminate equations, not by single and double position only, but by real algebra, proved by means of geometric constructions, and including the use of letters as symbols for known numbers, the unknown quantity being called res and its square census.
A binary form of order n contains n independent constants, three of which by linear transformation can be given determinate values; the remaining n-3 coefficients, together with the determinant of transformation, give us n -2 parameters, and in consequence one relation must exist between any n - I invariants of the form, and fixing upon n-2 invariants every other invariant is a rational function of its members.
Albert and Aquinas agree in declaring that the principle of individuation is to be found in matter, not, however, in matter as a formless substrate but in determinate matter (materia signata), which is explained to mean matter quantitatively determined in certain respects.
X is, in general, a determinate point, the barycentre of aA, 3B, &c. (or of A, B, &c. for the weights a, 0, &c.).
+X) happens to be zero, X lies at infinity in a determinate direction; unless - aA is the barycentre of (3B, yC, ...
Henry Thomas Colebrooke, one of the earliest modern investigators of Hindu science, presumes that the treatise of Aryabhatta extended to determinate quadratic equations, indeterminate equations of the first degree, and probably of the second.
In animal physiology he set himself to trace out the operation of determinate chemical and physical laws in the maintenance of life and health.
The composition of the distillate is determinate (by Avogadro's law) if the molecular weights and vapour pressure of the components at the temperature of distillation be known.
They differ, however, fundamentally in this respect, that, whereas evolution regards the process as from the indeterminate lower towards the determinate higher, emanation regards it as from the highest to the indefinitely lower.
The process of evolution from the indeterminate to the determinate is often expressed as a progress from the universal to the particular.
With sixteen teeth the pitch was well defined; with nine teeth it was fairly determinate; and even with two teeth it could be assigned with no great error.
- Various devices have been successfully employed for making sounds of determinate loudness in order to test the hearing of partially deaf people.
"If the sovereign power is to be understood in this fuller, less abstract sense, if we mean by it the real determinant of the habitual obedience of the people, we must look for its sources much more widely and deeply than the analytical jurists do; it can no longer be said to reside in a determinate person or persons, but in that impalpable congeries of the hopes and fears of a people bound together by common interest and sympathy, which we call the common will" (Green's Works, 2.404).
I) between the first and second, and two determinate notices (vii.
C. Within each state powers of taxation, to a determinate or to an indeterminate extent, as the case may be, are by the constitution and laws of the state conferred, almost always for strictly defined purposes, (1) upon counties, (2) upon cities, boroughs and incorporate villages, and (3) in nearly all the states, though in widely varying degrees, upon the primary geographical divisions of counties, such as the town of New England and the township of the Middle and Western states.
The other treatises of Apollonius mentioned by Pappus are - 1st, Aayov alroropii, Cutting off a Ratio; 2nd, Xcopiov a7rorop, Cutting off an Area; 3rd, Ocwpui j Av i Tog, Determinate Section; 4th, 'Eiraci)aL, Tangencies; 5th, 11-€1,o-as, Inclinations; 6th, Tinrot bri ret50t, Plane Loci.
The trees of the genus are closely allied in botanic features, as well as in general appearance, so that it is sometimes difficult to assign to them determinate specific characters, and the limit between species and variety is not always very accurately defined.
Hamilton, in fact, made the double mistake of limiting knowledge to what we can conceive, and confusing the determinate with the finite or limited.
This determinate sense of the spread is called the law of forward direction.
It was only very gradually that these dioceses acquired legislative independence and a determinate organization.
The medieval theologians followed in the same line, recognizing all the precepts of the Decalogue as moral precepts de lege naturae, though the law of the Sabbath is not of the law of nature, in so far as it prescribes a determinate day of rest (Thomas, summa, Ima IIaae, qu.
Instead of the mere " is " which is as yet nothing, we should rather say " becomes," and as " becomes " always implies " something," we have determinate being - " a being " which in the next stage of definiteness becomes " one."
The moment we stir a step further with Wundt in the direction of a more general conclusion (ein allgemeinerer Satz), we cannot infer from the premises the conclusion desired by Wundt, "Metals and fusible are connected "; nor can we infer " All metals are fusible, " nor "Metals are fusible," nor "Metals may be fusible," nor "All metals may be fusible," nor any assertory conclusion, determinate or indeterminate, but the indifferent contingent, "All metals may or may not be fusible," which leaves the question undecided, so that there is no syllogism.
The more fully analysed movement, that which proceeds downward from less determinate to more determinate universals, is named Division.
Resultant determinate judgments, presumes of course Doivi the doctrine of the interpenetration of ideas laid down in the Sophistes as the basis of predication, but its use precedes the positive development of that formula, though not, save very vaguely, the exhibition of it, negatively, in the antinomies of the one and the many in the Parmenides.
The ideal is progressively to determine a universe of discourse till true infimae species are reached, when no further distinction in the determinate many is possible, though there is still the numerical difference of the indefinite plurality of particulars.
Democritean physics without a calculus had necessarily proved sterile of determinate concrete results, and this was more than enough to ripen the naturalism of the utilitarian school into scepticism.
Similarly forms of thinking, the law of contradiction not excepted, have their meaning only in reference to determinate content, even though distributively all determinate contents are dispensable.
The problem of determining the possible configurations of equilibrium of a system of particles subject to extraneous forces which are known functions of the positions of the particles, and to internal forces which are known functions of the distances of the pairs of particles between which they act, is in general determinate For if n be the number of particles, the 3n conditions of equilibrium (three for each particle) are equal in number to the 351 Cartesian (or other) co-ordinates of the particles, which are to be found.
We have seen that a rigid structure may in general be rigidly connected with the earth by six links, and it now appears that any system of forces acting on the structure can in general be balanced by six determinate forces exerted by the links.
We have seen that the stresses produced by an equilibrating system of extraneous forces in a frame which is just rigid, according to the criterion of 6, are in general uniquely determinate; in particular, when there are no extraneous forces the bars are in general free from stress.
We may note that a frame of n joints which is just rigid must have 3116 bars; and that the stresses produced in such a frame by a given system of extraneous forces in equilibrium are statically determinate, subject to the exception of critical forms.
These co-ordinates may be chosen in an endless variety of ways, but their number is determinate, and expresses the number of degrees of freedom of the system.
This principle of least resistance renders determinate many problems in the statics of structures which were formerly considered indeterminate.
1 From this it would appear that, since by a nature is meant some sensible quality, superinduced upon, or possessed by, a body, so by a form we are to understand the cause of that nature, which cause is itself a determinate case or manifestation of some general or abstract quality inherent in a greater number of objects.
If, however, the circular ends of the catenoid are closed with solid disks, so that the volume of air contained between these disks and the film is determinate, the film will be in stable equilibrium however large a portion of the catenary it may consist of.
Although he denies liberty to the will in this sense - indeed, strictly speaking, neither liberty nor necessity, he says, is properly applied to the will, " for the will itself is not an agent that has a will " - he nevertheless insists that the subject willing is a free moral agent, and argues that without the determinate connexion between volition and motive which he asserts and the libertarians deny, moral agency would be impossible.
It is to be noticed here that the axes of co-ordinates may be any two lines at right angles to each other whatever; and that the equation of a curve will be different according to the selection of the axes of co-ordinates; but the order is independent of the axes, and has a determinate value for any given curve.
But whatever be the nature of the end chosen the libertarian is not concerned to deny that it must possess a fixed determinate character.
The recognition of such a necessary opposition is involved in the determinate act of choice.
The ends which at any moment the individual is free to choose or reject possess a determinate character: their existence or non-existence as possibilities is also to a very large extent determined for him.
He proves, by means of the six linear partial differential equations satisfied by the concomitants, that, if any concomitant be expanded in powers of xi, x 2, x 3, the point variables-and of u 8, u 2, u3, the contragredient line variables-it is completely determinate if its leading coefficient be known.
This point is called the centre of the given system of parallel forces; it is finite and determinate unless ~(P) = 0.
These Geheimrdte, a narrow body of secret counsellors, had already become a determinate concilium by 1527; and though at first only concerned with foreign affairs, they acquired, from the middle of the 16th century onwards, the power of dealing with imperial affairs in lieu of the Aulic Council.
A determinate musical pitch is not perceived, he says, till about 40 vibrations per second.