There is no recognition whatever of the principle of the indeterminate sentence.
But the bulk of the work consists of problems leading to indeterminate equations of the second degree, and these universally take the form that one or two (and never more) linear or quadratic functions of one variable x are to be made rational square numbers by finding a suitable value for x.
All that can be said at present about this difficult etymology is that in the non-Semitic Babylonian the medial m represented quite evidently an indeterminate nasal which could also be indicated by the combination rig.
55) Passover are established, with two indeterminate notices (iv.
Matter is the basework of each /3600s j it is the dark principle, the indeterminate, that which has no qualities, the µz 7 6v.
The whole world is represented by the figure of a tree, of which the seeds and roots are the first indeterminate matter, the leaves the accidents, the twigs and branches corruptible creatures, the blossoms the rational soul, and the fruit pure spirits or angels.
At some indeterminate later period, the " clerk " was tried for felony by a jury in the king's court and then "pleaded his clergy," after conviction there, and was remitted to the ordinary for ecclesiastical punishment.
In a pass examination the question has to be considered how far, if at all, excellence in one subject shall compensate for deficiency in another, a question which is indeterminate until the precise object of the whole examination is formulated.
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.
A few problems lead to indeterminate equations of the third and fourth degrees, an easy indeterminate equation of the sixth degree being also found.
He follows the methods of Diophantus; his work on indeterminate equations has no resemblance to the Indian methods, and contains nothing that cannot be gathered from Diophantus.
There are five states, all sawbwaships, under the supervision of the superintendent of the northern Shan States, besides an indeterminate number of Wa States and communities of other races beyond the Salween river.
The Diophantine analysis was a favourite subject with Pell; he lectured on it at Amsterdam; and he is now best remembered for the indeterminate equation ax 2 +1 = y 2, which is known by his name.
His share in the settlement of 1559 was considerable, and it coincided fairly with his own somewhat indeterminate religious views.
He supposed that the one and the two, which is indeterminate, and is the great s and little, are opposite principles or causes.
Atoms swerved as they fell endlessly downwards, and thus introduced an indeterminate or irrational element into the processes of the world.
More especially the cosmology of Anaximander resembles the modern doctrine of evolution in its conception of the indeterminate (rO filr€Lpov) out of which the particular forms of the cosmos are differentiated.
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.
In the Letter to Magister Theodore indeterminate problems are chiefly worked, and Leonardo hints at his being able to solve by a general method any problem of this kind not exceeding the first degree.
(" Indeterminate equations " belong properly to the theory of numbers.) 61.
The process of evolution from the indeterminate to the determinate is often expressed as a progress from the universal to the particular.
He thus became the inventor of a new form of literature; and, if in his hands the satura was rude and indeterminate in its scope, it became a vehicle by which to address a reading public on matters of the day, or on the materials of his wide reading, in a style not far removed from the language of common life.
5 1918 invited Prof. Voldemar to form the first independent administration on non-party lines and reach an understanding with the national minorities resident within the still indeterminate frontiers, viz.
Smith, on Linear Indeterminate Equations, Phil.
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.
Moritz Cantor suspects the influence of Diophantine methods, more particularly in the Hindu solutions of indeterminate equations, where certain technical terms are, in all probability, of Greek origin.
Great advances were made in the study of indeterminate equations, a branch of analysis in which Diophantus excelled.
Writing formulae (3r) and (33) for the energy and entropy with indeterminate constants A and B, instead of taking them between limits, we obtain the following expressions for the thermodynamic functions in the case of the vapour: " =Solog e 0 - R log e p - ncp/D+A".
They are not conceived of in any anthropomorphic form, their sex even may often be indeterminate ("sive mas, sive femina" is the constantly recurring formula of prayer), but the sphere of action of each is clearly marked and an appeal to a spirit outside his own special sphere would never even be thought of.
In 1907 the General Assembly passed a law under which the indeterminate sentence was established in the state, and the governor appoints a Board of Parole of three members, of whom one must be an attorney and not more than two are to belong to the same political party.
Since 1895 indeterminate sentences have been imposed on all convicts sentenced to the state prison otherwise than for life or as habitual criminals; i.e.
At the end of 1905, however, about 37 had been certainly recognized, besides some outlying cases of indeterminate type, in which continuous occultations by two bright stars, revolving in virtual contact, are doubtfully supposed to be in progress.
In 1799 he proved that carbonate of copper, whether natural or artificial, always has the same composition, and later he showed that the two oxides of tin and the two sulphides of iron always contain the same relative weights of their components and that no intermediate indeterminate compounds exist.
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.
Identifying the form of the good with the one, he supposed that the one, by combining with the indeterminate two, causes a plurality of forms, which like every combination of one and two are numbers but peculiar in being incommensurate with one another, so that each form is not a mathematical number (pa077pa-1.6s apt°pos), but a formal number (EDBnTLKOS apiepos).
Further he supposed that in its turn each form, or formal number, is a limited one which, by combining again with the indeterminate two, causes a plurality of individuals.
Hence finally he concluded that the good as the one combining with the indeterminate two is directly the cause of all forms as formal numbers, and indirectly through them all of the multitude of individuals in the world.
Wood potentially a table; primary, as an indeterminate something which is a substratum capable of becoming natural substances, of which it is always one; and it is primarily the matter of earth, water, air, fire, the four simple bodies (airxa 6w,uara) with natural rectilineal motions in the terrestrial world (De Gen.
The matter of a natural substance is not a primary matter which is one indeterminate substratum of all natural substances, but is only one body as able to be changed by a force which is another substance able to change it, e.g.
Hence, when the number of any proposed year in each of the cycles is known, its number in the Julian period can be determined by the resolution of a very simple problem of the indeterminate analysis.
In order to explain free will, he supposes, contrarily to Fouillee, that the laws of phenomena are indeterminate, contingent and liable to exceptions.
His most important achievement was to define "salts" - a term formerly used in the most loose and indeterminate way - as the compounds formed by the union of acids and bases, and further to distinguish between neutral, basic and acid salts.
Pythium is of interest as illustrating the dependence of zoospore-formation on conditions and the indeterminate nature of conidia.
The first is a new method for educating and reforming young offenders, already on the frontiers of habitual crime, no longer children, but at an age still susceptible of permanent improvement; the second is the legal acceptance of the principle of indefinite detention, the willingness to inflict an indeterminate sentence on those who have already forfeited the right to be at large.
Side by side with the new processes introduced, the idea of the indeterminate sentence was started and put in practice, by which release was made to depend upon reasonable hope of amendment and sentences were prolonged until it was more or less certain that the treatment had resulted in cure.
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.
Lastly, Wundt's view is an interesting piece of eclecticism, for he supposes that induction begins in the form of Aristotle's inductive syllogism, S-P, S-M, M-P, and becomes an inductive method in the form of Jevons's inverse deduction, or hypothetical deduction, or analysis, M-P, S-M, S-P. In detail, he supposes that, while an " inference by comparison," which he erroneously calls an affirmative syllogism in the second figure, is preliminary to induction, a second " inference by connexion," which he erroneously calls a syllogism in the third figure with an indeterminate conclusion, is the inductive syllogism itself.
For example, according to Hegel, being and not-being are both indeterminate and therefore the same.
In pure algebra Descartes expounded and illustrated the general methods of solving equations up to those of the fourth degree (and believed that his method could go beyond), stated the law which connects the positive and negative roots of an equation with the changes of sign in the consecutive terms, and introduced the method of indeterminate coefficients for the solution of equations.'
It has now become apparent that the traditional field of mathematics in the province of discrete and continuous number can only be separated from the general abstract theory of classes and relations by a wavering and indeterminate line.
The conquered peoples fell into an inferior caste, made to work for, and to pay for the subsistence of, their conquerors, as under the Arab domination; the principal taxes exacted from them were the kharaj, a tax of indeterminate amount upon realty, based on the value of lands owned by unbelievers - (in contradistinction to the tithe [ashar] which was a tax of fixed amount upon lands owned by believers) - and levied in payment of the privilege of gaining means of existence in a Mussulman country, and the jiziye, a compulsory payment, or poll-tax, to which believers were not subjected, in lieu of military service.
Ganessa, an eminent astronomer, mathematician and scholiast of Bhaskara, quotes this work and makes separate mention of the cuttaca (" pulveriser "), a device for effecting the solution of indeterminate equations.
But whereas Diophantus aimed at obtaining a single solution, the Hindus strove for a general method by which any indeterminate problem could be resolved.
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.
In the state reformatory at Elmira (which, like that at Napanoch, is for men between sixteen and thirty years of age who have been convicted of a state prison offence for the first time only), the plan of committing adult felons on an indeterminate sentence to be determined by their behaviour was first tested in America in 1877, and it has proved so satisfactory that it has been in part adopted for the state prisons.
There were in 1908 two penitentiaries, one at Joliet and one at Chester, and, in addition to the two reformatory institutions for young offenders under the supervision of the Board of Charities, there is a State Reformatory for boys at Pontiac. The indeterminate sentence and parole systems are important features of the treatment of criminals.
Wundt's point is that the conclusion of the inductive syllogism is neither so much as all, nor so little as some, but rather the indeterminate "M and P are connected."
The answer to Hegel is that being and not-being are at most similarly indeterminate, and to Bradley that each animal has its own different lungs, whereby they are only similar.
A man who has at length found something to do will not need to get a new suit to do it in; for him the old will do, that has lain dusty in the garret for an indeterminate period.
At the same time a supreme court of judicature was appointed, composed of a chief and three puisne judges, to exercise an indeterminate jurisdiction at Calcutta.