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.
The doctrine of Anaximenes, who unites the conceptions of a determinate and indeterminate original substance adopted by Thales and Anaximander in the hypothesis of a primordial and all-generating air, is a clear advance on these theories, inasmuch as it introduces the scientific idea of condensation and rarefaction as the great generating or transforming agencies.
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.
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.
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.
A few problems lead to indeterminate equations of the third and fourth degrees, an easy indeterminate equation of the sixth degree being also found.
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.
In it he lays the chief stress on the indeterminate nature of the Anglican form " Receive the Holy Ghost " at least from 1552 till the addition of the specific words, " for the office and work of a bishop (or priest) in the church of God," as also on the changes made in the Edwardine order " with the manifest intention...
(" Indeterminate equations " belong properly to the theory of numbers.) 61.
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.
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 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.
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.
55) Passover are established, with two indeterminate notices (iv.
His share in the settlement of 1559 was considerable, and it coincided fairly with his own somewhat indeterminate religious views.
Matter is the basework of each /3600s j it is the dark principle, the indeterminate, that which has no qualities, the µz 7 6v.
He supposed that the one and the two, which is indeterminate, and is the great s and little, are opposite principles or causes.
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.
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.
There is no recognition whatever of the principle of the indeterminate sentence.
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.