Under Abel's guidance, the prevailing obscurities of analysis began to be cleared, new fields were entered upon and the study of functions so advanced as to provide mathematicians with numerous ramifications along which progress could be made.
Such is this famous work, full of obscurities, redundancies and contradictions, in which the thread of the argument is sometimes lost in a labyrinth of reasonings and citations, both sacred and profane, but which nevertheless expresses, both in religion and politics, such audacious and novel ideas that it has been possible to trace in it, as it were, a rough sketch of the doctrines developed during the periods of the Reformation and of the French Revolution.
Its elementary nature was imperfectly understood; and the impure specimens obtained by the early chemists explain, in some measure, its confusion with tin, lead, antimony, zinc and other metals; in 1595 Andreas Libavius confused it with antimony, and in 1675 Nicolas Lemery with zinc. These obscurities began to be finally cleared up with the researches of Johann Heinrich Pott (1692-1777), a pupil of Stahl, published in his Exercitationes chemicae de Wismutho (1769), and of N.
But in working out the consequences of this view Say is not free from obscurities and inconsistencies; and by his comprehension of these immaterial products within the domain of economics he is confirmed in the error of regarding that science as filling the whole sphere which really belongs to sociology.
His true place in the history of speculation may be seen from the simple observation that the difficulties or obscurities in his scheme are really the points on which later philosophy has turned.
In order to avoid the uncertainty arising from the lack of vowels to distinguish forms consisting of the same consonants (for the vowel-points were not yet invented), the aramaising use of the reflexive conjugations (Hithpa`el, Nithpa`el) for the internal passives (Pu'al, Hoph`al) became common; particles were used to express the genitive and other relations, and in general there was an endeavour to avoid the obscurities of a purely consonantal writing.
Putting aside, then, the various obscurities of terminology, such as the distinction between the objects known, viz.
By this means the bulk of the statute law was immensely reduced, its obscurities and internal discrepancies in great measure removed, its provisions adapted, by the abrogation of what was obsolete, to the circumstances of Justinian's own time.
In others there are imperfections in rhythm, conventionalities of language, obscurities or over-subtleties of thought, which mar the reader's enjoyment.
His poem is rather lyrical than narrative, which may account for some obscurities in the connexion of thought; but his alphabetic scheme proves that he designed twenty-two stanzas, not sixty-six detached couplets.
And this is to be effected in the first place by showing that from the obscurities and inexplicabilities we meet with in nature we may reasonably expect to find similar difficulties in the scheme of religion.
That Locke was unable to reconcile these opposed notions is not surprising; that the difficulties and obscurities of the Essay arise from the impossibility of reconciling them is evident on the slightest consideration of the main positions of that work.
The difficulties or obscurities of the Kantian system, of which the above are merely the more prominent, may all be traced to the one source, the false or at least inadequate idea of the individual.
In consequence, his lecture-room was thronged with people of all sorts, anxious to hear a man who shunned the barren obscurities of the alchemists, and did not regard the quest of the philosopher's stone and the elixir of life as the sole end of his science.
All the contradictions and obscurities of history and the false path historical science has followed are due solely to the lack of a solution of that question.
Although these and other phenomena cannot yet be safely placed in a historical frame, the methodical labours of past scholars have shed much light upon the obscurities of the exilic and post-exilic ages, and one must await the more comprehensive study of the two or three centuries which are of the first importance for biblical history and theology.