The notion of imaginary intersections, thus presenting itself, through algebra, in geometry, must be accepted in geometry - and it in fact plays an all-important part in modern geometry.
The incessant change which experience brings before us, taken in conjunction with the thought of unity in productive force of nature, leads to the all-important conception of the duality, the polar opposition through which nature expresses itself in its varied products.
And Croesus was so amazed that he endowed the Oracle at Delphi with all kinds of gifts and planned to run all-important questions by this oracle.
The enemy's light guns, aided by effective searchlights, were offering a strenuous opposition to the small craft engaged on the all-important duty of clearing the channel of submerged defences.
Hamilton and George Boole, as one of several independent discoverers of the all-important principle of the quantification of the predicate.
It was now all-important for Caesar to secure practical irresponsibility by obtaining a military command.
Of the three divisions logic is the least important; ethics is the outcome of the whole, and historically the all-important vital element; but the foundations of the whole system are best discerned in the science of nature, which deals pre-eminently with the macrocosm and the microcosm, the universe and man, including natural theology and an anthropology or psychology, the latter forming the direct introduction to ethics.
Only a few papers and works can be mentioned here, with the remark that few authors have paid attention to the all-important innervation of the muscles.
This solid played an all-important part in the geometry and cosmology of the Greeks.
He rejected the Platonic hypothesis of forms, and affirmed that they are not separate but common, without however as yet having advanced to a constructive metaphysics of his own; while at the same time, after having at first adopted his master's dialectical treatment of metaphysical problems, he soon passed from dialogues to didactic works,, which had the result of separating metaphysics from dialectic. The all-important consequence of this first departure from Platonism was that Aristotle became and remained primarily a metaphysician.