All we can do is substitute our lips and "thereby arrive perhaps at a slightly more satisfying result than if we were reduced to caressing the beloved with a horny tusk".
In this case, it follows from equation (120) that the change of density accompanying any small change in pressure, dp, is such that This makes it possible to integrate the right-hand side of equation (131), and one thereby arrives at a version of Bernoulli's law for a steady compressible flow of gases which states that is constant along a streamline.
So it seems that here one first has to assume the existence of the required circle, then use logic to make various judgements about it, and only thereby arrives at a mathematical construction for it.
Olum explains that, hypothetically, one could take a shortcut through the bulk, thereby arriving at your destination sooner than if you had travelled along your four-dimensional surface, or brane (short for membrane) as it is known. .
Higher level theories abstract away from irrelevant variation in lower level features and thereby arrive at generalizations that are explanatory precisely because they do not include features irrelevant to the phenomenon to be explained (Putnam 1975, Strevens 2008).
This anomalous flow seems to be caused by the elastic component (N1 and N2) of the fluids and may be responsible for flow problems in polymer processing, the detection of which may be carried out by plotting N1/σ12 vs shear stress and thereby arriving at two almost linear functions.
We are now able to distinguish the enduring thing-substance, on the one side, from its variable manifestations from different points of view and on different occasions, on the other, and we thereby arrive at a new fundamental distinction between appearance and reality.
Director Lee Daniels does a good job of juxtaposing the violence with scenes of family life and, thereby, arriving at balance.
Many of us have been studying our entire lives how to conceal, repress, and close off, thereby arriving at a level of mastery in disguising our true self.
It's nowhere as simple as, say, comparing the $650,000 you received when you sold your home with the $700,000 you paid for it in 1996, thereby arriving at a loss of $50,000.
