For instance, having found that (x+a)2=x2+2axda2, we can deduce that (x+b+c) 2 = }xd(b+c)}2=x2+2(b+c)x+ (b+c)2.
His principal discovery is concerned with equations, which he showed to be derived from the continued multiplication of as many simple factors as the highest power of the unknown, and he was thus enabled to deduce relations between the coefficients and various functions of the roots.
In both classes, accepted tradition (written or oral) was reinterpreted in order to justify or to deduce new teaching (in its widest sense), to connect the present with a hallowed past, and to be a guide for the future; and the prevalence of this process, the innumerable different examples of its working, and the particular application of the term Midrash to an important section of Rabbinical literature complicates both the study of the subject and any attempt to treat it concisely.'
Before we deduce results from such abstract ideas as cause, substance, matter, we must ask what in reality do these mean - what is the actual content of consciousness which corresponds to these words?
Hence if the readings of the verniers on the azimuth circle are made when the transit is observed we can deduce the reading corresponding to the geographical meridian.
By the vibration experiment we obtain the value of the product of the magnetic moment (M) of the magnet into the horizontal component (H), while by the deflexion experiment we can deduce the value of the ratio of M to H, and hence the two combined give both M and H.
The conceptions of osmotic pressure and ideal semi-permeable membranes enable us to deduce other thermodynamic relations between the different properties of solutions.
It is not possible to deduce a more satisfactory value from the latent heat and the change of density, because these constants are very difficult to determine.
It is likely that man began with particular inference and with particular language; and that, gradually generalizing thought and language, he learnt at last to think and say " all," to infer universally, to induce and deduce, to reason, in short, and raise himself above other animals.
All M is P. Proceeding from one order to the other, by converting one of the premises, and substituting the conclusion as premise for the other premise, so as to deduce the latter as conclusion, is what he calls circular inference; and he remarked that the process is fallacious unless it contains propositions which are convertible, as in mathematical equations.
For example, as he says, the sphericity of the moon is the real ground of the fact of its light waxing; but we can deduce either from the other, as follows: - i.
Deduction is analysis when it is regressive from consequence to real ground, as when we start from the proposition that the angles of a triangle are equal to two right angles and deduce analytically that therefore (i) they are equal to equal angles made by a straight line standing on another straight line, and (2) such equal angles are two right angles.
Deduction is synthesis when it is progressive from real ground to consequence, as when we start from these two results of analysis as principles and deduce synthetically the proposition that therefore the angles of a triangle are equal to two right angles, in the order familiar to the student of Euclid.
The result is that both Sigwart and Wundt transform the inductive process of adducing particular examples to induce a universal law into a deductive process of presupposing a universal law as a ground to deduce particular consequences.
Locke, however, fails to " deduce " his categories.
The more logical method of procedure is to determine the specific heat independently of the total heat, and then to deduce the variations of total heat by equation (52).
But what could you have seen in the 1950s from which you could deduce the Internet?
Instead of first defining the conceptions of freedom and inevitability in themselves, and then ranging the phenomena of life under those definitions, history should deduce a definition of the conception of freedom and inevitability themselves from the immense quantity of phenomena of which it is cognizant and that always appear dependent on these two elements.