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Updated: May 19, 2025
Not till the special ends of all creatures are regarded as elements of one great End of creation, of Universal Order, do we obtain an idea whose equivalence to the idea of the Good requires no proof. The special ends are good, because, through their realization, the end of creation, which is the absolute Good, is realized; hence they acquire the sacred character that it has in the eye of reason.
For instance, it has been experimentally determined that a certain amount of fuel expended in heat is equivalent to a certain amount of mechanical force, not mechanical work, as M. Carnot puts it. For force is not expended in work until it is actually generated, and the amount generated, not that expended in work, is the real equivalence of the heat produced from fuel.
In the case of Italy the decimal system pervaded all the earliest arrangements: it may be sufficient to recall the number ten so usual in the case of witnesses, securities, envoys, and magistrates, the legal equivalence of one ox and ten sheep, the partition of the canton into ten curies and the pervading application generally of the decurial system, the -limitatio-, the tenth in offerings and in agriculture, decimation, and the praenomen -Decimus-. Among the applications of this most ancient decimal system in the sphere of measuring and of writing, the remarkable Italian ciphers claim a primary place.
Here was one, who had a matter to present to his readers, to himself at least, in the first instance, so valuable, so real and definite, that his primary aim, as regards form or expression in his verse, would be but its exact equivalence to those data within.
Fortunately there is an increasing number of lecturers whose matter is so real, so definite, and so valuable, that in an attempt to give it an exact equivalence in words, they utilize the most direct forms of expression.
Numerous attempts have been made to construct electromagnetic engines, in the hope of superseding steam; but had those who supplied the money understood the general law of the correlation and equivalence of forces, they might have had better balances at their bankers. Daily are men induced to aid in carrying out inventions which a mere tyro in science could show to be futile.
It can be constructed from base to summit by the application of his formula. As in the imaginary state of deer and beaver, we have a number of independent persons making their bargains upon this principle of the equivalence of labour; and that principle is supposed to be carried out so that the most remote processes of the industrial machinery can be analysed into results of this principle.
This occurs when the proposition ostensibly inferred from another, appears on analysis to be merely a repetition of the same, or part of the same, assertion, which was contained in the first. All the cases mentioned in books of Logic as examples of equipollency or equivalence of propositions, are of this nature.
Equality among men is produced by the rigorous and inflexible law of labor, the proportionality of values, the sincerity of exchanges, and the equivalence of functions, in short, by the mathematical solution of all antagonisms.
The sequence of the sections of the body in order of time seems originally to have been, that first the fore-body, then the hind-body, and finally the middle-body was formed. This is a circumstance which renders very doubtful the equivalence of the middle-body of the Malacostraca with the section of the body which in the Copepoda bears the swimming feet and in the Cirripedia the cirri.
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