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Updated: June 19, 2025
The propositions of Arithmetic affirm the modes of formation of given numbers, and are true of all things under the condition of being divided in a particular way. Algebraical propositions, on the other hand, affirm the equivalence of different modes of formation of numbers generally, and are true of all things under condition of being divided in any way.
The establishment of correlation and equivalence between the forces of the outer and the inner worlds serves to assimilate either to the other, according as we set out with one or the other. He who rightly interprets the doctrine propounded in "First Principles" will see that neither the forces of the outer, nor the forces of the inner, world can be taken as ultimate.
To speak of an equivalence between the two is simply to curtail, and make almost unintelligible, the Spinozistic or Leibnizian metaphysic. It is to accept this philosophy, such as it is, on the side of Extension, but to mutilate it on the side of Thought.
Let us, however, rejoice in all the good that we have. The remission of one disease will enable nature to combat the rest. The squills I have not neglected; for I have taken more than a hundred drops a day, and one day took two hundred and fifty, which, according to the popular equivalence of a drop to a grain, is more than half an ounce.
It matters little, for the present, that this series, as well as the equivalence of its elements, is expressed in practice more or less exactly by the equilibrium of wages and fortunes; our first business is with the relation of things, the economic law.
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.
It is therefore very important to study well the calorific phenomenon chosen as the unit of heat, and to determine with precision its mechanical equivalent, that is to say, the number of ergs necessary to produce this unit. This is a number which, on the principle of equivalence, depends neither on the method employed, nor the time, nor any other external circumstance.
The Ogulnian law of 454 accordingly threw these also open to plebeians, by increasing the number both of the pontifices and of the augurs from six to nine, and equally distributing the stalls in the two colleges between patricians and plebeians. Equivalence of Law and Plebiscitum
He understands thereby equivalence or the equality of values, which again is determined by the time of labour, and accordingly he makes it a presupposition of a free bargain that only products which represent equal times of labour can be exchanged. Thus a hat which took six hours to make, should be exchanged for a poem which was written in the same time.
The history of this principle is similar to that of all evolutions. It is well known that the conservation of energy was, at first, regarded from the point of view of the reciprocal transformations between heat and work, and that the principle received its first clear enunciation in the particular case of the principle of equivalence.
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