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Updated: May 24, 2025
Charles the Twelfth of Sweden had a design to have introduced a numeration by squares, instead of by decimation, which might have served the purposes of philosophy better than the present mode, which is said to be of Arabic invention. The alphabet is yet in a very imperfect state; perhaps seventeen letters could express all the simple sounds in the European languages.
The two boards are then separated and the notes remain arranged according to the treble and bass clefs. The children possess all the instinctive knowledge necessary as a preparation for clear ideas on numeration. The idea of quantity was inherent in all the material for the education of the senses: longer, shorter, darker, lighter.
The pupil has already been familiarised with such divisions in numeration, and he now proceeds to a comparison of their several parts, and of the relation of these parts to each other.... From thence he advances to globes, which furnish him with elementary notions of the circle, of curves generally, etc., etc. "Being tolerably familiar with solids, he may now substitute planes.
Money, therefore, in its original form, is a common medium of barter, that is accepted to that use by authority of law, a medium which, considered distinctly from that authority, is simply an article of merchandise possessing qualities that make it preferable as a means of barter, and which, for convenience of use, bears the stamp of the government-inspector, defining the exact quantity contained in each piece, but which, inasmuch as it is authorized, and partakes of the nature of law, has ideal qualities that make it the means of sale: these are, right of use, nomination, and numeration.
One great feature of good modern editions of classical study works, from Kreutzer to Paganini, is the double editorial numeration: one giving the sequence as in the original editions; the other numbering the studies in order of technical difficulty, so that they may be practiced progressively. "What special editorial work of mine has given me the greatest personal satisfaction in the doing?
In either of which, if it trips, the whole business of numbering will be disturbed, and there will remain only the confused idea of multitude, but the ideas necessary to distinct numeration will not be attained to. Number measures all Measurables.
If we would perfectly understand anything, we must be able to comprehend it in its threefold nature; therefore in symbolic numeration the multiplying of the unit by three implies the completeness of that for which the unit stands; and, again, the threefold repetition of a number represents its extension to infinity.
It was the evening of the sixteenth day before the calends of November, or, according to modern numeration, the eighteenth of October, the eve of the consular elections, when a considerable number of rough hardy-looking men were assembled beneath the wide low-browed arch of a blacksmith’s forge, situated near the intersection of the Cyprian Lane with the Sacred Way, and commanding a full view of the latter noble thoroughfare.
In order to think correctly it is necessary to consider the whole of numeration, computation, and all mathematical processes whatsoever as the division of the unit into its component parts and the establishment of relations between these parts. The progression and retrogression of numbers in groups expressed by the multiplication table gives rise to what may be termed "numerical conjunctions."
We ought not to call him by name, and offer him our affection, inviting him to accept our help; but, like the material objects which attract him by their smoothness, their luster, and their varied and interesting forms, and by ocular demonstration of the means of lofty intellectual exercise, as in the colored alphabets and the rods which contain the first secrets of numeration we, too, should wait; not coldly, but rather making the child feel that we contain a rich material which is at his disposal, ready to be taken as soon as he stretches out his hand to grasp it.
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