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Updated: May 8, 2025
Hence too, as Proclus well observes, it is evident that the soul does not collect her knowledge from sensibles, nor from things partial and divisible discover the whole and the one.
They are markedly divisible in character into three portions the north where is the Wilderness and Maze; the south where are the Privy and Pond Gardens, the Great Vine House and Queen Mary's Bower; and the east or Great Fountain Garden with its rich herbaceous border along the Broad Walk, its level lawns set with great jewels of floral colour, its compact yews, its radiating walks, its water-lily pond, and beyond the gleaming stretch of the Long Canal and the tall trees that border the Park.
He starts by assuming that, as all words are reducible to nouns as a first principle, so the whole of the nouns can be classified into forty "genera." These genera are each divisible into "differences," and the differences are sub-divisible into "species."
It is not necessary to believe that the duration that we actually experience as a second must itself be capable of being divided up into the number of parts indicated by the denominator of the fraction that we use in indicating such a time, and that each of these parts must be perceived as duration. There is, then, a sense in which we may affirm that time is infinitely divisible.
Namely, the number of elements in any set must contain no factors; that is, must be divisible by no numbers which are contained in the total number of elements. The following table is, therefore, calculated by Mr. Barth showing how many operations may be observed together in various cases.
The gemmules, by the hypothesis of Pangenesis, are the ultimate organized components of the body, the absolute organic atoms of which each body is composed; how then can they be divisible? If it is divisible into still smaller organic wholes, as a germ-cell is, it must be made up as the germ-cell is, of subordinate component atoms, which are then the true gemmules.
Voltaire's Visit lasted, in all, about Thirty-two Months; and is divisible into Three Acts or Stages.
The answer to this question is attempted by the theory of atoms: the doctrine which teaches that the whole material world is composed of simple particles which are no farther divisible, and from whose juxtaposition the chemical elements and, in respect to their other forms of existence and combination, the whole world of bodies, with all their forms, states, and changes, are composed.
What limit shall he set to the possible subdivision of real things? Unless he can find an ultimate reality which cannot in its turn become the appearance or sign of a further reality, it seems absurd to speak of a limit at all. We may, then, say that real space is infinitely divisible.
This foundation being laid, all the romance of the Epicurean philosophy disappears and vanishes out of sight in an instant. There never can be any divisible body truly infinite in extent, nor any number or any succession that is a true infinite. From hence it follows that there never can be an infinite successive number of combinations of atoms.
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