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Auguste Comte

The Philosophy of Mathematics

Although Mathematical Science is the most ancient and the most perfect of all, yet the general idea which we ought to form of it has not yet been clearly determined. Its definition and its principal divisions have remained till now vague and uncertain. Indeed the plural name — “The Mathematics” — by which we commonly designate it, would alone suffice to indicate the want of unity in the common conception of it.In truth, it was not till the commencement of the last century that the different fundamental conceptions which constitute this great science were each of them sufficiently developed to permit the true spirit of the whole to manifest itself with clearness. Since that epoch the attention of geometers has been too exclusively absorbed by the special perfecting of the different branches, and by the application which they have made of them to the most important laws of the universe, to allow them to give due attention to the general system of the science.
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  • Michel Isidroje citiraoпре 5 година
    since they are not established by any reasoning, must be founded on observation alone, and which form the necessary basis of all the deductions.
  • Michel Isidroje citiraoпре 5 година
    Thus the calculus of Taylor never has offered, and never can offer, in any question of geometry or of mechanics, that powerful general aid which we have seen to result necessarily from the analysis of Leibnitz
  • Michel Isidroje citiraoпре 6 година
    Clairaut, who first had occasion to remark their existence, saw in them a paradox of the integral calculus, since these solutions have the peculiarity of satisfying the differential equations without being comprised in the corresponding general integrals.

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