The Fluxional Calculus An Elementary Treatise

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" The truth of this proposition also appears from ch. 3, art. 13 i for if the second and the higher fluxional co- efficients do not become indeterminate, the value of ?/ in terms of . R will involve arbitrary constants, and consequently will be its complete value. (Lagrange, Calc. Des Fonctions, p. 223. ) 24. All that is known of the properties of singular solu- / tions and of the theory of arbitrary constants upon which they are founded, is due to the German and French mathe- maticians. If the... reader is desirous of further information, I must refer him to their works. The principal authors are Euler, Lagrange, Legendre, and Poisson. In his Calcul des Fonctions, Lagrange has dedicated the fourteenth and the three following chapters to this subject ; and Poisson has made some important additions in the ' Journal de I'E'cole Poly technique, 13^ cahier, p. 113. ' This branch of the subject is as important as any other ; for the problem which has given rise to the fluxional equation frequently depends upon the singular solution, and not upon the complete primitive.

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