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Titlebook: Cauchy‘s Calcul Infinitésimal; An Annotated English Dennis M. Cates Book 2019 Springer Nature Switzerland AG 2019 Cauchy.Calculus.Infinites

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Otto Sterns gesammelte Briefe – Band 1o the study that we have made to this subject. Let . always be the independent variable and . an infinitely small increment attributed to this variable. If we denote by . . several functions of .,  and by . . the simultaneous increments that they receive while we allow . to grow by . the differentia
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Brigitte Lengersdorf,Mandy Strzodkatter variables; and, if we designate by . . . . the arbitrary simultaneous increments attributed to . the corresponding increments . of the functions . will be related among themselves by the formula .Moreover, let .be the partial derivatives of the function . taken successively with respect to . .,
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Brigitte Lengersdorf,Mandy Strzodkaiginal value of the function multiplied by a power of this ratio. The exponent of this power is the .. By consequence, . will be a homogeneous function of . and of degree .,  if, . denoting a new variable, we have regardless of ., . ..
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Margret Liehn,Jens Köpcke,Leonid Kasakoverent variables with the help of the formulas in (.). After this elimination, the variables which remain, to number . should be considered as independent; and, the systems of values of these variables should be sought which render the function . or the function . discontinuous, as well as those whic
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,Osteochondrale Läsion des Talus,e make, as in the eighth lecture, .then, differentiate the two members of equation (.) with respect to the variable . we will find.If, in this last formula, we set . we will obtain the following .which is in accordance with equation (16) of the eighth lecture.
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,Osteochondrale Läsion des Talus,rivatives, up to that of order .,  are continuous in the vicinity of the particular value in question, and that the continuity remains valid for each of them between the two limits . Equation (.) of the seventh lecture will become ..
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