EULER’S THEOREM
EULER, Leonhard Institutiones Calculi differentialis cum eius usu in Analysi Finitoum ac doctina serierum. St. Petersburg Royal Academy of Sciences 1755
Rare first edition of this monument of analysis, “the first textbook on the differential calculus which has any claim to be regarded as complete” (Ball), the second installment of Euler’s trilogy summarizing his researches on the differential and integral calculus, and one of Euler’s rarest works. (The three parts were separately issued and—bibliographically distinct entities—were published over two decades, from 1748-1770.) According to Youschkevitch in the DSB, the work’s mathematically important achievements include the definition of a function as “a quantity whose values somehow change with the changes of independent variables; the elaboration of formulas of differentiation under substitution of variables; the theorem of homogeneous functions, subsequently named for Euler; and the application of Taylor’s series to finding extrema of f (x).
$US8850
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