When Johann Bernoulli published his lectures on integrals in 1742, integral calculus had become very advanced since the time of their composition in 1692. Nevertheless, these lectures are of excellent clarity and simplicity even when the book deals with major problems of Mathematical Physics. Just to pique some interest, we offer a commented translation of the first lecture and some general information about the whole treatise. In his introductory lecture, Johann Bernoulli develops many examples of how the integration of polynomials could lead to the integration of radicals and then provides some relevant changes of variables. When studying the integration of the integrable combinations appear for the first time; several developments will stem from them in the future.

Johann Bernoulli's first lecture from the first integral calculus textbook ever written: an annotated translation

Giovanni Mingari Scarpello;Daniele Ritelli
Investigation
2019

Abstract

When Johann Bernoulli published his lectures on integrals in 1742, integral calculus had become very advanced since the time of their composition in 1692. Nevertheless, these lectures are of excellent clarity and simplicity even when the book deals with major problems of Mathematical Physics. Just to pique some interest, we offer a commented translation of the first lecture and some general information about the whole treatise. In his introductory lecture, Johann Bernoulli develops many examples of how the integration of polynomials could lead to the integration of radicals and then provides some relevant changes of variables. When studying the integration of the integrable combinations appear for the first time; several developments will stem from them in the future.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/781533
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