Euler was the master in analysisng anything. This can be seen in his words in the preface of his book "Mmathematica" (translated by Ian Bruce), where he speaks on the text of Hermann "Phoronomiam":(adsbygoogle = window.adsbygoogle || []).push({});

Euler has given many insightful words on analysisng things in his preface of many other books, another piece of statements of interest would be of his statements in the preface of "Introduction to Analysis of the infinite" (English translated verstion of Blanton). "..Besides, and what distracts the reader the most, is the fact that everything is carried out synthetically, with the demonstrations presented in the manner of the old geometry, and the analysis hidden, and recoginiton of which is given only at the end of work..."

All the above indicates his personlaity of not leaving anything unresolved, consider the following passage from his book "Foundations of Differential Calculus" (English vesion of Blanton translation):

As I am beginner in understanding there differentials, I don't understand him. At one place, he says differentials to be "vanishing" increments or "nothing" quantities, and in the other place he says it to be "infinitely small". "....ratios might be more easily gathered together and represented in calculations, the vanishing increments themselves, although they are really nothing, are still usually represented by certain symbols. Along with these symbols, there is no reason not to give them a certain name. They are called differentials, and since they are without quantity, they are also said to be infinitely small. Hence, by their nature they are to be so interpreted as absolutely nothing, or they are considered to be equal to nothing..."

Is there any other fragment of statements where Euler has analysed the concept of "differentials" properly, or is there any different meaning that can be given to the above statements to understand them?

I am still reading this book, so I don't know whether he has analysed later on, if it is the case, I will report, but until then, I want to know whether anyone has idea on his stand on this concept; papers or books on this matter by Euler or any other person would be really helpful.

I think differentials to be closely related to infinitesimals, so I want know Eulers analysis on both of them (if they are different).

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# What is the Euler's stand on infinitesimals?

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