*OPUSCULA
ANALYTICA** ** *

*Translated
and annotated by*

Ian Bruce

*Introduction.*

This was the last book published by Euler in his lifetime
in 1783, and consists of a number of papers presented to the St. Petersburg
Academy of Sciences. A general summary of this work can be found in Ronald S.
Calinger's Leonhard Euler, pp. 529-30. It should be observed that such works
were not written to educate aspiring mathematicians, as were his calculus and
analytical books, but rather took the form of what we would now call research papers.

Click here for
the 1^{st} Chapter :* On series in which the products from
two contiguous terms constitute a given progression**.*

This
is rather a long paper, in which two methods are introduced for finding the
general term of a special kind of series of the form *a, ab, bc, cd, de, etc. *, where the series or rather sequence has
the terms designated by A, B, C, D, etc., where the first term *a* may not be known initially. This gives
rise to solutions in terms of infinite products that may be solved either by
integrals [E223] , or by continued fractions , originally investigated in E122.
Most of the work consists of setting up products of quadratic equations of
various kinds which can be recast as continued fractions, using the comparison
of coefficients to show how this is done in these cases.

Ian
Bruce. May. 16th ,
2017 latest revision. Copyright : I reserve the right to publish this translated
work in book form. You are not given permission to sell all or part of this
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