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## Details

Named Person: | Leonhard Euler; Leonhard Euler; Leonhard Euler; Leonhard Euler; Leonhard Euler; Leonhard Euler |
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Material Type: | Internet resource |

Document Type: | Book, Internet Resource |

All Authors / Contributors: |
Charles Edward Sandifer |

ISBN: | 0883855593 9780883855591 |

OCLC Number: | 82370957 |

Description: | xix, 391 p. : port., facsims. ; 26 cm. |

Contents: | Preface -- Interlude: 1725-1727. Construction of isochronal curves in any kind of resistant ; Method of finding reciprocal algebraic trajectories -- Interlude 1728. Solution to problems of reciprocal trajectories ; A new method of reducing innumerable differential equations of the second degree to equations of the first degree -- Interlude 1729-1731. On transcendental progressions, or those for which the general term cannot be given algebraically ; On the shortest curve on a surface that joins any two given points ; On the summation of innumerably many progressions -- Interlude 1732. General methods for summing progressions ; Observations on theorems that Fermat and others have looked at about prime numbers ; An account of the solution of isoperimetric problems in the broadest sense -- Interlude 1733. Construction of differential equations which do not admit separation of variables ; Example of the solution of a differential equation without separation of variables ; On the solution of problems of Diophantus about integer numbers ; Inferences on the forms of roots of equations and of their orders ; Solution of the differential equation axn dx = dy + y²dx -- Interlude 1734. On curves of fastest descent in a resistant medium ; Observations on harmonic progressions ; On an infinity of curves of a given kind, or a method of finding equations for an infinity of curves of a given kind ; Additions to the dissertation on infinitely many curves of a given kind ; Investigation of two curves, the abscissas of which are corresponding arcs and the sum of which is algebraic -- Interlude 1735. On sums of series of reciprocals ; A universal method for finding sums which approximate convergent series ; Finding the sum of a series from a given general term ; On the solution of equations from the motion of pulling and other equations pertaining to the method of inverse tangents ; Solution of a problem requiring the rectification of an ellipse ; Solution of a problem relating to the geometry of position -- Interlude 1736. Proof of some theorems about looking at prime numbers ; Further universal methods for summing series ; A new and easy way of finding curves enjoying properties of maximum or minimum -- Interlude 1737. On the solution of equations ; An essay on continued fractions ; Various observations about infinite series ; Solution to a geometric problem about lunes formed by circles -- Interlude 1738. On rectifiable algebraic curves and algebraic reciprocal trajectories ; On various ways of closely approximating numbers for the quadrature of the circle ; On differential equations which sometimes can be integrated ; Proofs of some theorems of arithmetic ; Solution of some problems that were posed by the celebrated Daniel Bernoulli -- Interlude 1739. On products arising from infinitely many factors ; Observations on continued fractions ; Consideration of some progressions appropriate for finding the quadrature of the circle ; An easy method for computing sines and tangents of angles both natural and artificial ; Investigation of curves which produce evolutes that are similar to themselves ; Considerations about certain series -- Interlude 1740. Solution of problems in arithmetic of finding a number, which, when divided by given numbers leaves given remainders ; On the extraction of roots of irrational quantities -- Interlude 1741. Proof of the sum of this series 1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/ 36 + etc ; Several analytic observations on combinations ; On the utility of higher mathematics. |

Series Title: | MAA tercentenary Euler celebration, v. 1.; MAA spectrum. |

Responsibility: | by C. Edward Sandifer. |

More information: |

### Abstract:

A portrait of Euler's early mathematics between 1725 and 1741, rich in technical detail.
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## Similar Items

### Related Subjects:(8)

- Euler, Leonhard, -- 1707-1783.
- Mathematics -- Switzerland -- 18th century.
- Euler, Leonhard.
- Euler, Leonhard -- Lebensabschnitte -- 1725-1741.
- Euler, Leonhard -- Mathematik -- Geschichte 1725-1741.
- Mathematik -- Euler, Leonhard -- Geschichte 1725-1741.
- Mathematics.
- Switzerland.

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by magnusvalison updated 2013-02-10