#### Title

#### English Title

Mechanics, volume 1

#### Enestrom Number

15

#### Fuss Index

441a

#### Original Language

Latin

#### English Summaries

Mechanica (this volume, along with E16) is Euler's outline of a program of studies embracing every branch of science, involving a systematic application of analysis. It laid the foundations of analytical mechanics, the result of Euler's consideration of the motion produced by forces acting on both free and constrained points. It was also the first published work in which the number e appeared. ¶ This volume focuses on the kinematics and dynamics of a point-mass, introducing infinitely small bodies that can be considered to be points under certain assumptions. Euler focuses on single mass-points except for a few pages at the end of Chapter I, where he looks at the motion of one point relative to another moving point. He then looks at the nature of rest and uniform motion. In Chapter II, Euler states Newton's second law of motion. Throughout this volume, he considers the free motion of a point-mass in a vacuum and in a resisting medium so that all forces under consideration are known. Mathematically, acceleration is given to within an arbitrary multiplicand, and in each example he considers, the arguments of the force function are limited to position and speed. Thus, Euler devotes this volume to integrating particular second-order differential equations and to interpreting his results. ¶ For about half of this volume, Euler analyzes motion along straight lines. The remainder is mainly concerned with motion in a plane, with a few pages looking at motion along a skew curve. He introduces fixed rectangular Cartesian coordinates for the position of the mass-point but uses arc length as the independent variable to set up his differential equations of motion. He also resolves the enforced acceleration into components along the tangent and normal to the path. In three dimensions, he uses two orthogonal normals, one of which he forces to be parallel to a fixed plane.

#### Published as

Quarto book

#### Published Date

1736

#### Written Date

1734

#### Archive Notes

Source: https://archive.org/details/mechanicasivemot01eule/page/n4

#### Content Summary

*Mechanica* (this volume, along with E16) is Euler's outline of a program of studies embracing every branch of science, involving a systematic application of analysis. It laid the foundations of analytical mechanics, the result of Euler's consideration of the motion produced by forces acting on both free and constrained points. It was also the first published work in which the number *e* appeared. This volume focuses on the kinematics and dynamics of a point-mass, introducing infinitely small bodies that can be considered to be points under certain assumptions. Euler focuses on single mass-points except for a few pages at the end of Chapter I, where he examines the motion of one point relative to another moving point. He then looks at the nature of rest and uniform motion. In Chapter II, Euler states Newton's second law of motion. Throughout this volume, he considers the free motion of a point-mass in a vacuum and in a resisting medium so that all forces under consideration are known. Mathematically, acceleration is given to within an arbitrary multiplicand, and in each example he considers, the arguments of the force function are limited to position and speed. Thus, Euler devotes this volume to integrating particular second-order differential equations and interpreting his results. For about half of this volume, Euler analyzes motion along straight lines. The remainder is mainly concerned with motion in a plane, with a few pages exploring motion along a skew curve. He introduces fixed, rectangular Cartesian coordinates for the position of the mass-point but uses arc length as the independent variable to set up his differential equations of motion. He also resolves the enforced acceleration into components along the tangent and normal to the path. In three dimensions, he uses two orthogonal normals, one of which he forces to be parallel to a fixed plane. (Based on Clifford Truesdell's *An idiot's fugitive essays on science: methods, criticisms, training, circumstances*.)

#### Original Source Citation

St. Petersburg: Imperial Academy of Sciences, Volume 1, pp. 1-480.

#### Opera Omnia Citation

Series 2, Volume 1, pp.1-407.

#### Record Created

2018-09-25

*Title Page and Introduction*

E015Ch1-2.pdf (1815 kB)

*Chapters 1-2*

E015Ch3.pdf (2148 kB)

*Chapter 3*

E015Ch4.pdf (2157 kB)

*Chapter 4*

E015Ch5part1.pdf (2104 kB)

*Chapter 5 (part 1)*

E015Ch5part2.pdf (1864 kB)

*Chapter 5 (part 2)*

E015Ch6part1.pdf (1484 kB)

*Chapter 6 (part 1)*

E015Ch6part2.pdf (1338 kB)

*Chapter 6 (part 2)*

E015figs.pdf (218 kB)

*Figures*

*Title Page and Introduction*

E015Ch1-2.pdf (1815 kB) *Chapters 1-2*

E015Ch3.pdf (2148 kB) *Chapter 3*

E015Ch4.pdf (2157 kB) *Chapter 4*

E015Ch5part1.pdf (2104 kB) *Chapter 5 (part 1)*

E015Ch5part2.pdf (1864 kB) *Chapter 5 (part 2)*

E015Ch6part1.pdf (1484 kB) *Chapter 6 (part 1)*

E015Ch6part2.pdf (1338 kB) *Chapter 6 (part 2)*

E015figs.pdf (218 kB) *Figures*