There remains only the assumption that the ponderable masses within the rigid earth-crust are supporters of the soul-life of the earth. - Bernhard Riemann

As is known, scientific physics dates its existence from the discovery of the differential calculus. Only when it was learned how to follow continuously the course of natural events, attempts, to construct by means of abstract conceptions the connection between phenomena, met with success. To do this two things are necessary: First, simple fundamental concepts with which to construct; second, some method by which to deduce, from the simple fundamental laws of the construction which relate to instants of time and points in space, laws for finite intervals and distances, which alone are accessible to observation (can be compared with experience).

IV. Thesis. Immortality. Antithesis. A thing in and by itself endowed with transcendental freedom, radical evil, intelligible character and lying at the basis of our temporal appearance.

For Space, when the position of points is expressed by rectilinear co-ordinates, <math>ds = \sqrt{ \sum (dx)^2 }</math>; Space is therefore included in this simplest case. The next case in simplicity includes those manifoldnesses in which the line-element may be expressed as the fourth root of a quartic differential expression. ...I restrict myself... to those manifoldnesses in which the line element is expressed as the square root of a quadric differential expression. ...Manifoldnesses in which, as in the Plane and in Space, the line-element may be reduced to the form <math>\sqrt{ \sum (dx)^2 }</math>, are... only a particular case of the manifoldnesses to be here investigated; they require a special name, and therefore these manifoldnesses... I will call flat. In order now to review the true varieties of all the continua which may be represented in the assumed form, it is necessary to get rid of difficulties arising from the mode of representation, which is accomplished by choosing the variables in accordance with a certain principle.