There are no degrees of being, a gradual difference of only states or relations being thinkable. Accordingly, if an agent strives to preserve or to r… - Bernhard Riemann

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.

Mind-masses, once formed, are imperishable, their combinations are indissoluble; only the relative strength of these combinations is altered by the incoming of new mind masses.

The word hypothesis has now a somewhat different significance from that given it by Newton. We are now accustomed to understand by hypothesis all thoughts connected with the phenomena.
Newton was far from the crude thought that explanation of phenomena could be attained by abstraction.