Geometry and integral laws of physics Reading the English translation of Einstein's seminal paper on GR.
http://einsteinpapers.press.princeton.edu/vol6-trans/90?ajax
This paragraph below on p78 doesn't make much sense to me.
Could you provide a second English translation or even adding math notation.

"Before Maxwell, the laws of nature with respect to their space dependence were in principle integral laws; this is to say that in elementary laws the distances between finitely distinct points did occur. Euclidean geometry is the basis for this description of nature. This geometry means originally only the essence of conclusions from geometric axioms; in this regard it has no physical content. But geometry becomes a physical science by adding the statement that two points of a "rigid" body shall have a distinct distance from each other that is independent of the position of the body. After this amendment, the theorems of this amended geometry are (in a physical sense) either factually true or not true. It is geometry in this extended sense which forms the basis of physics. Seen from this aspect, the theorems of geometry are to be looked as integral laws of physics insofar as they deal with distance of points at a finite range."

Specifically I do not get the points here
integral laws; this is to say that in elementary laws the distances between finitely distinct points did occur.
For example?
This geometry means originally only the essence of conclusions from geometric axioms; in this regard it has no physical content
For example?
Seen from this aspect, the theorems of geometry are to be looked as integral laws of physics
What is the definition of an integral law?
 A: Integral laws: should be understood in opposition to differential laws.
You can see the laws of nature as differential laws, that make no reference to finite properties such as the distance $r$ but rather to differential properties such as $dr$. For example, you could say that the divergence of the electric field is equal to the charge density at each point.
Or you can see the laws of nature as "integral" laws, in the sense that they are not differential i.e. they refer to things like distance "r". For example that the electric force on a charge is proportional to the inverse of the distance from the charge exerting the force.
The "integral" laws have "finite" properties, in the sense that they are not inffinitesima ($r$ instead of $dr$).
Geometry: Geometry can be seen as abstract math, in which case it is just a deduction from mathematical axioms. In this case it has no physical meaning, it has no bearing on the natural world but rather is just a mathematical game.
If, however, you maintain some link to physical reality - e.g. identifying mathematical angels with measured angels - then you are now considering a physical theory, namely that reality conforms to some theory of geometry.
For example, the statement that "a straight line continues infinitely in both directions" is true mathematically, as an abstract object. But need not be valid in the real world, which might not contain anything perfectly conforming to the mathematical concept of a "straight line".
Definition of integral law: In this section, he apparently means to say that the law of nature involves finite (non-infinitesimal) elements, which can be seen as "integrals" of infinitesimal elements.
A: I could be wrong because I don't have the full text. But based on other readings of Einstein he was always very clear on what is mathematics, in this case geometry, and what is physics, i.e. real things. 
I'd think that by integral laws he means that things need to be integrated to connect effects at two finitely different points. I.e., that physics will be local and to get the effect at a distance you integrate the infinitesimally different effects at two infinitesimally close points. I.e., no action at a distance. But more than that
More on the difference between math, a form of logic, and physics. Geometry (one of the mathematics fields) can describe two point apart, but it is just a construct. You need to put some physics into it to have it mean more than just math. For the rigid body, i.e., any two points at a distance from each other will maintain that distance. That is physics, a lot of physics has to go into making the distance remain rigid, intermolecular forces, etc. and that those forces or effects or whatever you want to call them to describe the physics is really local and acts on only infinitesimally close points. To get further away, to another distant point, integrate all those effects. 
I do not see anything in there about special relativity, or general relativity through geometry, it is a much more basic observation, one of local causality, and that without that you're just doing math. 
