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Some definitions and mathematical relations
§ 4. a. We want to say, that a rotation in a plane corresponds to a certain direction of the perpendicular, and namely it shall be the direction into that side, at which an observer must be located, so that for him the rotation is counter-clockwise.

b. The mutually perpendicular coordinate axes OX, OY, OZ are chosen by us, so that the direction of OZ corresponds to a rotation around a right angle of OX to OY.

c. A space, a surface and a line we denote by the letters $$\tau$$, $$\sigma$$ and $$s$$ throughout, and infinitely small parts by $$d\ \tau$$, $$d\ \sigma$$ and $$d\ s$$.

The perpendicular to a surface will by sketched by n, and is always drawn into a certain side, the "positive" one. As regards the line, a certain direction will be called "positive", and namely we note, when we are dealing with the border line s of a surface $$\sigma$$, the following rule: If P is a fixed point of $$\sigma$$, very near to s, and if a second point Q traverses the nearest part of s in positive direction, then the rotation of PQ shall correspond to the direction of the perpendicular to $$\sigma$$.

As regards a closed surface, the outer side shall be positive.

d. Usually we denote vectors by German letters; these sometimes also serve to denote the magnitude only. By $$\mathfrak{A}_l$$ we understand the component of the vector $$\mathfrak{A}$$ into the direction l; by $$\mathfrak{A}_x, \mathfrak{A}_y, \mathfrak{A}_z$$ therefore the components into the axis-directions.