Notes from Mathilde Scholl 1904–1906

GA 91 — 9 November 1904, Berlin

4. Sine, Cosine, Tangent, Cotangent

You can plot the angle Alpha a degree.

(BC:AC) – The ratio (BC:AC) is the ratio of the angle Alpha. The ratio is called the sin. (sine) of the angle. ((AC:AB =) cosine of Alpha)
(BC:AC = \sin(\alpha))
(AB:AC = \cos(\alpha))
(BC:AB \tan(\alpha) = tg \alpha)((BC:AB = )tangent (a))
(AB:BC \cot(\alpha)) ((AB:BC =) cotangent (a))

You can determine a crooked line in a plane by calculating the distances between it and two straight lines. This method was first used in the last few centuries, by Cartesius. This method is called analytical geometry.

(x^2 + y^2 = r^2 =) the equation of the circle.

By determining the lawfulness of the distance on a particular system of intersecting lines, you get the circle.

(0) is the center of the coordinate axis system. The ancients (Ptolemy) assumed the center of the earth, but Copernicus assumed the sun. He related everything to the Sun. However, he still took into account the fact that the Earth has its own motion in addition to its motion around the Sun, and that this motion is like the Earth's motion around the Sun. In schools, the third sentence of Copernicus is usually left out. In the Copernican system, the Earth actually moves in a helical path (Rod of Hermes).

Ptolemy's system was based on the astral plan. Copernicus's discovery meant that the relative motion of the planetary system was based on a different point of origin (the physical point of origin).

In Dante's Divine Comedy, everything is based on the astral plan; the Earth is the center.

At the angle you can see the curvature of the line. The mathematician determines the angle according to the tangent. With each new distance, the tangent becomes different, larger or smaller.

tan a is absolutely variable with respect to the curve at very small distances. Then tan a is called a differential quotient. One goes from finite quantities to infinitely small quantities. Newton also called it flexion calculus (calculus of motion). Leibniz made the discovery at the same time. It was necessary to find the infinite on the physical plane itself.

(\tan(\alpha) = \frac{x}{y}) (if (a) and (b) are variable)

Two lines going to infinity, between them an infinitely large area.

Fl. ((ab) = \infty) (infinitely large)
Fl. ((ac)= \infty =2 \infty)
(Dividing one infinity by the other gives (2))
(\frac{\infty}{\infty} = 2)

An infinite straight line is a circle. However, this is not possible in three-dimensional space because it would take an infinite amount of time. If it is not a three-dimensional but a two-dimensional space, then it is different. Then time itself is the fourth dimension. Then not only movement in that direction takes place, but also another change. Suppose you move in one direction (a ball that gets bigger and bigger). Then, when the ball has reached a certain size, it will be possible for the ball to diverge on the other side. But then there must have been forces holding it together. In the astral space, the effect as a fourth dimension is added.