Todo

WICHTIG!! bestimmt die Hälfte der Note!!

• Aufsatz (@2025-05-07@23:59)

WICHTIG!! bestimmt die andere Hälfte der Note!!

• Quiz 2 (@2025-05-15)
• Quiz 1 (@2025-05-29)

Aufsatz

• task
• draft
• final version / PDF

Vorlesung

#timestamp 2025-04-17

Synthesis
Starting with the simple, and then slowly derive what you want, until you reach the result (the most complex part)

-> difficult to follow, since the results probably weren't derived in this order
-> classical way of thinking, comes hand in hand with Geometry

Analytics
Start with what you want (complex), and then try to derive it.

-> normally the way we are thinking about problems
-> modern, "easier" way, often uses Algebra

#timestamp 2025-05-08

proposition 11

!!!!!
choose variables QR and QT

using parallels and similiar triangles

Newton wants to get inverse force formula, by using the following chain:

Similiar triangles:

• Pxv, PEC
• QTx, PEF
• SCE, SHI -> HI and CI are parallel to the tangent

-> problematic: GP (becuase if P changes, GP also changes), and also PE, but he shows that PE is constant (?how)

parallelogram $GP\times DK$ is like $2AC\times 2BC$ (?)

CA^2 to PF2^ or (by Lem. XII) as CD^2 to CB^2

the same otherwise - not needed for quiz

proposition 14
lineola $:=$ ininitesimally small line

proposition 15
The minor axis is the geometric mean between the major axis and the latus rectum. So, the area formed by multiplying the major and minor axes is proportional to a combination of the square root of the latus rectum and the 3/2 power of the major axis. But, from an earlier result (Corollary to Proposition XIV), this same area is also proportional to a combination of the square root of the latus rectum and the orbital period. If we remove the square root of the latus rectum from both sides, we’re left with this: the 3/2 power of the major axis equals the orbital period.

#timestamp 2025-05-15

https://www.sciencehike.com/Newton-Principia

#timestamp 2025-05-22

• reason - norms, should
• power - action, is

-> law

• designed by reason, enforced by power
• emergent regularity from acts of power

-> emergent worldview with mechanical pyhsics (?)

• cartesian model: God intervenes always, but he intervenes as the laws he "defined"
• newton's view: God may intervene aoccasionaly to "rewind" machine, but the world, the machine is built according to the laws it should follow

-> school of thinking, slightly after Newton

• look at reason, not power (what is the reason for the behaviour, what could be the law and what is the best law)?
  • this is still partly presented in physics: trajectories follow the path of least resistance, the "best" path

-> of course, all this reflected the change of the political meaning of law -> there is not a ruler that enforces the law, but the people follow a trajectory, and are pushed in a way to follow the laws

-> the "laws of nature" appear first in the 1660s,

-> protestant concept of providence ()

• is not understandable on our level, but together with the laws (of nature) fulfills

free will: one could look at fate/necessity as something deterministic, which simplifies (maybe?) the question of free will

Look at a ball. It will always fall back to the ground. One could pick it up, throw it (free will), but sooner as later the ball will fall back to the ground (necessity/fate), regardless of what one does to it.