I have to shake my head sometimes but no further comment is necessary about that pair however Paul should know better as he had so much trouble previously with images showing Venus to the left and right of the Sun as an evening and morning appearance.

https://www.youtube.com/watch?v=FtV0PV9MF88

That video comment was useful as it begins by pointing out that the only websites relating to direct/retrogrades of Venus and Mercury are astrological websites but failed to mention that there are any amount of websites like APOD showing the resolution for the slower moving planets. This is where the actual loops or direct/retrogrades of Venus and Mercury come in.

https://www.universetoday.com/wp-con...Dec27-2013.jpg

That image contains far more information than usual but the added dimension are the background stars, the central Sun and how those stars transition from left to right or from an evening to morning appearance due solely to the orbital motion of the Earth.

There is no theorem/theory, it is not like solving a crossword puzzle, a sudoko puzzle or an algebra puzzle - it is using normal judgments of motion by ignoring the daily rotational element of the Earth's motion and focusing on long term orbital motions of the planets, including our home planet, with the Sun at the centre of these motions.

I wouldn't care to deal with people who can be bullied into silence as the nuisance is just that - a nuisance, nothing more or less.