I don't know. Surely now we can measure it in more precise way.
But this is not important. When we should check if a planet is visible we tend to use a modern software, not Almagest.
Hi Margherita,
Fair point. I was just relating Kolev's point. Please take up any arguments with him!
The point is that Ptolemy would consider if a planet was free from the Sun, or retrograde or whatever with an astronomical observation, even if wrong. He did not use planetary orbs.
Absolutely I totally agree. The in mundo approach to heliacal phase is therefore a tecnique proposed by Ptolemy irrespective of the correctness his mathematical method.
I don't think it's very difficult. Myself I have a lot of formulas (but no intention to use them) but inside CieloeTerra they use them. Once upon a time, in DOS times, they had a software (impossible to run under XP, it crashes every 20 seconds) which graphically showed positions of planets in their epycles. If they did in DOS.....
I dont know if you are right here.

I am neither a mathematician or astronomer so I am do not feel competent to agree or disagree. Hopefully some other members of the forum can pick this point up. It seems odd though that a mathematician like Kolev would make the claim that all current calculation programmes fail to properly identify heliacal phase by location without some good foundation. Do you think he is just trying to promote his update to the Placidus programme?
Looking at his posts the key difference between what he is factoring in and other programmes is what he refers to ''atmospheric quality'.
Rumen Kolev states:
The quality of the atmosphere on a given place is usually stable in the course of the years as to allow that stars and planets brighter than +1 magnitude to be seen with the same parameters. I have observed this many times. So, the planets being generally brighter than +1, they appear and disappear regularly having the same parameters and the babylonians could compute this.
The extinction (thickness) of the atmosphere can be measured very easily and it stays almost the same over the years. It has some cycle of change but it is not much. If you compute the thickness of the atmosphere at a given place now, the chances are that it has been the same or very close to that value 15 or 30 years ago.
My algorithm takes in account of course the thickness (the extinction) of the atmosphere. I hope to put it in this coming version 6.0 of my program Placidus so that at last I can look at a chart and see immediately wheteher a planet is visible or not. The algorithm of Schoch does not take in account the atmospheric extinction!
It is valid very roughly and only for very transparent atmosphere with extinction of around 0.12. But Schoch does not take in account also the magnitude of the planets! All assyriologysts for the last hundred years computed with his algorithm! I wonder how could they sleep at night!
I never saw anything of Brady's knowledge in any old text.
Paranatellonta are very different from Brady's paran, they share just the name.
Well that is a little hard.

However, you are basically right that while Brady's astronomy is top notch her knowledge of traditional sources for meanings of fixed stars is not especially impressive. However, her software Starlight does allow easy calculation of in mundo stars rising or on the angles. I agree she rather misuses the word paran with Paranatellonta but that is another discussion!
Clearly there was software was around to do this before Brady produced her Starlight programme. However, she has popularised so called 'visual astrology' in an unprecedented way and given many astrologers a much better appreciation of what is in the real sky vs the hypothetical squeezing of the sky into the band of the ecliptic. I think she does deserve credit for that.
Rumen Kolev suggests the Ptolemaic or visual approach to heliacal phase was not entirely lost to medieval astrology. In particular he mentions the 16th century astrologer/mathematician Naibod:
In his book 'Enarratio Elementorum Astrologiae....", published in 1560, Naibod discusses the concept 'combustus' and writes that a planet is combust during the whole time of its invisibility. He critisizes the 'predominant' view of his time to procalim a planet 'under the beams' if it is less than a cetain fixed number of degrees distant from the Sun.
He then gives tables, much like those of Ptolemy, to compute the days of emergence (heliacal rising) and setting of the planets.
Mark