Deb wrote:I'm not sure why you say that because that kind of mathematical approach appears to be much older - this is why Babylonian mathematical expertise was so highly regarded.

I'm not an expert of ancient astronomy or mathematics at all, so I inferred the arguments from Alexander Jones. He says Apollinarius and Ptolemy, the "moderns" as labelled by Porphyry used geometrical solutions that are fairly recent compared to Babylonian arithmetical methods. In fact, it's told that the first author who discussed spheric geometry was Menelaus of Alexandria who flourished around 100 CE.

Deb wrote:Why not? The oldest surviving reference dates to the 1st century BC, but it is clear that the astronomer/astrologers of that time were using the techniques of older sources.

Look, Deb, I know there are different opinions on the origins of astrology, even regarding how we should separate astrology per se from the science of celestial omens. That's why I articulated it in a personal tone; I know only sources not earlier than 1st century CE. So I'm really curious what you mean by 1st century BCE reference.
But putting aside this, I think an astronomer dealing with advanced ascension times (not with those inherited from Babylonian sources) must have lived later than Hipparchus who worked around mid-2nd century BCE. This definitely excludes an earlier date.

first author who discussed spheric geometry was Menelaus of Alexandria who flourished around 100 CE.

It is this kind of comment that puzzles me and I wonder what it is specifically suggesting, since Pythagoras is known for his influence on spherical geometry, and Euclid?s repute was built on it. The Encyclopedia Brittanica vol 11 includes a mathematical treatise by Apollonius of Perga. In his biography there it is said he went by the name of ?the great geometer? and that he worked on problems of a trigonometrical nature. A couple of online links demonstrate his mathematical accomplishments:
http://fabpedigree.com/james/mathmen.htm#Apollo
http://www.bookrags.com/biography/apoll ... perga-wom/

So since Apollonia of Perga is one of the names, along with Hipparchus, who is immortalised as being an important source for Ptolemy's idea, I just think it?s wise to retain him as a possible candidate for your man, even though its also a good idea to assume he might be someone else altogether.

I know only sources not earlier than 1st century CE. So I'm really curious what you mean by 1st century BCE reference.

Sorry, that was a typo mistake and I did mean 1st century, not 1st century BC. This is what I have myself in a footnote about the earliest references:

The earliest documentary Greek horoscope mentioning the terms is P. Oxy. II 307 (46AD; Greek Horoscopes #46). The earliest reference in a literary Greek horoscope is found in the writings of Antigonus of Nicaea (c.150), who mentions all the terms in a chart dated to 40 AD. Various authors have suggested that they derive from the techniques of Nechepso and Petosiris, which seems likely but remains unproven.

Unfortunately we run dry of example charts and detailed surviving texts from before this period. However when the terms do become evidenced they are described as being part of an ancient system which suggests that they could have been older. Having references from the 1st century does not mean that the system was put together in the 1st century; it only proves that the system was definitely put together and used in something which has managed to survive, by the 1st century (or sometime before then). Hence I keep an open mind about when the development of the system began.

Best wishes with your research,
Deb

Deb wrote:It is this kind of comment that puzzles me and I wonder what it is specifically suggesting, since Pythagoras is known for his influence on spherical geometry, and Euclid?s repute was built on it.

I think you mean geometry, not trigonometrical theorems needed to solve problems in spherical geometry. But once again, I confess I'm rather poor at history of maths. So let me quote Jones (Ptolemy's first commentator, pp. 14-15):

If ours is the Apollinarius who wrote an astrological work cited by Porphyry and Paul of Alexandria, his career probably falls in the first or early second century of our era. Both Paul and Porphyry write that Apollinarius, like Ptolemy, used geometrically derived values for the ascensional arcs of the equator that rise simultaneously with the zodiacal signs. Porphyry groups Apollinarius and Ptolemy together as "moderns" (neoteroi) in this respect, as opposed to the "ancients" such as Thrasyllus (died A.D. 36?) and the apocryphal Egyptian Petosiris who used Babylonian-style arithmetical methods to obtain the ascensional arcs; and indeed the theorems in spherical geometry necessary to compute the ascensional arcs correctly first appear in the Spherics of Menelaus (ca. A.D. 100).

Deb wrote:So since Apollonia of Perga is one of the names, along with Hipparchus, who is immortalised as being an important source for Ptolemy's idea, I just think it?s wise to retain him as a possible candidate for your man, even though its also a good idea to assume he might be someone else altogether.

Believe me, Deb, I'd love to do that but I'm afraid I can't do it in this case.

Deb wrote:However when the terms do become evidenced they are described as being part of an ancient system which suggests that they could have been older. Having references from the 1st century does not mean that the system was put together in the 1st century; it only proves that the system was definitely put together and used in something which has managed to survive, by the 1st century (or sometime before then).

Of course I don't believe that astrological techniques like terms were developed in the 1st century CE! Since early astrologers, such as Thrasyllus or Critodemus used them, they must have been developed earlier. Given the fact that there was a considerable disagreement which system of terms should be used and there were also some suggestions based on different "rational" approach I would say they were developed earlier in the 1st century BCE. However, a longer gap without any sources doesn't seem to be acceptable to me.

Thanks a lot,
Levente

I don?t have a copy of that work by Jones here to check the context of his comment; but it does seems strange to me that Ptolemy himself ascribes the mathematics of his system to Apollonius of Perga, who is said to have been born around 262 BC. And this makes so much sense because Euclid, Apollonius of Perga and Ptolemy were all important mathematical scholars who lived in Alexandria. This Apollonius, who studied under Euclid, definitely did influence Ptolemy - so who is the other one ? I don?t know. I think it is going to be very difficult to disentangle the two.

BTW, there is a new book edited by Alexander Jones called ?Ptolemy in Perspective? in which you will be interested in the paper that Stephan Heilen wrote called ?Ptolemy?s Doctrine of the Terms and its Reception?. It?s a thorough examination, and very informative , although in my opinion not quite perfect I think that Stephan Heilen?s historical research work is excellent, but it?s a little frustrating that he tends to assume that ancient astrologers were all inclined towards falsification. So part of his theory is that Ptolemy simply made up the account of the old document containing the set of terms he recorded in the Tetrabiblos ? a view I have heard expressed by various sources, but which I don?t agree with at all. In his paper Heilen suggests that I appear to be unaware of this theory, but that?s not the case ? I just don?t believe the arguments stack up enough to be taken seriously (ironically, this is the view that many academics have about astrology ...).

You can read Heilen?s paper on Google books on this link:

http://books.google.co.uk/books?id=Y61q ... en&f=false

Deb

PS - for what its worth, I'll plan to post my paper online when I next update the site.

This is the gorgeous link for Alexander Jones' book:
http://books.google.hu/books?id=Z7AOdKb ... &q&f=false

Thanks for the reference on the Heilen article, I've already checked it. I was delighted to see your work had also been mentioned; I remember we had some discussion about the Ptolemaic terms some years ago.
Unfortunately there are many instances where different judgments can be erected on the very same sources. It's probable that there'll never be a definitive answer whether Ptolemy's old manuscript was a real aged parchment or this story is only a rhetorical tool to give weight to his own device. There may be arguments for one or the other side but it always remains subjective to decide which is weighty enough and which is to be dismissed. That's why reality as it was and reality as sources make us see it is always different. We may say that no matter Ptolemy's papyrus had existed or not, the Egyptian system was overwhelmingly the term table used; but only the sources make us say this, while we can't know what huge amount of different sources which would lead us to another direction were lost during the centuries. I think we ought to accept this fact and try not to bias sources too much.

Deb wrote:PS - for what its worth, I'll plan to post my paper online when I next update the site.

Yeah!

Levente

Do you know Levente, I completely agree with you

Just letting you know that my article on Ptolemy's terms is now online, and available for download on this page:

http://www.skyscript.co.uk/terms.html

At some stage I do want to revisit this topic, or publish it in a more formal format, so I won't be keeping this as a long-term download. (so anyone interested please download now).

Cheers
Deb