IntroductionIn 1994, together with Jose Luis Mancha, we published an article on a medieval table for the unequal of the planets, i.e., planetary velocity. In some manuscripts this table had a column headed Dieta lunae in circulo signorum, that is, Daily of the Moon on the zodiacal circle. In contrast to the other columns, the entries in this column made no sense astronomically, for here the lunar motion is 13;53°, which does not correspond to any physical of the Moon.1 In 2003 we published the same table of planetary velocities, based on many manuscripts and printed editions in addition to those we had identified when we wrote the article of 1994, but we still did not understand the rationale for this particular column of numbers.2 In 2012, however, we were finally able to identify the astrological context for this column of numbers without understanding all the details, but we did determine many of its key features and its astrological purpose.3 We can now add that the entries in the column of numbers for lunar progress are unrelated to the Moon, that they make no sense without embedding them in their astrological context, and that they do not belong at all in an astronomical table for planetary velocities. In general, the entries in the relevant astrological tables containing this column for the daily progress are unreliable due to many copyists' errors, suggesting that medieval astrologers did not fully understand these tables or the way they are to be used. As we will see, the structure of these tables is simple enough: there is a base entry and subsequent entries are integer multiples of it. Although these tables are astrological, they also are included in some early editions of astronomical texts, notably the Parisian Alfonsine Tables.In Section 1 we begin with a reconstruction of these tables and their arithmetic structure, and in the following sections we consider the evidence from ancient, medieval, and early modern texts. We will not be concerned with the rules for making astrological judgements that take into account the numerical data. While we consider Arabic sources as background, we focus on the tradition in the West, based on the thirteenth-century versions in Castilian and Latin of Kitab al-baric, composed in Arabic by cAli Ibn Abi 1-Rijal (Kairouan, eleventh century). We will also refer to a Hebrew version of these tables by Abraham Bar Hiyya produced in Spain in the twelfth century, presumably derived from an Arabic source that has not been identified. In Section 2 we present Ptolemy's version of the relevant astrological doctrine. In Section 3 we discuss the tables and their traditions, paying close attention to early printed editions of astronomical and astrological texts in Latin as well as to a few manuscripts in Arabic and Hebrew (including one text in Hebrew characters, where the language is Judeo-Portuguese). In Section 4 we adduce non-tabular evidence for what we call the astrological month, including a quotation from Bar Hiyya's procedure for using these tables, for it is the clearest such description we have found. In Section 5 we distinguish this astrological doctrine from another astrological context, in which a few of the same key terms are found. Finally, we offer some conclusions, based on the evidence in the previous Sections. The Tables are displayed in the Appendix.1. ReconstructionThe astrological context for these tables has to do with anniversaries and judgements based on them. The radix is the date and time of a nativity, and we will call any subsequent date and time the anniversary, not necessarily an integer number of years after nativity. Judgements related to the anniversary concern the prediction of success or failure of individual enterprises, whereas the horoscope for the radix deals with more general issues in the life of an individual. For the radix the astrologer cast a horoscope; in particular, five items are needed at the radix, called hylegs:4 the position of the ascendant (the point on the ecliptic that is rising on the horizon at the radix), the position of the Sun, the position of the Moon, the lot of fortune,5 and the midheaven (the point on the ecliptic that is crossing the meridian above the horizon at the radix). …
Read full abstract