"Astronomical Shoptalk in Paris, ca 1246: An Edition and Translation of John of London’s Letter to R. de Guedingue" by C. Philipp E. Nothaft
Article first published in Aestimatio (savante, fonds Érudit) Volume 2, Numéro 2, 2021
https://www.erudit.org/fr/revues/aestim ... 1095434ar/

John of London
https://en.wikipedia.org/wiki/John_of_London
"John of London (fl. 13th century), mathematician, was described by Roger Bacon as one of two "perfect" mathematicians, together with Pierre de Maricourt. Bacon probably knew John in Paris in the 1260s.
No works are certainly attributed to him, but he may be the author of an influential table of stellar co-ordinates. He may also be the "Master John of London" who designed a form of astrolabe and was described by Roger of Lincoln as "astronomus famosus" ("renowned astronomer")."

C. Philipp E. Nothaft is a research fellow at Trinity College Dublin and 50-fellow at All Souls College, Oxford. His current research focuses on the practice of mathematical astronomy in highmedieval Latin Europe.
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Abstract
A unique source on the practical aspects of the scientia astrorum (astronomy and astrology) in medieval Europe has come down to us in the shape of a letter written shortly after 1246 by John of London, an astronomer based in Paris. John used the letter to answer eight questions on technical problems posed to him by his addressee, a certain R. de Guedingue, with subject matters ranging from

1) the rate of precession,
2) the planetary hours,
3) the projection of rays,
4) domification,
5) the prime meridian used in recording geographic longitudes,
6) the quality of certain astrological texts,
7) the reference frame used for the coordinates of stars on an astrolabe's rete, and
8 ) the calendrical beginnings of the four seasons as well as the beginning and end of the so-called Dog Days.


The article makes this source available via a critical edition (based upon three manuscripts) and an accompanying English translation in January 2023. An introduction discusses the background and transmission of John’s letter as well as the identities of the letter writer and addressee. The edition and translation are followed by commentaries elucidating the background to each of the eight questions and John’s answers to them.
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I would like to focus on the 4th point domification and here is the translation of the letter of London by Nothaft

[4] With regard to the fourth question, you must know that in every climate the horizon and meridian are the beginning of four houses: the 1st, 4th, 7th, and 10th. And the beginnings of the other houses differ according to the length of the unequal hours of day and night, such that the length of two hours makes one house. And this is what Ptolemy indicates concerning the construction of the houses and this is the method that was used to make tables for the construction of the houses according to the location of Toledo, as he who inspects these tables will be able to see.

Do not look for any other way of dividing the houses than what the wise men of old have shown us and have made canons for. When it is said, however, that the houses in any region are demarcated through a division of the eastern and western azimuth into six equal parts above the horizon and that one imagines there to be six circles that run through these six divisions and through the intersection of the meridian and the horizon of a given region and through the parts opposite the aforementioned azimuth below the horizon--this opinion is very different from the position of the ancients and therefore should not be paid much heed. For even though the aforementioned six circles divide the whole hemisphere above and below into six equal parts, if one were to call that part of the whole zodiacal [circle] that falls between these circles a "house", one house would barely contain half of a sign and another more than one and a half signs. And since the zodiacal circle is a lifegiving circle and contains also the principal signs and has a greater influence on this world--because of the planets that wander below it--than any other part of the heaven, it seems to me that this is the reason that motivated the ancients to constitute the houses according to a circle that is at equal distance from the equator, through which the hours of
any given day are divided, so that there would not be an excess of one house over another, as is the case with the aforementioned method."

And here the commentary of Nothaft regarding this question.

"Question 4
The fourth question revolves around domification, that is, the problem of dividing the ecliptic into 12 houses for the purpose of drawing up a horoscopic chart. It was evidently occasioned by the existence of different systems or approaches to domification known to Arabic astrologers and transmitted to the Latin world via translations.85 (On the background, see North 1986, 1-69; Samso 2020, 257-273.)
John here recommends what amounts to the standard method in medieval astrology, which he believed to go back to Ptolemy. It divides the ecliptic into four arcs determined by the meridian and horizon line and further subdivides their projections onto the celestial equator into three segments of equal size. In effect, each of these segments will correspond to the right ascension in two diurnal or nocturnal hours.
Besides being easily applied with the aid of an astrolabe, this method--as John knew also underpinned most computational tables made for the purpose of domification, including those commonly included among the Toledan Tables [FPedersen 2002, 3.1075-1108 (BH 11-12)].

John was aware of at least one alternative method of domification, which John D. North has dubbed the "prime vertical method" [North 1986, 27-40; Samso 2020, 262-267]. The great circle to be divided into 12 arcs of equal size is here not the celestial equator but the circle perpendicular to the meridian, known as the "prime vertical"--or what John of London calls the azimuth orientalis et occidentalis [�22]. To project these arcs onto the ecliptic, one draws circles (so-called horizons) that pass through the boundaries between them as well as the north and south points of the horizon. John is only the second identifiable Latin author to make any mention of this method, which appears to have been the invention of Islamic astrologers. Prior to his letter, it had received a brief description in De quatuor partibus iudiciorum astronomie, an astrological textbook written by Roger of Hereford (fl. 1176).86 John considered it a deviant method that had to be rejected, not least because it made the sizes of the individual houses vary to a much greater extent than the standard method [��22-23]. His opinion no doubt conformed to the mainstream of astrological opinion. So far, no Latin horoscope from the Middle Ages that uses the prime vertical method has been identified.

Thank you for bringing this article to our attention, Ouranos!

And thanks from me too, for bringing this to our attention!
It sounds to me like he is recommending Placidus and arguing against Regiomontanus - do we have any confirmation of that?

I haven't had time to read it yet, but dividing the prime vertical sounds like Campanus (which indeed tends to distribute cusps very unevenly along the ecliptic).