Pri Pri Pri Di… computus manualis

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compotus John Damascene Easter
John of Damacus’ Hand (John Damascene) Computing Easter

“In addition to the longhand methods, computus manuscripts often included mnemonics and lists for easy reference. One example of this is the medieval mnemonic “post epi pri pri pri di di di pascha fi”, which reminds the reader that in a given year Easter is the third Sunday after the third new moon after Epiphany, a system which works in all but two very specific cases.

A common variation on the standard computus manuscript was the so-called computus manualis which explained how to use the hand as a way to calculate by counting along the fingers and around the palm, and allocating each joint of each finger to the months, dominical letters, and other important pieces of information.

quoted from:

Thomas F. Glick, Steven Livesey, Faith Wallis, Medieval Science, Technology, and Medicine: An Encyclopedia, Routledge (2014) p.111.

– which gives a short bibliography including:
.
Laurel Means, ‘Ffor as moche as yche man may not haue the astrolabe’: popular Middle English variations on the computus, Speculum, (1992), 595-623.
 .
Manuscripts listed ..
 .
Arianus, Computus cum commento.  The only copy in England is in Worcester Cathedral Library and is discussed by a conservator-blogger here.
 .
Leiden: Anianus (ca. 1250-1300), Computus manualis>, cum commentario et figuris atramento delineatis VLO 21 at Leiden  (the listing is hereView online here.
.
 .
Brit.Lib. Harley MS 3647.  Northern French c.1292. Dimensions 250 x 180 mm (text space: 150/155 x 95/100 mm; with tables, drawings and diagrams…)  Folios digitised here.
..

 also – G/books has a listing for a Computus manualis ad usum Oxoniensium, Kyrforth, 1519. which appears to be the same work that is presently listed with Abebooks as:
.
The Ancient Kalendar of the University of Oxford.with Computus Manualis.from C. Kyrfoth’s edition, Oxon, 1519-20.

Concerning the “Jewish Passover” computations which are mentioned by Michael of Rhodes  in connection with one of his mnemonic hands, there is a passage in Stern and Burnett which reads:

“In elucidating the difference, the author makes reference to the principle of counting the years of the cycle on the phalanges of one’s fingers, starting with the tip of the thumb for year 1 and finding the 19th year on the tip of one’s little or auricular finger. The author explicitly states that this is the principle ‘taught in the computus manualis’, which is probably simply meant to denote the general practice of finger-reckoning, but which may perhaps be a reference to a short metrical treatise of this name ascribed to a certain Johannes of Polonia, which is often found in the same codices as the Computus Iudaicus“..

.

 Sacha Stern, Charles Burnett (eds.), Time, Astronomy and Calendars in the Jewish Tradition, Brill (2013) p. 337.
.
I can find only two “Johannes of Polonia” listed in the Biographical Index of the Middle Ages. These are:
.
1) who died in 1392.  The reader is then referred to Johannes [Jan] Radlica Bishop of Krakow.
2) (flourished 1417). A copyist, born in Poland, but worked in Padua.
– for more see the Biog. Index (published by Walter de Gruyter, 2008) p.648.
.
and..
.
I should have included in the previous post about Michael of Rhodes that
“Michael’s manuscript contains more than 180 pages of mathematics..”  (see the dedicated website).
.

and  to show just how long the ‘computus manualis’ remained in vogue, here’s an eighteenth-century version (click to enlarge):

computus manualis 18thC
WINTER, GABRIEL Computus manualis, eller: tide-räkning på finger-lederna; utarbetad efter nya stylen, ungdomen til tjenst, af GVberna eli iter. Åbo, J. Merckell, 1758
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