Abbreviatio compoti cuiusdam idiotae

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Abbreviatio compoti cuiusdam idiotae is the most extensive text in the field of astronomy / computistics by the medieval Benedictine monk and scientist Hermann the Lame . This - loosely translated - short introduction to computus by someone who is not sufficiently educated - is supplemented by the Epistula de quantitate mensis lunaris ( letter about the length of the lunar month ) and Prognostica de defectu solis et lunae ( forecast of solar and lunar eclipses ). The Abbreviatio and Epistula were written around 1042, the Prognostica between 1049 and 1052. All three treatises deal with the problem of the precise timing of the lunar orbit.

Abbreviatio compoti cuiusdam idiotae

In the first 24 chapters Hermann discusses the basic principles of church calendar calculations , the Julian calendar year with a four-year leap , the construction of the 19-year Meton cycle with moon switching months -tagen and moon jump and based thereon moon age calculation epacts , eventually merging weekday and Lunar arithmetic to determine the Easter date and definition of the 532 year Easter cycle . In doing so, he follows the themes that Beda Venerabilis has collected in his computist work De temporum ratione , but dispenses with the Christian / salvation-historical references of his predecessor. In the following he leaves the paths of the patrum traditio (traditional knowledge of the Church Fathers); in chapter 25 he asks:

... que causa quisve error sit, ut lune etas compoto nostro regulisque antiquorum supradictis persepe non conveniat

... why the calculated moon status according to the rules of ancient scholars does not correspond to the observed one

Beda Venerabilis had already worried about this ( De temporum ratione , 43). Unlike Beda, who accepts the discrepancy with recourse to the knowledge of old authorities, especially the church fathers , Hermann looks for a mathematical solution by determining the exact length of the synodic month . He does not start from astronomical observations of the sky, but only uses traditional knowledge. According to the tradition available to Hermann (including Beda Venerabilis: De temporum ratione , 44, 45, 56), the 19-year Meton cycle lasts 228 solar months of 30 days and 10.5 hours and at the same time 235 lunar months of 29 days and 12 Hours. As he calculates in Chapter XXVII, this results in a discrepancy of 7 days and 6 hours. He divides these into the lunar months and calculates their length to 29 days, 12 hours, 2 solar puncti , 14 ostenta and 160 athomi (Chapter 32). He had previously defined the small time units according to Beda Venerabilis ( De temporum ratione , 3), but without the athomi , the use of which was rejected by Beda Venerabilis. In the following chapters Hermann calculates various moon age tables.

Epistula de quantitate mensis lunae

At about the same time, Hermann describes the exact calculation of the length of a synodic lunar month in a letter to his friend Herrandus. The considerations correlate with chapters 25-36 of the Abbreviatio .

Prognostica de defectu solis et lunae

With this writing ( prediction of solar and lunar eclipses ) Hermann goes beyond the range of traditional computistics and creates an innovative astronomical calculation, although here too he is based on the traditional computational treatises.

In Chapters I to III he presents the basis of his calculation, which he partly used in ancient authors such as Pliny the Elder ( Naturalis historia , II, 44-48) and Macrobius ( Commentary on Cicero's Somnium Scipionis , I.6,49- 53; I.15,10-12) finds:

  • Eclipses only found in the new moon and full moon instead
  • Eclipses only occur when the lunar orbit crosses the ecliptic in a knot
  • He calculated the time interval between two new or full moons, the synodic month, in the Abbreviatio
  • Similarly, in Chapter II, he now calculates the duration of the sidereal month , which he assumes corresponds to the duration between two descending or ascending nodes. Its calculated value corresponds to 27.32185039 days and deviates only slightly from the average value recognized today.

From this he draws the conclusion that, based on a proven eclipse, he can determine the following by calculating the times at which a new or full moon passes through the associated ecliptic node. He prepares this task in the following chapters by creating numerous moon age tables.

Then he does the practical test. In Chapter XIII he checks to what extent his calculation agrees with the lunar eclipse of September 16, 1046, which he was able to observe himself. In fact, the calculation results in a full moon moon age, but the moon is arithmetically more than 2 days away from the ecliptic. With this Hermann ends the writing and does not come to the actual intention of calculating eclipses in advance. It remains to be seen whether the arithmetical means available to him were insufficient despite the abacus , or whether he had doubts about his solution. In fact, his approach is flawed, since for the determination of the eclipses not the sidereal, but the draconian , which takes into account the precession of the moon, is relevant . Moreover, Hermann's optimistic statement in the Abbreviation Chapter XXV is wrong

... absurdum putavit regulas seqendo lunam necdum esse contendere = ... only the foolish will claim that the moon does not follow the rules .

On the contrary, the moon's movement is influenced by numerous forces and is difficult to calculate

Living on and tradition

Hermann's manuscripts, supplemented by tables, were received and developed a few decades later by several scholars in Lorraine ( Gerlandus Compotista ) and south-west England (Malcher von Malvern ).

Of the Abbreviatio , 18 manuscripts are currently known in the important libraries of several European countries, eight of these texts also contain the Prognostica . For her edition, which is the first ever, Nadja Germann mainly used the manuscript British Library , Arundel 356 around 1080.

The epistula was first edited by Gabriel Meier ( The seven liberal arts in the Middle Ages , 1887). Arno Borst included the text in his elaboration A research report by Hermann the Lame .

Text output

  • Arno Borst: A research report by Hermann the Lame. In: German Archive for Research into the Middle Ages 40, 1984, pp. 474–477.
  • Nadja Germann: De Temporum Ratione. Quadrivium and knowledge of God using the example of Abbos von Fleury and Hermanns von Reichenau , Appendix.

literature

  • Arno Borst: A research report by Hermann the Lame. In: German Archive for Research into the Middle Ages 40, 1984, pp. 379–477 ( digitized version ).
  • Nadja Germann: De Temporum Ratione. Quadrivium and knowledge of God using the example of Abbos von Fleury and Hermanns von Reichenau , Leiden / Boston 2006.
  • Martin Hellmann: Abacus and arithmetic in the work of Hermann the Lame in Felix Heinzer, Thomas Zotz (Ed.): Hermann the Lame. Reichenau monk and universal scholar of the 11th century (= publications of the Commission for Historical Regional Studies in Baden-Württemberg, Series B, Research. Vol. 208). Kohlhammer, Stuttgart 2016, ISBN 978-3-17-030723-0 .
  • Immo Warntjes: Hermann the Lame and the calculation of time in Felix Heinzer, Thomas Zotz (Hrsg.): Hermann the Lame. Reichenau monk and universal scholar of the 11th century (= publications of the Commission for Historical Regional Studies in Baden-Württemberg, Series B, Research. Vol. 208). Kohlhammer, Stuttgart 2016, ISBN 978-3-17-030723-0 .

Individual evidence

  1. ↑ Immo Warntjes: Hermann the Lame and the Calculation of Time , p. 288
  2. ↑ Immo Warntjes: Hermann the Lame and the Calculation of Time , p. 307
  3. ^ Nadja Germann: De Temporum Ratione. Quadrivium and knowledge of God using the example of Abbos von Fleury and Hermanns von Reichenau , p. 206
  4. ^ Nadja Germann: De Temporum Ratione. Quadrivium and knowledge of God using the example of Abbos von Fleury and Hermanns von Reichenau , p. 218
  5. ↑ Immo Warntjes: Hermann the Lame and the Calculation of Time , p. 288
  6. ^ Nadja Germann: De Temporum Ratione. Quadrivium and knowledge of God using the example of Abbos von Fleury and Hermanns von Reichenau , p. 219f
  7. ^ Arno Borst: A research report by Hermann the Lame. , P. 437f
  8. ↑ Martin Hellmann: Abacus and arithmetic in the work of Hermann des Lahmen , p. 270f
  9. ^ Nadja Germann: De Temporum Ratione. Quadrivium and knowledge of God using the example of Abbos von Fleury and Hermanns von Reichenau , p, 231
  10. ^ Arno Borst: A research report by Hermann the Lame. , P. 438
  11. ↑ Hans-Ulrich Keller : Astrowissen , pp. 63, 71
  12. ↑ Immo Warntjes: Hermann the Lame and the calculation of time , p. 311f
  13. ^ Nadja Germann: De Temporum Ratione. Quadrivium and knowledge of God using the example of Abbos von Fleury and Hermanns von Reichenau , Appendix
  14. ^ Arno Borst: A research report by Hermann the Lame. , P. 395