Editor’s NoteCritical Apparatus1Editor’s NoteCritical Apparatus10. Capitulum decimum
- 2Primum plenilunium post equinoctium vernale, etiamsi in ipso die
- Critical Apparatus3equinoctii contigerit, est terminus designans pascha, quia proxima
- 4dominica post illud plenilunium celebratur dies pasche. Et in ipso die
- 5plenilunii, hoc est luna 14a, occidebatur in lege agnus paschalis. Et nos
- 6dicimus lunam 14am proximam post vernale equinoctium terminum
- Critical Apparatus7pasche, quia non illo die celebramus pascha, sed ille dies determinat
- Critical Apparatus8nobis, quod in proxima dominica sequente est pascha celebrandum. Et
- Critical Apparatus9ex iam dictis patet, quod luna debet dici 14a in ipso die plenilunii. Et
- Critical Apparatus10inde patet, quod ipsa debet dici prima non in die coniunctionis eius
- 11cum sole, sed in die proximo sequente, quo possibile est, ut primo
- 12appareat accensa a sole, quia, si inciperet tempus primationis ab hora
- 13coniunctionis lune cum sole, necessario diceretur luna 15a in die
- Critical Apparatus15Que cum ita sint, manifestum est, quod iam accidit nobis error in
- 16sumptione termini paschalis et etiam in sumptione diei pasche duabus
- 17de causis. Nos enim ponimus equinoctium vernale esse 12° Kalendas
- 18Aprilis et ibi ponimus infimum terminum pasche. Et manifestum est
- 19tam per instrumentum considerationis quam per tabulas astronomi-
- Critical Apparatus20cas, ibi non esse equinoctium in hoc tempore nostro, sed secundum
- Critical Apparatus21tabulas Toletanas fundatas supra quantitatem anni et motum octave
- Critical Apparatus22spere, quos posuit Thebit, equinoctium vernale in hoc nostro tempore
- Critical Apparatus23est pridie Idus Martii. Et constat, quod, si equinoctium fuit 12o
- pg 16224Kalendas Aprilis in tempore priorum doctorum, qui primo tradide-
- 25runt doctrinam de inveniendo termino pasche, quod in hoc tempore
- 26nostro non est equinoctium eodem die, immo necesse est nunc
- Critical Apparatus27equinoctium precedere diem illum per rationem eandem, quam
- 28diximus in capitulo primo de antecessione solstitii hiemalis.
- 29Item, ut supra ostensum est, erramus in positione quantitatis
- Critical Apparatus30lunationis equalis. Ex quo errore, ut ostendimus, accidet per longitu-
- 31dinem temporis lunam dici primam, quando erit plena et quando erit
- 32in quavis distantia a sole. Et ita non dicetur 14a in die plenilunii. Et
- Critical Apparatus33nunc in hoc nostro tempore est error iste manifestus, quia numquam
- Critical Apparatus34est nunc plenilunium, quando dicimus lunam 14am, sed quando ipsa
- Critical Apparatus35est 13a vel 12a. Et hoc manifestum est per eclipses lunares, que nunc
- Critical Apparatus36semper accidunt antequam luna sit 14a. Propterea preter hoc, quod
- 37erramus in ponendo equinoctium 12° Kalendas Aprilis, erramus etiam
- 38in sumptione termini paschalis. Et cum erramus in termino pasche,
- Critical Apparatus39necesse est nobis frequenter errare in sumptione ipsius diei pasche et
- 40ceterorum festorum mobilium.
- 41Modus autem verificandi hunc errorem est, ut verificetur anni
- 42quantitas et verificata ponatur in kalendario. Vel etiam absque verifica-
- 43tione quantitatis anni cognoscatur semper dies equinoctii vernalis per
- 44instrumentum considerationis vel per tabulas astronomicas verificatas.
- 45Et per id, quod supra docuimus de sumptione primationum secun-
- 46dum veritatem, cognoscatur dies plenilunii primi post illud equinoc-
- 47tium et dies ille ponatur terminus pasche. Verumtamen, quia sancta
- 48ecclesia nondum mutavit antiquam doctrinam de inveniendis festis
- 49mobilibus, illam doctrinam explanabimus.
- 50Dicimus ergo, quod equinoctium vernale est 12o Kalendas Aprilis.
- Editor’s Note51Ibi enim secundum Rabanum fuit equinoctium in primo anno seculi.
- Critical Apparatus52Et credo, quod ibi fuerit equinoctium in tempore doctorum, qui istam
- 53doctrinam primo tradiderunt, ad quos nondum pervenit scientia vere
- 54quantitatis anni nec scientia antecessionis solstitii et equinoctii. Et
- 55ponimus plenilunium, cum luna est 14a. Et cum ibi ponamus locum
- Critical Apparatus56equinoctii, ibidem ponendus est infimus terminus pasche. Quapropter
- pg 16457necesse est, ut primum pascha ponatur 11° Kalendas Aprilis, quia,
- 58quando terminus pasche accidit in die sabbati, erit dies pasche in
- 59crastino. Et primatio signata per 16 8o Idus Martii erit prima incensio
- 60lune paschalis, quia luna ibidem existente prima erit eadem 14a 12°
- 61Kalendas Aprilis.
- 62Et quia 19 primationes consequenter scripte in kalendario ab 8°
- 63Idus Martii usque ad Nonas Aprilis omnes et sole habent in die 14a
- 64lune plenilunium proximum post equinoctium vernale, primatio
- 65signata per 8 in Nonis Aprilis erit ultima incensio lune paschalis et 14°
- 66Kalendas Maii, in quo die luna huius primationis est semper 14a, erit
- 67ultimus terminus pasche. Et cum iste terminus accidit die dominica,
- 68erit dominica sequens 7° Kalendas Maii dies pasche. Quapropter 7°
- 69Kalendas Maii est ultimum pascha.
- Critical Apparatus70Et quando accidit lunam esse primam super aliquam 17 primatio-
- Critical Apparatus71num, que sunt inter 8° Idus Martii et Nonas Aprilis, fiat similiter
- 72semper computatio a loco primationis, usque dum occurrat luna 14a,
- 73et ibi ponatur terminus pasche. Et proxima dominica sequente
- Critical Apparatus74celebretur pascha. Hanc itaque artem inveniendi terminum paschalem
- Critical Apparatus75retinent per hos versus:
- Critical Apparatus78Habitis autem termino pasche et die pasche de facili habentur
- Critical Apparatus79termini et loca vera aliorum festorum mobilium, scilicet septuagesime,
- Critical Apparatus80quadragesime, rogationum et pentecostes, quia terminus septuagesime
- 81precedit terminum pasche 9 integris septimanis et similiter dominica
- 82septuagesime precedit diem pasche totidem septimanis et terminus et
- Critical Apparatus83dies quadragesime precedunt terminum et diem pasche 6 integris
- 84septimanis et terminus et dies pasche precedunt terminum et diem
- 85rogationum 5 septimanis integris et iterum terminus et dies pasche
- Critical Apparatus86precedunt terminum et diem pentecostes 7 integris septimanis.
- Critical Apparatus87Si autem primo vis invenire terminum septuagesime et per illum
- 88reliquos terminos sequentium festorum mobilium, considera, quota
- pg 16689est luna in die epiphanie, et computato numero etatis eius super diem
- 90epiphanie procedas continue computando usque ad 40 et diem, super
- Critical Apparatus91quem occurrit 40, ponas terminum septuagesime. Et sequenti
- Critical Apparatus92dominica celebrabitur septuagesima. Si autem fuerit annus bisextilis et
- Critical Apparatus93dies, super quem occurrit 40, fuerit dies sabbati, tunc non erit dies
- 94crastinus dominica septuagesime, sed erit terminus septuagesime et
- Critical Apparatus95secunda dominica a die, super quem occurrit 40, erit dominica septua-
- Critical Apparatus96gesime. Et istam artem retinent per hos versus:
- Critical Apparatus101Est autem et alius modus inveniendi festa mobilia, scilicet per
- 102claves terminorum. Et est clavis termini alicuius festi mobilis
- 103numerus quidam positus in loco determinato in kalendario. A quo
- Critical Apparatus104loco facta computatione per dies consequenter scriptos in kalendario
- 105usque ad finem illius numeri, ubi terminatur numerus ille, ibi ponitur
- 106terminus illius festi mobilis. Et quia omnes termini festorum
- 107mobilium periciunt periodum suam in 19 annis et redeunt ad loca
- 108prima, unicuique anno cycli decennovennalis appropriatus est
- Critical Apparatus109numerus unus, qui est clavis terminorum illius anni.
- Critical Apparatus110Locus autem clavium termini septuagesime est super primum G
- Critical Apparatus111Ianuarii, scilicet 7° Idus illius, et locus clavium termini quadragesime
- Critical Apparatus112est super ultimum G Ianuarii, scilicet 5° Kalendas Februarii, et locus
- Critical Apparatus113clavium termini pasche est super secundum G Martii, scilicet 5° Idus
- 114illius. Locus autem clavium terminorum rogationum est super tertium
- Critical Apparatus115G Aprilis, scilicet 17° Kalendas Maii, et locus clavium terminorum
- 116pentecostes est super ultimum G Aprilis, scilicet 3o Kalendas Maii.
- 117Clavis autem terminorum in primo anno cycli decennovennalis est
- 11826, quia, si incipiamus computare secundum numerum naturalem a 5°
- 119Idus Martii per dies continue sequentes usque ad 26, ubi occurrit 26,
- pg 168120erit terminus pasche in primo anno cycli, et hoc est in Nonis Aprilis.
- Critical Apparatus121Ibi enim est eodem anno luna 14a. Et per consimilem computationem
- Critical Apparatus122a 7° Idus Ianuarii factam invenitur eodem anno terminus septuagesime
- 123in Kalendis Februarii. Et penitus eodem modo inveniuntur eodem
- Critical Apparatus124anno terminus rogationum et terminus pentecostes facta computa-
- Critical Apparatus125tione a 17o Kalendas Maii et 3° Kalendas Maii usque ad 26.
- Critical Apparatus126Ex clave primi anni cycli decennovennalis formatur clavis secundi
- Critical Apparatus127anni et ex clave secundi anni formatur clavis tertii anni, et ita deinceps
- Critical Apparatus128semper ex clave precedentis anni formatur clavis anni sequentis hoc
- Critical Apparatus129modo: Si clavis alicuius anni sit maior 21, subtrahatur ab ipso 11 et,
- Critical Apparatus130quod relinquitur, erit clavis sequentis anni. Si vero clavis alicuius anni
- Critical Apparatus131fuerit minor 21, addantur ei 19 et aggregatum erit clavis sequentis
- Critical Apparatus132anni. Ratio autem, quare debeant subtrahi 11 vel addi 19, est, quod,
- 133quotiens primatio paschalis sequentis anni precedit primationem
- 134paschalem proximo antecedentis anni, precedit eam 11 diebus, et
- 135quotiens primatio paschalis sequentis anni sequitur primationem
- Critical Apparatus136paschalem antecedentis anni, sequitur eam 19 diebus.
- 137Posset autem quivis numerus minor quam 26, dummodo esset
- Critical Apparatus138maior quam 15, poni pro clave primi anni cycli. Et similiter quivis
- Critical Apparatus139maior numerus quam 26 prepositis vel postpositis locis clavium
- 140secundum quantitatem differentie numeri positi pro clave ad 26.
- 141Si autem in anno bisextili ceciderit terminus septuagesime in die
- 142sabbati, non est celebranda septuagesima in crastino, sed in die nono a
- 143termino, quia a termino septuagesime sunt 9 septimane integre in
- 144kalendario usque ad terminum pasche. Et cum in anno bisextili fuerit
- 145terminus septuagesime die sabbati, erit terminus pasche die dominica
- 146et celebrabitur pascha 8° die post eius terminum. Unde cum dies
- 147bisextilis inter initium septuagesime et pascha computetur et a die
- Critical Apparatus148septuagesime usque ad diem pasche sint tantum 9 septimane, necesse
- 149est, ut septuagesima celebretur 9o die post terminum eius.
- Critical Apparatus150Loca autem clavium retinent per hos versus:
- pg 170Editor’s Note151 In Iano prima supremaque, Marte secunda,
- 152 tertia G monstrat Aprilis et ultima claves.
- Critical Apparatus153Formatio vero clavium habetur per hos versus:
The first full moon after the vernal equinox, even if it falls on the day of the equinox itself, is the boundary indicating the date of Easter, because the Easter day is celebrated on the nearest Sunday after this full moon. And on the day of the full moon itself, that is, the 14th day of the Moon, the paschal lamb was killed in accordance with the law. And we refer to the 14th day of the Moon that comes closest after the vernal equinox as the 'paschal boundary', because this is not the day on which we celebrate Easter, but instead it informs us that Easter must be celebrated on the nearest Sunday after it. And from what has been said already it is clear that the Moon must be called 'the 14th' when it is the day of the full moon. And from this it is plain that it must be called 'the first' not on the day of its conjunction with the Sun, but on the nearest day after it, on which it is possible for [the Moon] to become visible for the first time, having been kindled by the Sun. For if the time of the new moon were to start from the hour of the Moon's conjunction with the Sun, the Moon would necessarily have to be called 'the 15th' when it is the day of the full moon.
With this being so, it is obvious that we already commit an error in the way we locate the paschal boundary and also in the way we determine the date of Easter, which happens for two reasons. For we assume the vernal equinox to be on 21 March and put there the lowest paschal boundary. And it is obvious from observational instruments as much as from astronomical tables that the equinox is not found there at our present time, but according to the Toledan Tables, which are based on the length of the year and the motion of the eighth sphere assumed by Thābit, the pg 163vernal equinox in our present time falls on 14 March. And it is evident that, if the equinox was on 21 March at the time of the first teachers, who were the first to transmit the rule of finding the paschal boundary, the equinox is no longer on the same date in our present time. Much rather, it is necessary that the equinox now precedes this day for the reason we discussed in the first chapter with regard to the anticipation of the winter solstice.
Likewise, as shown above, we err in assuming the length of the mean lunation. We have shown that this error over long periods of time leads us to call the Moon 'the first' when it is already full or when it will be at any other distance from the Sun. And this way it is not called 'the 14th' on the day of the full moon. And this error is evident in our present time, for nowadays there is never a full moon when we call the Moon 'the 14th', but when [the calendrical Moon] is in its 12th or 13th day. And this is conspicuous from lunar eclipses, which nowadays always occur before the Moon is in its 14th day. For this reason, we err not just in placing the equinox on 21 March, but also in our calculation of the paschal boundary. And if we err about the paschal boundary, it is necessary for us to frequently err in calculating the day of Easter itself and of the other mobile feasts.
The way to correct this error is to determine the true length of the year and to adjust the calendar accordingly. Or even without determining the true length of the year, one can always find the day of the vernal equinox with the help of observational instruments or accurate astronomical tables. And one should use what we taught above concerning the accurate calculation of new moon dates to determine the day of the first full moon after this equinox and put this day down as the paschal boundary. Yet since Holy Church has not yet changed the ancient rule of finding the mobile feasts, we shall explain this rule.
We say, then, that the vernal equinox is on 21 March. For this is where the equinox was in the first year of the world according to Rabanus. And I believe that this was the date of the equinox at the time of the teachers who first transmitted this rule, whom knowledge of the true length of the year had not yet reached, nor [did they have] knowledge of the anticipation of the solstice and equinox. And we assume that there is a full moon whenever the Moon is in its 14th day. And when we put the equinox on the same date, we must place there the lowest boundary date for Easter. It pg 165is hence necessary for the first Easter to fall on 22 March, for when the paschal boundary falls on a Saturday, the day after will be the Easter day. And the new moon marked by the number 16 [next to] 8 March will be the first kindling of the paschal lunation, for if the Moon is in its first day on this date, it will be in its 14th day on 21 March.
And since the 19 new moons that are written in sequence in the calendar from 8 March to 5 April are the only ones where the corresponding 14th day is the full moon that comes next after the vernal equinox, the new moon that is indicated by 8 on 5 April will be the latest new moon of the paschal lunation and 18 April, on which day the Moon that belongs to this new moon is always in its 14th day, will be the latest paschal boundary. And whenever this boundary falls on a Sunday, the following Sunday, on 25 April, will be the Easter day. This is why 25 April is the latest Easter.
And whenever it happens that the Moon reaches the first day on any of the 17 new moons that are between 8 March and 5 April, there shall always be the same calculation from the date of the new moon until the 14th day of the Moon has been reached, which is where the paschal boundary must be placed. And Easter shall be celebrated on the Sunday that follows next. They memorize this method of finding the paschal boundary with the help of these verses:
- Search for where the Moon is new after 7 March,
- once [this Moon] is 14 [days old], Easter will be revealed.
Now, once one has found the paschal boundary and the date of Easter, it is easy to obtain the boundaries and true dates of the other mobile feast days, which are Septuagesima, Quadragesima, Rogation Sunday, and Pentecost. For the boundary of Septuagesima precedes the paschal boundary by nine whole weeks and, likewise, Septuagesima Sunday precedes the date of Easter by just as many weeks and the boundary and date of Quadragesima precede the boundary and date of Easter by six whole weeks and the boundary and date of Easter precede the boundary and date of Rogation Sunday by five whole weeks and, again, the boundary and date of Easter precede the boundary and date of Pentecost by seven whole weeks.
But if you wish first to find the boundary of Septuagesima Sunday and through it the remaining boundaries of the following mobile feasts, you must take into account the age of the Moon on the day of Epiphany, and pg 167once you have counted the number corresponding to its age on the day of Epiphany, you must proceed to count continuously up to 40, and the day on which the number 40 falls you shall make the boundary of Septuagesima. And on the following Sunday Septuagesima will be celebrated. In cases, however, where the year is bissextile and the day on which the number 40 falls is a Saturday, the following day will not be Septuagesima Sunday, but it will be the boundary of Septuagesima and the second Sunday from the day on which the number 40 falls will be Septuagesima Sunday. And they memorize this method with the help of these verses:
- Start counting lunar days from the feast of the star and complete
- 40 days and the result will be Septuagesima.
- Forsake the first Sunday and retain the second one
- if [the day in question] falls on Saturday and there is a bissextile day.
There is, however, another method of finding the mobile feasts, namely that of using boundary keys. And the boundary key of any mobile feast is a certain number placed on a fixed date in the calendar. And if one counts from this position the days written in sequence in the calendar up to the end of this number, the date on which this number finishes will be where the boundary of this mobile feast is placed. And since all boundaries of mobile feasts complete their period in 19 years and return to their original places, each year of the 19-year cycle has a number to itself that is the boundary key of this year.
The place for the boundary keys of Septuagesima is the first date in January with the letter G, which is 7 January, and the place for the boundary keys for Quadragesima is the last date in January with the letter G, which is 28 January, and the place for the boundary keys of Easter is the second date in March with the letter G, which is 11 March. The place for the boundary keys of Rogation Sunday is the third date in April with the letter G, which is 15 April, and the place for the boundary keys of Pentecost is the last date in April with the letter G, which is 29 April.
Now, in the first year of the 19-year cycle the boundary key is 26, for if we start counting according to natural numbers from 11 March up to 26 through the days that follow in continuous sequence, the date where 26 falls will be the boundary of Easter in the first year of the cycle, and that pg 169is on 5 April. For there the Moon is in its 14th day in the year in question. And by making the same kind of count from 7 January one will find in the same year the boundary of Septuagesima on 1 February. And in exactly the same manner one can find in the same year the boundary of Rogation Sunday and the boundary of Pentecost, if the count up to 26 is made from 15 April and from 29 April.
From the key of the first year of the 19-year cycle the key of the second year is formed and from the key of the second year the key of the third year is formed, and so on, such that the key of the following year is always formed from the key of the preceding year, in the following way: if the key of a given year is greater than 21, one must subtract 11 from it and what remains will be the key of the following year. If, on the other hand, the key of a given year is smaller than 21, one must add 19 to it, and the sum will be the key of the following year. The reason why one must subtract 11 or add 19 is that whenever the Easter new moon of the following year falls earlier than the Easter new moon of the year immediately before it, it precedes it by 11 days; and every time the Easter new moon of the following year falls later than the Easter moon of the preceding year, it follows 19 days after it.
One could use any number smaller than 26 as the key of the first year of the cycle, as long as it is greater than 15. And, similarly, [one could use] any number greater than 26, if the places for the keys are pre- or postponed according to the difference between 26 and the number that has been chosen as the key.
But if the boundary of Septuagesima falls on a Saturday in a bissextile year, Septuagesima must not be celebrated on the following day, but on the ninth day from the boundary, because there are nine whole weeks from the boundary of Septuagesima to the boundary of Easter. And in cases where the boundary of Septuagesima falls on a Saturday in a bissextile year, the boundary of Easter will be on a Sunday, and Easter will be celebrated on the eighth day after its boundary. Inasmuch as the bissextile day is counted between the beginning of Septuagesima and Easter and there are only nine weeks from the day of Septuagesima to the day of Easter, it is hence necessary for Septuagesima to be celebrated on the ninth day after its boundary.
The places for the keys are memorized with the help of these verses:
- pg 171 In January it is the first and the last [G], in March the second,
- in April the third and the final G that show the keys.
The method of forming the keys is had with the help of these verses:
- If the key is 20 or smaller than that
- you must add 19 to get the key that follows it.
- Take away 11 if it is 22
- or higher. The [resulting] number will be the next key.
|1220||14 March, 04:06h|
|1221||14 March, 10:01h|
|1222||14 March, 15:56h|
|1223||14 March, 21:51h|
|1224||14 March, 03:47h|
|1225||14 March, 09:42h|
|1226||14 March, 15:37h|
|1227||14 March, 21:33h|
|1228||14 March, 03:28h|
|1229||14 March, 09:24h|
|1230||14 March, 15:19h.|
|Septuagesima Sunday||18 January–22 February (nine weeks before Easter)|
|Quadragesima Sunday||8 February–14 March (six weeks before Easter)|
|Rogation Sunday||26 April–30 May (five weeks after Easter)|
|Pentecost/Whitsunday||10 May–13 June (seven weeks after Easter).|