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The Canterbury Tales and Other Works of Chaucer (Middle English), by Geoffery Chaucer, [14th cent.], at

A Treatise on the Astrolabe

Part 2

Rub To fynde the degre in which the sonne is
RubA day by day, after his cours aboute.
 Rekne and knowe which is the day of thy
 month, and ley thy rewle upon that same day,
 and than wol the verrey poynt of thy rewle
 sitten in the bordure upon the degre of thy
 Ensample as thus: The yeer of oure Lord
 1391, the 12 day of March at midday, I wolde
 knowe the degre of the sonne. I soughte in
 the bakhalf of myn Astrelabie and fond the
10 cercle of the daies, the whiche I knowe by
 the names of the monthes writen under the
 same cercle. Tho leyde I my reule over this
 foreseide day, and fond the point of my reule
 in the bordure upon the firste degre of Aries,
 a litel within the degre. And thus knowe I this
 Anothir day I wolde knowen the degre of
 my sonne, and this was at midday in the 13
 day of Decembre. I fond the day of the
20 month in manere as I seide; tho leide I my
 rewle upon this forseide 13 day, and fond
 the point of my rewle in the bordure upon
 the firste degre of Capricorne a lite within the
 degre. And than had I of this conclusioun the
 ful experience.
Rub To knowe the altitude of the sonne or of
RubA othre celestial bodies.
 Put the ryng of thyn Astrelabie upon thy
 right thombe, and turne thi lift syde ageyn
 the light of the sonne; and remewe thy rewle
 up and doun til that the stremes of the sonne
 shine thorugh bothe holes of thi rewle. Loke
 than how many degrees thy rule is areised fro
 the litel cros upon thin est lyne, and tak there
 the altitude of thi sonne. And in this same
 wise maist thow knowe by night the altitude
10 of the mone or of brighte sterres.
 This chapitre is so generall evere in oon
 that there nedith no more declaracioun; but
 forget it not.
Rub To knowe every tyme of the day by light
RubA of the sonne; and every tyme of the nyght by
RubB the sterres fixe; and eke to knowe by nyght or
RubC by day the degre of eny signe that ascendith on
RubD the est orisonte, which that is clepid comounly
RubE the ascendent, or ellis horoscopum.
 Tak the altitude of the sonne whan the list,
 as I have seid, and set the degre of the sonne,
 in caas that it be beforn the myddel of the day,
 among thyn almykanteras on the est syde of
 thin Astrelabie; and if it be after the myddel
 of the day, set the degre of thy sonne upon the
 west syde. Tak this manere of settyng for a
 general rule, ones for evere. And whan thou
 hast set the degre of thy sonne upon as
10 many almykanteras of height as was the altitude
 of the sonne taken by thy rule, ley
 over thi label upon the degre of the sonne; and
 than wol the point of thi labell sitte in the
 bordure upon the verrey tyde of the day.
 Ensample as thus: The yeer of oure lord
 1391, the 12 day of March, I wolde knowe the
 tyde of the day. I tok the altitude of my sonne,
 and fond that it was 25 degrees and 30 minutes
 of height in the bordure on the bak
20 side. Tho turned I myn Astrelabye, and by
 cause that it was before mydday, I turned
 my riet and sette the degre of the sonne, that
 is to seyn the firste degre of Aries, on the right
 side of myn Astrelabye upon 25 degrees and
 30 mynutes of height among myn almykanteras.
 Tho leide I my label upon the degre of my
 sonne, and fond the point of my label in the
 bordure upon a capital lettre that is clepid
 an X. Tho rekned I alle the capitale lettres
30 fro the lyne of mydnight unto this forseide
 lettre X, and fond that it was 9 of the
 clokke of the day. Tho loked I doun upon myn
 est orizonte, and fond there the 20 degre of
 Geminis ascendyng, which that I tok for myn
 ascendent. And in this wise had I the experience
 for evermo in which manere I shulde
 knowe the tyde of the day and eke myn ascendent.
 Tho wolde I wite the same nyght folewyng
40 the houre of the nyght, and wroughte
 in this wise: Among an heep of sterres
 fixe it liked me for to take the altitude of the
 faire white sterre that is clepid Alhabor, and
 fond hir sittyng on the west side of the lyne
 of midday, 12 degrees of heighte taken by my
 rewle on the bak side. Tho sette I the centre
 of this Alhabor upon 12 degrees among myn
 almykanteras upon the west side, by cause that
 she was founde on the west side. Tho
50 leyde I my label over the degre of the
 sonne, that was discendid under the west
 orisounte, and rekned all the lettres capitals
 fro the lyne of midday unto the point of my
 label in the bordure, and fond that it was
 passed 9 of the clokke the space of 10 degrees.
 Tho lokid I doun upon myn est orisounte, and
 fond there 10 degrees of Scorpius ascendyng,
 whom I tok for myn ascendent. And thus
 lerned I to knowe onys for ever in which
60 manere I shuld come to the houre of the
 nyght, and to myn ascendent, as verrely as
 may be taken by so smal an instrument.
 But natheles this rule in generall wol I warne
 the for evere: Ne make the nevere bold to
 have take a just ascendent by thin Astrelabie,
 or elles to have set justly a clokke, whan eny
 celestial body by which that thou wenyst governe
 thilke thinges be nigh the south lyne.
 For trust wel, whan the sonne is nygh the
70 meridional lyne, the degre of the sonne
 renneth so longe consentrik upon the almykanteras
 that sothly thou shalt erre fro the
 just ascendent. The same conclusioun sey I by
 the centre of eny sterre fix by nyght. And
 more over, by experience I wot wel that in
 oure orisounte, from xi of the clokke unto oon
 of the clokke, in taking of a just ascendent in
 a portatif Astrelabie it is to hard to knowe --
 I mene from xi of the clokke before the
80 houre of noon til oon of the clokke next
Rub A special declaracioun of the ascendent.
 The ascendent sothly, as wel in alle nativites
 as in questions and eleccions of tymes, is a
 thing which that these astrologiens gretly observen.
 Wherfore me semeth convenyent, syth
 that I speke of the ascendent, to make of it
 speciall declaracioun.
 The ascendent sothly, to take it at the largest,
 is thilke degre that ascendith at eny of
 these forseide tymes upon the est orisounte.
10 And therfore, yf that eny planete ascende
 at thatt same tyme in thilke forseide degre,
 than hath he no latitude fro the ecliptik lyne,
 but he is than in the degre of the ecliptik
 which that is the degre of his longitude. Men
 sayn that thilke planete is in horoscopo.
 But sothly the hous of the ascendent, that
 is to seyn, the first hous or the est angle, is a
 thing more brod and large. For, after the statutes
 of astrologiens, what celestial body
20 that is 5 degrees above thilke degre that
 ascendith, or withinne that nombre, that is
 to seyn neer the degree that ascendith, yit
 rekne they thilke planete in the ascendent.
 And what planete that is under thilke degre
 that ascendith the space of 25 degres, yit seyn
 thei that thilke planete is "like to him that is
 the hous of the ascendent." But sothly, if he
 passe the boundes of these forseide spaces,
 above or bynethe, thei seyn that the planete
30 is "fallyng fro the ascendent." Yit saien
 these astrologiens that the ascendent and
 eke the lord of the ascendent may be shapen
 for to be fortunat or infortunat, as thus: A
 "fortunat ascendent" clepen they whan that no
 wicked planete, as Saturne or Mars or elles
 the Tayl of the Dragoun, is in the hous of the
 ascendent, ne that no wicked planete have
 noon aspect of enemyte upon the ascendent.
 But thei wol caste that thei have a fortunat
40 planete in hir ascendent, and yit in his felicite;
 and than sey thei that it is wel.
 Further over thei seyn that the infortunyng of
 an ascendent is the contrarie of these forseide
 thinges. The lord of the ascendent, sey thei
 that he is fortunat whan he is in god place
 fro the ascendent, as in an angle, or in a succident
 where as he is in hys dignite and comfortid
 with frendly aspectes of planetes and
 wel resceyved; and eke that he may seen
50 the ascendent; and that he be not retrograd,
 ne combust, ne joyned with no
 shrewe in the same signe; ne that he be not
 in his discencioun, ne joyned with no planete
 in his descencioun, ne have upon him noon
 aspect infortunat; and than sey thei that he is
 Natheles these ben observaunces of judicial
 matere and rytes of payens, in whiche my
 spirit hath no feith, ne knowing of her
60 horoscopum. For they seyn that every
 signe is departid in thre evene parties by
 10 degrees, and thilke porcioun they clepe a
 face. And although that a planete have a latitude
 fro the ecliptik, yit sey somme folk, so
 that the planete arise in that same signe with
 eny degre of the forseide face in which his
 longitude is rekned, that yit is the planete
 in horoscopo, be it in nativyte or in eleccion,
Rub To knowe the verrey equacioun of the
RubA degre of the sonne yf so be that it falle bitwene
RubC thyn almykanteras.
 For as muche as the almykanteras in thin
 Astrelabie ben compowned by two and two,
 where as somme almykanteras in sondry astrelabies
 be compowned by 1 and 1, or elles by 2
 and 2, it is necessarie to thy lernyng to teche
 the first to knowe and worke with thin oune
 instrument. Wherfore whan that the degre of
 thi sonne fallith bytwixe 2 almykanteras, or
 ellis yf thin almykanteras ben graven with
10 over-gret a poynt of a compas (for bothe
 these thinges may causen errour as wel in
 knowing of the tide of the day, as of the verrey
 ascendent), thou must worken in this
 Set the degre of thy sonne upon the hyer
 almykanteras of bothe, and wayte wel where
 as thin almury touchith the bordure and set
 there a prikke of ynke. Sett doun agayn the
 degre of the sunne upon the nether almykanteras
20 of bothe, and sett there another
 pricke. Remeve than thin almury in
 the bordure evene amiddes bothe prickes, and
 this wol lede justly the degre of thi sonne to
 sitte bitwene bothe almykanteras in his right
 place. Ley than thy label over the degre of
 thi sonne, and fynd in the bordure the verrey
 tyde of the day, or of the night. And as verraily
 shalt thou fynde upon thin est orisonte
 thin ascendent.
Rub To knowe the spryng of the dawenyng
RubA and the ende of the evenyng, the whiche ben
RubB called the two crepuscules.
 Set the nadir of thy sonne upon 18 degrees
 of height among thyn almykanteras on the west
 syde; and ley thy label on the degre of thy
 sonne, and than shal the point of thy label
 shewen the spryng of the day. Also set the
 nader of thy sonne upon 18 degrees of height
 among thin almykanteras on the est side, and
 ley over thy label upon the degre of the sonne,
 and with the point of thy label fynd in the
10 bordure the ende of the evenyng, that is
 verrey nyght.
 The nader of the sonne is thilke degre that
 is opposyt to the degre of the sonne, in the
 7 signe, as thus: every degre of Aries by
 ordir is nadir to every degre of Libra by ordre,
 and Taurus to Scorpioun, Gemini to Sagittarie,
 Cancer to Capricorne, Leo to Aquarie, Virgo
 to Piscis. And if eny degre in thy zodiak be
 derk, his nadir shal declare hym.
Rub To knowe the arch of the day, that some
RubA folk callen the day artificiall, fro sonne arisyng
RubB tyl it go to reste.
 Set the degre of thi sonne upon thin est
 orisonte, and ley thy label on the degre of
 the sonne, and at the point of thy label in the
 bordure set a pricke. Turne than thy riet
 aboute tyl the degre of the sonne sitte upon
 the west orisonte, and ley thy label upon the
 same degre of the sonne, and at the poynt of
 thy label set another pricke. Rekne than
 the quantite of tyme in the bordure bitwixe
10 bothe prickes, and tak there thyn arch of
 the day. The remenaunt of the bordure
 under the orisonte is the arch of the nyght.
 Thus maist thou rekne bothe arches, or every
 porcioun, of whether that the liketh. And by
 this manere of worching maist thou se how
 longe that eny sterre fix dwelleth above the
 erthe, fro tyme that he riseth til he go to reste.
 But the day naturall, that is to seyn 24 hours,
 is the revolucioun of the equinoxial with as
20 muche partie of the zodiak as the sonne of
 his propre moeving passith in the mene
Rub To turne the houres inequales in houres
RubA equales.
 Know the nombre of the degrees in the
 houres inequales, and depart hem by 15, and
 tak there thin houres equales.
Rub To knowe the quantite of the day vulgar,
RubA that is to seyn fro spryng of the day unto
RubB verrey nyght.
 Know the quantite of thy crepuscles, as I
 have taught in the 3 chapitre bifore, and adde
 hem to the arch of thy day artificial, and tak
 there the space of all the hool day vulgar unto
 verrey night. The same manere maist thou
 worche to knowe the quantite of the vulgar
Rub To knowe the quantite of houres inequales
RubA by day.
 Understond wel that these houres inequales
 ben clepid houres of planetes. And understond
 wel that som tyme ben thei lenger by
 day than by night, and som tyme the contrarie.
 But understond wel that evermo generaly
 the houre inequal of the day with the
 houre inequal of the night contenen 30 degrees
 of the bordure, which bordure is evermo answeryng
 to the degrees of the equinoxial.
10 Wherfore departe the arch of the day artificial
 in 12, and tak there the quantite of
 the houre inequale by day. And if thou abate
 the quantite of the houre inequale by day out
 of 30, than shal the remenaunt that levith parforme
 the houre inequale by night.
Rub To knowe the quantite of houres
RubA equales.
 The quantite of houres equales, that is to
 seyn the houres of the clokke, ben departid by
 15 degrees alredy in the bordure of thin Astrelaby,
 as wel by night as by day, generaly for
 evere. What nedith more declaracioun?
 Wherfore whan the list to knowe hou many
 houres of the clokke ben passed, or eny part
 of eny of these houres that ben passed, or ellis
 how many houres or parties of houres ben
10 to come fro such a tyme to such a tyme by
 day or by night, know the degre of thy
 sonne, and ley thy label on it. Turne thy ryet
 aboute joyntly with thy label, and with the
 poynt of it rekne in the bordure fro the sonne
 arise unto that same place there thou desirist,
 by day as by nyght. This conclusioun wol I declare
 in the laste chapitre of the 4 partie of this
 tretys so openly that ther shal lakke no word
 that nedith to the declaracioun.
Rub Special declaracioun of the houres of
RubA planetes.
 Understond wel that evermo, fro the arisyng
 of the sonne til it go to reste, the nadir of
 the sonne shal shewe the houre of the planete;
 and fro that tyme forward al the night til the
 sonne arise, than shal the verrey degre of the
 sonne shewe the houre of the planete.
 Ensample as thus: The xiij day of March
 fyl upon a Saturday, peraventure, and atte risyng
 of the sonne I fond the secunde degre
10 of Aries sittyng upon myn est orisonte, all
 be it that it was but litel. Than fond I the
 2 degre of Libra, nadir of my sonne, discending
 on my west orisonte, upon which west orisonte
 every day generaly, atte sonne arist, entrith the
 houre of eny planete, after which planete the
 day berith his name, and endith in the next
 strike of the plate under the forseide west
 orisonte. And evere as the sonne clymbith upper
 and upper, so goth his nadir downer
20 and downer, teching by suche strikes the
 houres of planetes by ordir as they sitten
 in the hevene. The firste houre inequal of
 every Saturday is to Saturne, and the secunde
 to Jupiter, the thirde to Mars, the fourthe
 to the sonne, the fifte to Venus, the sixte to
 Mercurius, the seventhe to the mone. And
 then ageyn the 8 is to Saturne, the 9 to
 Jupiter, the 10 to Mars, the 11 to the sonne,
 the 12 to Venus. And now is my sonne gon
30 to reste as for that Saturday. Than shewith
 the verrey degre of the sonne the houre
 of Mercurie entring under my west orisonte at
 eve; and next him succedith the mone, and
 so furth by ordir, planete after planete in houre
 after houre, all the nyght longe til the sonne
 arise. Now risith the sonne that Sonday by
 the morwe, and the nadir of the sonne upon
 the west orisonte shewith me the entring of the
 houre of the forseide sonne. And in this
40 manere succedith planete under planete fro
 Saturne unto the mone, and fro the mone up
 ageyn to Saturne, houre after houre generaly.
 And thus knowe I this conclusyoun.
Rub To knowe the altitude of the sonne in
RubA myddes of the day that is clepid the altitude
RubB meridian.
 Set the degre of the sonne upon the lyne
 meridional, and rekne how many degres of
 almykanteras ben bitwyxe thin est orisonte and
 the degre of thy sonne; and tak there thin altitude
 meridian, this to seyn, the highest of the
 sonne as for that day. So maist thou knowe in
 the same lyne the heighest cours that eny sterre
 fix clymbeth by night. This is to seyn that whan
 eny sterre fix is passid the lyne meridional,
10 than begynneth it to descende; and so doth
 the sonne.
Rub To knowe the degre of the sonne by thy
RubA ryet, for a maner curiosite.
 Sek besily with thy rule the highest of the
 sonne in mydde of the day. Turne than thin
 Astrelabie, and with a pricke of ynke marke
 the nombre of that same altitude in the lyne
 meridional; turne than thy ryet aboute tyl thou
 fynde a degre of thy zodiak according with the
 pricke, this is to seyn, sitting on the pricke.
 And in soth thou shalt finde but 2 degrees in
 all the zodiak of that condicioun; and yit
10 thilke 2 degrees ben in diverse signes.
 Than maist thou lightly, by the sesoun of
 the yere, knowe the signe in which that is the
Rub To knowe which day is lik to which
RubA day as of lengthe.
 Loke whiche degrees ben ylike fer fro the
 hevedes of Cancer and Capricorne, and loke
 when the sonne is in eny of thilke degrees;
 than ben the dayes ylike of lengthe. This is
 to seyn that as longe is that day in that month,
 as was such a day in such a month; there varieth
 but litel.
 Also, yf thou take 2 dayes naturales in the
 yere ylike fer fro either point of the equinoxiall
10 in the opposyt parties, than as longe
 is the day artificiall of that oon day as is the
 night of that othir, and the contrarie.
Rub This chapitre is a maner declaracioun
RubA to conclusiouns that folewen.
 Understond wel that thy zodiak is departed
 in two halve circles, as fro the heved of Capricorne
 unto the heved of Cancer, and ageynward
 fro the heved of Cancer unto the heved
 of Capricorne. The heved of Capricorne is
 the lowest point where as the sonne goth in
 wynter, and the heved of Cancer is the heighist
 point in which the sonne goth in somer. And
 therfore understond wel that eny two degrees
10 that ben ylike fer fro eny of these two
 hevedes, truste wel that thilke two degrees
 ben of ilike declinacioun, be it southward or
 northward, and the daies of hem ben ilike of
 lengthe and the nyghtes also, and the shadewes
 ilyke, and the altitudes ylike atte midday
 for evere.
Rub To knowe the verrey degre of eny maner
RubA sterre, straunge or unstraunge, after his longitude;
RubB though he be indetermynat in thin
RubC Astralabye, sothly to the trouthe thus he shal
RubD be knowe.
 Tak the altitude of this sterre whan he is on
 the est syde of the lyne meridionall, as nye
 as thou mayst gesse; and tak an ascendent anon
 right by som manere sterre fix which that thou
 knowist; and forget not the altitude of the firste
 sterre ne thyn ascendent. And whan that this
 is don, aspye diligently whan this same firste
 sterre passith eny thyng the south westward;
 and cacche him anon right in the same
10 nombre of altitude on the west syde of this
 lyne meridional, as he was kaught on the
 est syde; and tak a newe ascendent anon-ryght
 by som maner sterre fix which that thou knowist,
 and forget not this secunde ascendent. And
 whan that this is don, rekne than how many
 degrees ben bitwixe the firste ascendent and
 the secunde ascendent; and rekne wel the myddel
 degre bitwene bothe ascendentes, and set
 thilke myddel degre upon thyn est orizonte;
20 and wayte than what degre that sitte upon
 the lyne meridional, and tak there the verrey
 degre of the ecliptik in which the sterre
 stondith for the tyme. For in the ecliptik is the
 longitude of a celestiall body rekned, evene
 fro the heved of Aries unto the ende of Pisces;
 and his latitude is rekned after the quantite of
 his declynacioun north or south toward the
 polys of this world.
 As thus: Yif it be of the sonne or of
30 eny fix sterre, rekne hys latitude or his
 declinacioun fro the equinoxiall cercle; and
 if it be of a planete, rekne than the quantite
 of his latitude fro the ecliptik lyne, all be it
 so that fro the equinoxiall may the declinacioun
 or the latitude of eny body celestiall be rekned
 after the site north or south and after the quantite
 of his declinacioun. And right so may the
 latitude or the declinacioun of eny body celestiall,
 saaf oonly of the sonne, after hys site
40 north or south and after the quantite of his
 declinacioun, be rekned fro the ecliptik
 lyne; fro which lyne alle planetes som tyme
 declinen north or south saaf oonly the forseide
Rub To knowe the degrees of longitudes of
RubA fixe sterres after that they be determynat in
RubB thin Astrelabye, yf so be that thei be trewly
RubC sette.
 Set the centre of the sterre upon the lyne
 meridionall, and tak kep of thy zodiak, and
 loke what degre of eny signe that sitte upon
 the same lyne meridionall at that same tyme,
 and tak there the degre in which the sterre
 stondith. and with that same degre cometh that
 same sterre unto that same lyne fro the orisonte.
Rub To knowe with which degre of the zodiak
RubA eny sterre fix in thin Astrelabie arisith
RubB upon the est orisonte, all though his dwellyng
RubC be in another signe.
 Set the centre of the sterre upon the est
 orisonte, and loke what degre of eny signe that
 sitt upon the same orisonte at that same tyme.
 And understond wel that with that same degre
 arisith that same sterre.
 And thys merveylous arisyng with a straunge
 degre in another signe is by cause that the
 latitude of the sterre fix is either north or south
 fro the equinoxiall. But sothly the latitudes
10 of planetes be comounly rekened fro the
 ecliptyk, by cause that noon of hem declyneth
 but fewe degrees out fro the brede of the
 zodiak. And tak god kep of this chapitre of
 arisyng of celestialle bodies; for truste wel that
 neyther mone ne sterre, as in our embelif
 orisonte, arisith with that same degre of his
 longitude saaf in oo cas, and that is whan they
 have no latitude fro the ecliptyk lyne. But
 natheles som tyme is everich of these planetes
20 under the same lyne.
Rub To knowe the declinacioun of eny degre
RubA in the zodiak fro the equinoxiall cercle.
 Set the degre of eny signe upon the lyne
 meridionall, and rekne hys altitude in the
 almykanteras fro the est orisonte up to the same
 degre set in the forseide lyne, and set there a
 prikke; turne up than thy riet, and set the heved
 of Aries or Libra in the same meridionall lyne,
 and set there a nother prikke. And whan that
 this is don, considre the altitudes of hem bothe;
 for sothly the difference of thilke altitudes
10 is the declinacioun of thilke degre fro the
 equinoxiall. And yf it so be that thilke degre
 be northward fro the equinoxiall, than is
 his declinacyoun north; yif it be southward,
 than is it south.
Rub To knowe for what latitude in eny regioun
RubA the almykanteras of eny table ben compowned.
 Rekene how many degrees of almykanteras
 in the meridionall lyne ben fro the cercle equinoxiall
 unto the cenyth, or elles from the pool
 artyk unto the north orisonte; and for so gret
 a latitude, or for so smal a latitude, is the table
Rub To knowe in speciall the latitude of
RubA oure countre, I mene after the latitude of Oxenford,
RubB and the height of oure pool.
 Understond wel that as fer is the heved of
 Aries or Libra in the equinoxiall fro oure orisonte
 as is the cenyth fro the pool artik; and
 as high is the pool artik fro the orisonte as the
 equinoxiall is fer fro the cenyth. I prove it
 thus by the latitude of Oxenford: understond
 wel that the height of oure pool artik fro oure
 north orisonte is 51 degrees and 50 mynutes;
 than is the cenyth fro oure pool artik 38 degrees
10 and 10 mynutes; than is the equinoxial
 from oure cenyth 51 degrees and 50
 mynutes; than is oure south orisonte from oure
 equinoxiall 38 degres and 10 mynutes. Understond
 wel this rekenyng. Also forget not
 that the cenyth is 90 degrees of height from
 the orisonte, and oure equinoxiall is 90 degres
 from oure pool artik. Also this shorte rule is
 soth, that the latitude of eny place in a regioun
 is the distaunce fro the cenyth unto
20 the equinoxiall.
Rub To prove evidently the latitude of eny
RubA place in a regioun by the preve of the height
RubB of the pool artik in that same place.
 In som wynters nyght whan the firmament
 is cler and thikke sterred, wayte a tyme til
 that eny sterre fix sitte lyne-right perpendiculer
 over the pool artik, and clepe that sterre A;
 and wayte another sterre that sitte lyne-right
 under A, and under the pool, and clepe that
 sterre F. And understond wel that F is not
 considrid but oonly to declare that A sitte
 evene over the pool. Tak than anoon-right
10 the altitude of A from the orisonte, and forget
 it not; let A and F goo fare wel tyl
 ageynst the dawenyng a gret while, and com
 than ageyn, and abid til that A is evene under
 the pool, and under F; for sothly than wol F
 sitte over the pool, and A wol sitte under the
 pool. Tak than eftsonys the altitude of A from
 the orisonte, and note as wel his secunde altitude
 as hys firste altitude. And whan that this
 is doon, rekene how many degrees that the
20 firste altitude of A excedith his secunde altitude,
 and tak half thilke porcioun that is
 excedid and adde it to his secunde altitude,
 and tak there the elevacioun of thy pool, and
 eke the latitude of thy regioun; for these two
 ben of oo nombre, this is to seyn, as many degres
 as thy pool is elevat, so muche is the latitude
 of the regioun.
 Ensample as thus: Peraventure the altitude of
 A in the evenyng is 56 degrees of height;
30 than wol his secunde altitude or the dawenyng
 be 48 degres, that is 8 degrees lasse
 than 56, that was his first altitude att even.
 Tak than the half of 8 and adde it to 48 that
 was his secunde altitude, and than hast thou
 52. Now hast thou the height of thy pool and
 the latitude of the regioun. But understond
 wel that to prove this conclusioun and many
 another faire conclusioun, thou must have a
 plomet hongyng on a lyne, heygher than
40 thin heved, on a perche; and thilke lyne
 must hange evene perpendiculer bytwixe
 the pool and thin eye; and than shalt thou
 seen yf A sitte evene over the pool, and over
 F atte evene; and also yf F sitte evene over the
 pool and over A or day.
Rub Another conclusioun to prove the
RubA height of the pool artik fro the orisonte.
 Tak eny sterre fix that never descendith under
 the orisonte in thilke regioun, and considre
 his heighist altitude and his lowist altitude
 fro the orisonte, and make a nombre of
 bothe these altitudes; tak than and abate half
 that nombre, and take there the elevacioun of
 the pool artik in that same regioun.
Rub Another conclusioun to prove the latitude
RubA of the regioun.
 Understond wel that the latitude of eny
 place in a regioun is verrely the space bytwixe
 the cenyth of hem that dwellen there and the
 equinoxiall cercle north or south, takyng the
 mesure in the meridional lyne, as shewith in
 the almykanteras of thin Astrelabye. And thilke
 space is as much as the pool artike is high in
 that same place fro the orisonte. And than is
 the depressioun of the pool antartik, that
10 is to seyn, than is the pool antartik, bynethe
 the orisonte the same quantite of
 space neither more ne lasse.
 Than if thou desire to knowe this latitude
 of the regioun, tak the altitude of the sonne
 in the myddel of the day, whan the sonne is
 in the hevedes of Aries or of Libra; for than
 moeveth the sonne in the lyne equinoxiall;
 and abate the nombre of that same sonnes altitude
 out of 90 degrees, and than is the
20 remenaunt of the nombre that leveth
 the latitude of the regioun. As thus:
 I suppose that the sonne is thilke day at
 noon 38 degrees of height; abate than 38
 degrees oute of 90; so leveth there 52; than is
 52 degrees the latitude. I say not this but for
 ensample; for wel I wot the latitude of Oxenford
 is certeyn minutes lasse; thow might
 preve the same.
 Now yf so be that the semeth to longe a
30 tarieng to abide til that the sonne be in the
 hevedes of Aries or of Libra, than wayte
 whan the sonne is in eny othir degre of the
 zodiak, and considre the degre of his declinacioun
 fro the equinoxiall lyne; and if it so be
 that the sonnes declinacioun be northward fro
 the equinoxiall, abate than fro the sonnes altitude
 at non the nombre of his declinacioun,
 and than hast thou the height of the hevedes
 of Aries and Libra. As thus: My sonne
40 is peraventure in the 10 degre of Leoun,
 almost 56 degrees of height at non,
 and his declinacioun is almost 18 degrees
 northward fro the equinoxiall; abate than thilke
 18 degrees of declinacioun out of the altitude
 at non; than leveth there 38 degrees and odde
 minutes. Lo there the heved of Aries or Libra
 and thin equinoxiall in that regioun. Also if
 so be that the sonnes declinacioun be southward
 fro the equinoxiall, adde than thilke
50 declinacioun to the altitude of the sonne at
 noon, and tak there the hevedes of Aries
 and Libra and thin equinoxial; abate than the
 height of the equinoxial out of 90 degrees;
 than leveth there the distance of the pool of
 that regioun fro the equinoxiall. Or elles, if
 the list, tak the highest altitude fro the equinoxial
 of eny sterre fix that thou knowist, and
 tak his netherest elongacioun (lengthing) fro
 the same equinoxial lyne, and work in the
60 manere forseid.
Rub Declaracioun of the ascensioun of
RubA signes.
 The excellence of the spere solide, amonges
 othir noble conclusiouns, shewith manyfest the
 diverse ascenciouns of signes in diverse places,
 as wel in the right cercle as in the embelif
 cercle. These auctours writen that thilke signe
 is cleped of right ascensioun with which more
 part of the cercle equinoxiall and lasse part of
 the zodiak ascendith. and thilke signe ascendith
 embelif with which lasse part of the
10 equinoxiall and more part of the zodiak
 ascendith. Ferther-over, they seyn that in
 thilke cuntrey where as the senith of hem that
 dwellen there is in the equinoxial lyne, and
 her orisonte passyng by the two poles of this
 world, thilke folk han this right cercle and
 the right orisonte; and evermore the arch of
 the day and the arch of the night is there ilike
 longe; and the sonne twies every yer passing
 thorugh the cenith of hir heed, and two
20 someres and two wynters in a yer han these
 forseide peple. And the almycanteras in
 her Astrelabyes ben streight as a lyne, so as
 shewith in the figure.
 The utilite to knowe the ascensions of signes
 in the right cercle is this: Truste wel that
 by mediacioun of thilke ascensions these astrologiens,
 by her tables and her instrumentes,
 knowen verreily the ascensioun of every degre
 and minute in all the zodiak in the embelif
30 cercle, as shal be shewed. And nota that
 this forseide right orisonte, that is clepid
 Orison Rectum, dividith the equinoxial into
 right angles; and the embelif orisonte, where
 as the pool is enhaunced upon the orisonte,
 overkervith the equinoxiall in embilif angles,
 as shewith in the figure.
Rub This is the conclusioun to knowe the
RubA ascensions of signes in the right cercle, that is
RubB circulus directus.
 Set the heved of what signe the lyst to knowe
 his ascendyng in the right cercle upon the lyne
 meridionall, and wayte where thyn almury
 touchith the bordure, and set there a prikke;
 turne than thy riet westward til that the ende
 of the forseide signe sitte upon the meridional
 lyne and eftsonys wayte where thin almury
 touchith the bordure, and set there another
 pricke. Rekene than the nombre of degres
10 in the bordure bitwixe bothe prikkes, and
 tak the ascensioun of the signe in the right
 cercle. And thus maist thou werke with every
 porcioun of thy zodiak.
Rub To knowe the ascensions of signes in the
RubA embelif cercle in every regioun, I mene, in
RubB circulo obliquo.
 Set the heved of the signe which as the list
 to knowe his ascensioun upon the est orisonte,
 and wayte where thin almury touchith the bordure,
 and there set a prikke. Turne than thy
 riet upward til that the ende of the same signe
 sitte upon the est orisonte, and wayte eftsonys
 where as thin almury touchith the bordure,
 and set there a nother prikke. Rekene than
 the nombre of degrees in the bordure bitwyxe
10 bothe prikkes and tak there the ascensioun
 of the signe in the embelif cercle.
 And understond wel that alle the signes in thy
 zodiak, fro the heved of Aries unto the ende
 of Virgo, ben clepid signes of the north fro
 the equinoxiall. And these signes arisen bitwyxe
 the verrey est and the verrey north in
 oure orisonte generaly for evere. And alle the
 signes fro the heved of Libra unto the ende
 of Pisces ben clepid signes of the south fro
20 the equinoxial; and these signes arisen
 evermore bitwixe the verrey est and the
 verrey south in oure orisonte. Also every signe
 bitwixe the heved of Capricorne unto the ende
 of Geminis arisith on oure orisonte in lasse
 than 2 houres equales. And these same signes
 fro the heved of Capricorne unto the ende of
 Geminis ben cleped tortuose signes, or croked
 signes, for thei arise embelyf on oure orisonte.
 And these croked signes ben obedient to
30 the signes that ben of right ascensioun.
 The signes of right ascencioun ben fro the
 heved of Cancer unto the ende of Sagittarie;
 and these signes arisen more upright, and thei
 ben called eke sovereyn signes and everich of
 hem arisith in more space than 2 houres. Of
 whiche signes Gemini obeieth to Cancer, and
 Taurus to Leo, Aries to Virgo, Pisces to Libra,
 Aquarius to Scorpioun, and Capricorne to Sagittarie.
 And thus evermore 2 signes that
40 ben ilike fer fro the heved of Capricorne
 obeyen everich of hem to othir.
Rub To knowe justly the 4 quarters of the
RubA world, as Est, West, North, and South.
 Tak the altitude of thy sonne whan the list,
 and note wel the quarter of the world in which
 the sonne is for the tyme by the azymutz.
 Turne than thin Astrelabie, and set the degre
 of the sonne in the almykanteras of his altitude
 on thilke syde that the sonne stant, as is the
 manere in takyng of houres, and ley thy label
 on the degre of the sonne; and rekene how
 many degrees of the bordure ben bitwixe
10 the lyne meridional and the point of thy
 label, and note wel that nombre. Turne
 than ageyn thin Astrelabie, and set the point
 of thy gret rule there thou takist thin altitudes
 upon as many degrees in his bordure fro his
 meridional as was the point of thy label fro
 the lyne meridional on the wombe side. Take
 than thin Astrelabie with bothe hondes sadly
 and slighly, and let the sonne shyne thorugh
 bothe holes of thy rule, and slighly in thilke
20 shynyng lat thin Astrelabie kouche adoun
 evene upon a smothe ground, and than wol
 the verrey lyne meridional of thin Astrelabie
 lye evene south, and the est lyne wol lye est,
 and the west lyne west, and the north lyne
 north, so that thou worke softly and avysely
 in the kouching. And thus hast thou the 4
 quarters of the firmament.
Rub To knowe the latitude of planetes fro
RubA the wey of the sonne, whethir so they be north
RubB or south fro the forseide wey.
 Loke whan that a planete is in the lyne
 meridional, yf that hir altitude be of the same
 height that is the degre of the sonne for that
 day, and than is the planete in the verrey wey
 of the sonne and hath no latitude. And if the
 altitude of the planete be heigher than the
 degre of the sonne, than is the planete north
 fro the wey of the sonne such a quantite of
 latitude as shewith by thin almykanteras.
10 And if the altitude of the planete be lasse
 than the degre of the sonne, than is the
 planete south fro the wey of the sonne such
 a quantite of latitude as shewith by thin
 almykanteras. This is to seyn, fro the wey
 where as the sonne went thilke day, but not
 fro the wey of the sonne in every place of the
Rub To knowe the cenyth of the arising of
RubA the sonne, this is to seyn, the partie of the
RubB orisonte in which that the sonne arisith.
 Thou must first considere that the sonne arisith
 not alwey verrey est, but somtyme by northe
 the est and somtyme by south the est. Sothly
 the sonne arisith nevere moo verrey est in oure
 orisonte, but he be in the heved of Aries or
 Libra. Now is thin orisonte departed in 24 parties
 by thin azimutes in significacioun of 24 parties
 of the world; al be it so that shipmen rekene
 thilke parties in 32. Than is there no
10 more but wayte in which azimut that thy
 sonne entrith at his arisyng, and take there
 the cenith of the arisyng of the sonne.
 The manere of the divisioun of thin Astrelabie
 is this, I mene as in this cas: First
 it is divided in 4 plages principalis with the
 lyne that goth from est to west; and than with
 another lyne that goth fro south to north; than
 is it divided in smale parties of azymutz, as est,
 and est by south, where as is the first azymut
20 above the est lyne; and so furth fro
 partie to partie til that thou come ageyn
 unto the est lyne. Thus maist thou understonde
 also the cenyth of eny sterre, in which partie
 he riseth.
Rub To knowe in which partie of the firmament
RubA is the conjunccyoun.
 Considere the tyme of the conjunccyoun by
 the kalender, as thus: Loke hou many houres
 thilke conjunccioun is fro the midday of the
 day precedent, as shewith by the canon of
 thy kalender. Rekene than thilke nombre of
 houres in the bordure of thin Astrelabie, as
 thou art wont to do in knowyng of the houres
 of the day or of the nyght, and ley thy label
 over the degre of the sonne, and than wol
10 the point of thy label sitte upon the houre
 of the conjunccioun. Loke than in which
 azymut the degre of thy sonne sittith, and in
 that partie of the firmament is the conjunccioun.
Rub To knowe the cenyth of the altitude of
RubA the sonne.
 This is no more to seyn but eny tyme of
 the day tak the altitude of the sonne, and by
 the azymut in which he stondith maist thou
 seen in which partie of the firmament he is.
 And the same wise maist thou seen by night,
 of eny sterre, wheither the sterre sitte est or
 west, or north or south, or eny partie bitwene,
 after the name of the azimut in which is the
Rub To knowe sothly the degre of the longitude
RubA of the mone, or of eny planete that hath
RubB no latitude for the tyme fro the ecliptik lyne.
 Tak the altitude of the mone, and rekne thy
 altitude up among thyn almykanteras on
 which syde that the mone stondith, and set
 there a prikke. Tak than anon-right upon the
 mones syde the altitude of eny sterre fix which
 that thou knowist, and set his centre upon his
 altitude among thyn almykanteras there the
 sterre is founde. Wayte than which degre of
 the zodiak touchith the prykke of the altitude
10 of the mone, and tak there the degre
 in which the mone stondith. This conclusioun
 is verrey soth, yf the sterres in thin
 Astrelabie stonden after the trouthe. Comoun
 tretes of the Astrelabie ne maken non excepcioun
 whether the mone have latitude or
 noon, ne on wheyther syde of the mone the
 altitude of the sterre fixe be taken.
 And nota that yf the mone shewe himself
 by light of day, than maist thou worche
20 this same conclusioun by the sonne, as wel
 as by the fixe sterre.
Rub This is the worchinge of the conclusioun
RubA to knowe yf that eny planete be direct
RubB or retrograd.
 Tak the altitude of eny sterre that is clepid
 a planete, and note it wel; and tak eke anon
 the altitude of any sterre fix that thou knowist,
 and note it wel also. Com than ageyn the
 thridde or the fourthe nyght next folewing, for
 than shalt thou perceyve wel the moeving of
 a planete, wheither so he moeve forward or
 bakward. Awayte wel than whan that thy
 sterre fixe is in the same altitude that she
10 was whan thou toke hir firste altitude.
 And tak than eft-sones the altitude of the
 forseide planete and note it wel; for truste wel
 yf so be that the planete be on the right syde
 of the meridional lyne, so that his secunde altitude
 be lasse than hys first altitude was, than
 is the planete direct; and yf he be on the west
 syde in that condicioun, than is he retrograd.
 And yf so be that this planete be upon the est
 side whan his altitude is ytaken, so that his
20 secunde altitude be more than his first altitude,
 than is he retrograd. And if he be on
 the west syde, than is he direct. But the contrarie
 of these parties is of the cours of the
 mone; for certis the mone moeveth the contrarie
 from othre planetes as in hir epicicle, but
 in noon othir manere.
Rub The conclusioun of equaciouns of
RubA houses after the Astrelabie.
 Set the begynnyng of the degre that ascendith
 upon the ende of the 8 houre inequal; than
 wol the begynnyng of the 2 hous sitte upon
 the lyne of mydnight. Remeve than the degre
 that ascendith, and set him on the ende of the
 10 houre inequal, and than wol the begynnyng
 of the 3 hous sitte up on the mydnight lyne.
 Bring up ageyn the same degre that ascended
 first, and set him upon the est orisonte, and
10 than wol the begynnyng of the 4 hous sitte
 upon the lyne of mydnight. Tak than the
 nader of the degre that first ascendid, and set
 him on the ende of the 2 houre inequal; and
 than wol the begynnyng of the 5 hous sitte
 upon the lyne of mydnight. Set than the nader
 of the ascendent on the ende of the 4 houre
 inequal, and than wol the begynnyng of the
 6 hous sitte on the mydnight lyne. The begynnyng
 of the 7 hous is nader of the ascendent,
20 and the begynnyng of the 8 hous
 is nader of the 2, and the begynnyng
 of the 9 hous is nader of the 3, and the begynnyng
 of the 10 hous is nader of the 4,
 and the begynnyng of the 11 hous is nader
 of the 5, and the begynnyng of the 12 hous
 is nader of the 6.
Rub Another maner of equaciouns of houses
RubA by the Astrelabye.
 Tak thin ascendent, and than hast thou thy
 4 angles; for wel thou wost that the opposit
 of thin ascendent, that is to seyn, the begynnyng
 of the 7 hous, sitt upon the west orisonte,
 and the begynnyng of the 10 hous sitt upon
 the lyne meridional, and his opposyt upon the
 lyne of mydnight. Than ley thy label over the
 degre that ascendith, and rekne fro the point
 of thy label alle the degrees in the bordure
10 tyl thou come to the meridional lyne; and
 departe alle thilke degrees in 3 evene parties,
 and take there the evene equacions of 3
 houses; for ley thy label over everich of these
 3 parties, and than maist thou se by thy label,
 in the zodiak, the begynnyng of everich
 of these same houses fro the ascendent; that
 is to seyn, the begynnyng of the 12 hous next
 above thin ascendent, the begynnyng of the
 11 hous, and than the 10 upon the meridional
20 lyne, as I first seide. The same wise
 worch thou fro the ascendent doun to the
 lyne of mydnyght, and thus hast thou othre
 3 houses; that is to seyn, the begynnyng of
 the 2, and the 3, and the 4 hous. Than is the
 nader of these 3 houses the begynnyng of the
 3 houses that folewen.
Rub To fynde the lyne meridional to dwelle
RubA fix in eny certeyn place.
 Tak a round plate of metal; for werpyng,
 the brodder the better; and make there upon
 a just compas a lite within the bordure. And
 ley this rounde plate upon an evene ground,
 or on an evene ston, or on an evene stok fix
 in the ground; and ley it evene by a level.
 And in the centre of the compas styke an
 evene pyn, or a wyr, upright, the smaller the
 better; set thy pyn by a plom-rule evene
10 upright, and let this pyn be no lenger than
 a quarter of the dyametre of thy compas,
 fro the centre amiddes. And wayte bisely
 aboute 10 or 11 of the clokke, whan the sonne
 shineth, whan the shadewe of the pyn entrith
 enythyng within the cercle of thy compas an
 heer-mele; and marke there a pricke with inke.
 Abid than stille waityng on the sonne til after
 1 of the clokke, til that the shadwe of the wyr,
 or of the pyn, passe enything out of the
20 cercle of the compas, be it nevere so lyte,
 and set there another pricke of ynke. Tak
 than a compas, and mesure evene the myddel
 bitwixe bothe prickes, and set there a prikke.
 Tak me than a rule and draw a strike evene
 a-lyne, fro the pyn unto the middel prikke; and
 tak there thi lyne meridional for evermore, as
 in that same place. And yif thou drawe a
 cross-lyne overthwart the compas justly over
 the lyne meridional, than hast thou est and
30 west and south, and par consequens,
 the opposit of the south lyne, i.e. the north.
Rub Descripcion of the meridional lyne, of
RubA longitudes and latitudes of citees and townes,
RubB as wel as of climates.
 Thys lyne meridional is but a maner descripcioun,
 or lyne ymagined, that passith upon the
 poles of this world and by the cenyth of oure
 heved. And it is cleped the lyne meridional,
 for in what place that eny man is at any tyme
 of the yer, whan that the sonne, by mevynge
 of the firmament, cometh to his verrey meridian
 place, than is it verrey mydday, that we clepen
 oure non, as to thilke man. And therfore
10 is it clepid the lyne of midday. And nota
 that evermore of eny 2 cytes or of 2 townes,
 of which that oo town approchith ner toward
 the est than doth that othir town, trust
 wel that thilke townes han diverse meridians.
 Nota also that the arch of the equinoxial that
 is contened or bownded bitwixe the 2 meridians
 is clepid the longitude of the toun. And
 yf so be that two townes have ilike meridian
 or oon meridian, than is the distaunce of
20 hem bothe ilike fer fro the est, and the contrarie;
 and in this manere thei change not
 her meridian. But sothly thei chaungen her
 almykanteras, for the enhaunsyng of the pool
 and the distance of the sonne.
 The longitude of a climat is a lyne ymagined
 fro est to west ilike distant fro the equinoxiall.
 And the latitude of a climat may be
 cleped the space of the erthe fro the begynnyng
 of the first clymat unto the verrey
30 ende of the same clymat evene direct
 ageyns the pool artyke. Thus sayn somme
 auctours; and somme of hem sayn that yf men
 clepe the latitude of a cuntrey the arch meridian
 that is contened or intercept bitwix the
 cenyth and the equinoxial, than say they that
 the distance fro the equinoxial unto the ende
 of a clymat evene ageynst the pool artik is the
 latitude of a clymat forsoothe.
Rub To knowe with which degre of the zodiak
RubA that eny planete ascendith on the orisonte,
RubB wheither so that his latitude be north
RubC or south.
 Know by thin almenak the degre of the
 ecliptik of eny signe in which that the planete
 is rekned for to be, and that is clepid the
 degre of his longitude. And know also the
 degre of his latitude fro the ecliptik north or
 south. And by these ensamples folewynge in
 speciall maist thou worche in general in every
 signe of the zodiak:
 The degree of the longitude peraventure
10 of Venus or of another planete was 1 of
 Capricorne, and the latitude of him was
 northward 4 degrees fro the ecliptik lyne. Than
 tok I a subtil compas, and clepid that oo point
 of my compas A, and that other point F. Than
 tok I the point of A and sette it in the ecliptik
 lyne in my zodiak in the degre of the longitude
 of Venus, that is to seyn, in the 1 degre
 of Capricorne; and than sette I the point of
 F upward in the same signe by cause that
20 latitude was north upon the latitude of
 Venus, that is to seyn, in the 4 degre fro the
 heved of Capricorne; and thus have I 4 degrees
 bitwixe my two prickes. Than leide I down
 softly my compas, and sette the degre of the
 longitude upon the orisonte; tho tok I and
 waxed my label in manere of a peire tables to
 receyve distinctly the prickes of my compas.
 Tho tok I thys forseide label, and leyde it fix
 over the degre of my longitude; tho tok I
30 up my compas and sette the point of A in
 the wax on my label, as evene as I koude
 gesse, over the ecliptik lyne in the ende of the
 longitude, and sette the point of F endelong
 in my label upon the space of the latitude,
 inward and over the zodiak, that is to seyn
 northward fro the ecliptik. Than leide I doun
 my compas, and loked wel in the wey upon
 the prickes of A and of F; tho turned I my ryet
 til that the pricke of F satt upon the orisonte;
40 than saw I wel that the body of
 Venus in hir latitude of 4 degrees septemtrionals
 ascendid, in the ende of the 8 degre,
 fro the heved of Capricorne.
 And nota that in this manere maist thou
 worche with any latitude septemtrional in alle
 signes. But sothly the latitude meridional of
 a planete in Capricorne ne may not be take by
 cause of the litel space bitwixe the ecliptyk
 and the bordure of the Astrelabie; but
50 sothely in all othre signes it may.
 Also the degre peraventure of Jupiter, or of
 another planete, was in the first degre of Piscis
 in longitude, and his latitude was 2 degrees
 meridional; tho tok I the point of A and sette
 it in the first degre of Piscis on the ecliptik;
 and than sette I the point of F dounward in
 the same signe by cause that the latitude was
 south 2 degres, that is to seyn, fro the heved
 of Piscis; and thus have I 2 degres bitwixe
60 bothe prikkes. Than sette I the degre of
 the longitude upon the orisonte; tho tok I
 my label, and leide it fix upon the degre of the
 longitude; tho sette I the point of A on my
 label evene over the ecliptik lyne in the ende
 of the degre of the longitude, and sette the
 point of F endlong in my label the space of
 2 degres of the latitude outward fro the zodiak
 (this is to seyn southward fro the ecliptik toward
 the bordure), and turned my riet
70 til that the pricke of F saat upon the orisonte.
 Than say I wel that the body of
 Jupiter in his latitude of 2 degrees meridional
 ascendid with 8 degres of Piscis in horoscopo.
 And in this manere maist thou worche with
 any latitude meridional, as I first seide, save in
 Capricorne. And yif thou wilt pleye this craft
 with the arisyng of the mone, loke thou rekne
 wel hir cours houre by houre, for she ne dwellith
 not in a degre of hir longitude but litel
80 while, as thow wel knowist. But natheles
 yf thou rekne hir verrey moevyng by thy
 tables houre after houre, [thou shalt do wel
Rub Umbra Recta.
 Yif it so be that thou wilt werke by umbra
 recta, and thou may come to the bas of the
 tour, in this maner shalt thou werke. Tak the
 altitude of the tour by bothe holes, so that
 thy rewle ligge even in a poynt. Ensample as
 thus: I see him thorw at the poynt of 4; than
 mete I the space betwixe me and the tour,
 and I finde it 20 foot; than beholde I how 4
 is to 12, right so is the space betwixe thee
110 and the tour to the altitude of the tour.
 For 4 is the thridde part of 12, so is the
 space between thee and the tour the thridde
 part of the altitude of the tour; than thryes 20
 foot is the heyghte of the tour, with adding of
 thyn owne persone to thyn eye. And this rewle
 is general in umbra recta, fro the poynt of
 oon to 12. And yif thy rewle falle upon 5, than
 is 5 12-partyes of the heyght the space between
 thee and the tour; with adding of
120 thyn owne heyghte.
Rub Umbra Versa.
 Another maner of the werkinge, by umbra
 versa. Yif so be that thou may nat come to
 the bas of the tour, I see him thorw at the nombre
 of 1; I sette ther a prikke at my fot; than
 go I neer to the tour, and I see him thorw at
 the poynt of 2, and there I sette another prikke;
 and I beholde how 1 hath him to 12, and ther
 finde I that it hath him twelfe sythes; than
 beholde I how 2 hath him to 12, and thou
110 shalt finde it sexe sythes; than thou shalt
 finde that 12 passith 6 by the numbre of
 6; right so is the space between thy two prikkes
 the space of 6 tymes thyn altitude. And note,
 that at the ferste altitude of 1, thou settest a
 prikke; and afterward, whan thou seest him at
 2, ther thou settest another prikke; than thou
 findest betwyx thes two prikkys 60 foot; than
 thou shalt finde that 10 is the 6-party of 60.
 And then is 10 feet the altitude of the tour.
120 For other poyntis, yif it fille in umbra versa,
 as thus: I sette caas it fill upon 2, and at
 the secunde upon 3; than schalt thou finde
 that 2 is 6 partyes of 12; and 3 is 4 partyes of
 12; than passeth 6 4, by nombre of 2; so is the
 space between two prikkes twyes the heyghte
 of the tour. And yif the differens were thryes,
 than shulde it be three tymes; and thus mayst
 thou werke fro 1 to 12; and yif it be 4, 4 tymes;
 or 5, 5 tymes; et sic de ceteris.
Rub Umbra Recta.
 Another maner of wyrking, by umbra recta:
 Yif it so be that thou mayst nat come to the
 baas of the tour, in this maner thou schalt
 werke. Set thy rewle upon 1 till thou see the
 altitude, and set at thy foot a prikke. Than
 set thy rewle upon 2, and behold what is the
 differense between 1 and 2, and thou shalt
 finde that it is 1. Than mete the space between
 two prikkes, and that is the 12 partie
10 of the altitude of the tour. And yif ther
 were 2, it were the 6 partye; and yif ther
 were 3, the 4 partye; et sic deinceps. And
 note, yif it were 5, it were the 5 party of 12;
 and 7, 7 party of 12; and note, at the altitude
 of thy conclusion, adde the stature of thyn
 heyghte to thyn eye.
Rub Another maner conclusion, to knowe
RubA the mene mote and the argumentis of any
RubB planete. To know the mene mote and the argumentis
RubC of every planete fro yeer to yeer, from
RubD day to day, from houre to houre, and from
RubE smale fraccionis infinite.
 In this maner shalt thou worche; consider
 thy rote first, the whiche is made the beginning
 of the tables fro the yer of oure Lord
 1397, and enter hit into thy slate for the laste
 meridie of December; and than consider the
 yer of oure Lord, what is the date, and behold
 whether thy date be more or lasse than the
 yer 1397. And yf hit so be that hit be more,
 loke how many yeres hit passeth, and with
10 so many enter into thy tables in the first
 lyne theras is writen anni collecti et expansi.
 And loke where the same planet is
 writen in the hed of thy table, and than loke
 what thou findest in direct of the same yer of
 oure Lord which is passid, be hit 8, or 9, or
 10, or what nombre that evere it be, til the
 tyme that thou come to 20, or 40, or 60. And
 that thou findest in direct wryt in thy slate under
 thy rote, and adde hit togeder, and that is
20 thy mene mote, for the laste meridian of
 the December, for the same yer which that
 thou hast purposed. And if hit so be that hit
 passe 20, consider wel that fro 1 to 20 ben
 anni expansi, and fro 20 to 3000 ben anni collecti;
 and if thy nomber passe 20, than tak that
 thou findest in direct of 20, and if hit be more,
 as 6 or 18, than tak that thou findest in direct
 thereof, that is to sayen, signes, degrees, minutes,
 and secoundes, and adde togedere
30 unto thy rote; and thus to make rotes. And
 note, that if hit so be that the yer of oure
 Lord be lasse than the rote, which is the yer
 of oure Lord 1397, than shalt thou wryte in
 the same wyse first thy rote in thy slate, and
 after enter into thy table in the same yer that
 be lasse, as I taught before; and than consider
 how many signes, degrees, minutes, and secoundes
 thyn entringe conteyneth. And so be
 that ther be 2 entrees, than adde hem togeder,
40 and after withdraw hem from the
 rote, the yer of oure Lord 1397; and the
 residue that leveth is thy mene mote for the
 laste meridie of December, the whiche thou
 hast purposid; and if hit so be that thou wolt
 witen thy mene mote for any day, or for any
 fraccioun of day, in this maner thou shalt
 worche. Make thy rote fro the laste day of
 December in the maner as I have taught,
 and afterward behold how many monethes,
50 dayes, and houres ben passid from the
 meridie of December, and with that enter
 with the laste moneth that is ful passed, and
 take that thou findest in direct of him, and
 wryt hit in thy slate; and enter with as mony
 dayes as be more, and wryt that thou findest
 in direct of the same planete that thou worchest
 for; and in the same wyse in the table of
 houres, for houres that ben passed, and adde
 alle these to thy rote; and the residue is the
60 mene mote for the same day and the same
Rub Another manere to knowe the mene
RubA mote.
 Whan thou wolt make the mene mote of eny
 planete to be by Arsechieles tables, tak thy
 rote, the which is for the yer of oure Lord
 1397; and if so be that thy yer be passid the
 date, wryt that date, and than wryt the nomber
 of the yeres. Than withdraw the yeres
 out of the yeres that ben passed that rote.
 Ensampul as thus: the yer of oure Lord 1400,
 I wolde wyten, precise, my rote; than wrot
10 I first 1400. And under that nomber I
 wrot a 1397; than withdrow I the laste
 nomber out of that, and than fond I the residue
 was 3 yer; I wiste that 3 yer was passed
 fro the rote, the which was writen in my
 tables. Than afterward soghte I in my tables
 the annis collectis et expansis, and among myn
 expanse yeres fond I 3 yeer. Than tok I alle
 the signes, degrees, and minutes, that I fond
 direct under the same planete that I
20 wroghte for, and wrot so many signes,
 degrees, and minutes in my slate, and afterward
 added I to signes, degrees, minutes, and
 secoundes, the whiche I fond in my rote the
 yer of oure Lord 1397; and kepte the residue;
 and than had I the mene mote for the laste
 day of December. And if thou woldest wete
 the mene mote of any planete in March, April,
 or May, other in any other tyme or moneth of
 the yer, loke how many monethes and
30 dayes ben passed from the laste day of December,
 the yer of oure Lord 1400; and so
 with monethis and dayes enter into thy table
 ther thou findest thy mene mote iwriten in
 monethes and dayes, and tak alle the signes,
 degrees, minutes, and secoundes that thou findest
 ywrite in direct of thy monethes, and adde
 to signes, degrees, minutes, and secoundes that
 thou findest with thy rote the yer of oure
 Lord 1400, and the residue that leveth is the
40 mene mote for that same day. And note,
 if hit so be that thou woldest wite the mene
 mote in any yer that is lasse than thy rote,
 withdraw the nomber of so many yeres as hit
 is lasse than the yer of oure Lord a 1397, and
 kep the residue; and so many yeres, monethes,
 and dayes enter into thy tables of thy mene
 mote. And tak alle the signes, degrees, and
 minutes, and secoundes, that thou findest in
 direct of alle the yeres, monethes, and
50 dayes, and wryt hem in thy slate; and
 above thilke nomber wryt the signes, degrees,
 minutes, and secoundes, the which thou
 findest with thy rote the yer of oure Lord a
 1397; and withdraw alle the nethere signes
 and degrees fro the signes and degrees, minutes,
 and secoundes of other signes with thy
 rote; and thy residue that leveth is thy mene
 mote for that day.
Rub For to knowe at what houre of the day,
RubA or of the night, shal be flod or ebbe.
 First wite thou certeinly, hou that haven
 stondeth, that thou list to werke for; that is
 to say in which place of the firmament the
 mone beyng, makith full see. Than awayte
 thou redily in what degree of the zodiak that
 the mone at that tyme is ynne. Bring furth
 than the label, and set the point therof in
 that same cost that the mone makith flod, and
 set thou there the degree of the mone according
10 with the egge of the label. Than
 afterward awayte where is than the degree
 of the sonne, at that tyme. Remeve thou than
 the label fro the mone, and bring and set it
 justly upon the degree of the sonne. And the
 point of the label shal than declare to thee, at
 what houre of the day or of the night shal
 be flod. And there also maist thou wite by the
 same point of the label, whethir it be, at that
 same tyme, flod or ebbe, or half flod, or
20 quarter flod, or ebbe, or half or quarter
 ebbe; or ellis at what houre it was last, or
 shal be next by night or by day, thou than
 shalt esely knowe, &c. Furthermore, if it so
 be that thou happe to worke for this matere
 aboute the tyme of the conjunccioun, bring
 furth the degree of the mone with the label
 to that coste as it is before seyd. But than thou
 shalt understonde that thou may not bringe
 furth the label fro the degree of the mone
30 as thou dide before; for-why the sonne is
 than in the same degree with the mone.
 And so thou may at that tyme by the point of
 the label unremevid knowe the houre of the
 flod or of the ebbe, as it is before seyd, &c.
 And evermore as thou findest the mone passe
 fro the sonne, so remeve thou the label than
 fro the degree of the mone, and bring it to
 the degree of the sonne. And work thou than
 as thou dide before, &c. Or ellis know
40 thou what houre it is that thou art inne,
 by thyn instrument. Than bring thou furth
 fro thennes the label and ley it upon the degree
 of the mone, and therby may thou wite
 also whan it was flod, or whan it wol be next,
 be it night or day; &c.

Next: Fragment A