Treatise on The Astrolabe : addressed to his son Lowys / by Geoffrey Chaucer ; edited from the earliest MSS. by Walter W. Skeat

[folio 9]

Her bygynnen the conclusions of the Astrelabie.

1. To fynde the degree in which the sonne is day by day, after hir cours a-bowte.

[Hic incipiunt conclusiones astrolabii; & prima est ad inveniendum gradus solis in quibus singulis diebus secundum cursum sol est existens.]

¶ Rekene and knowe which is the day of thi monthe ¶ & ley thi reule vp that same day, & thanne wol the verray point of thy rewle sitten in the bordure, vp-on the degree of thy sonne. ¶ Ensample as thus ; the yer of oure lord 1391, the 12 day of March at Midday, I wolde knowe the degree of the sonne. ¶ I sowhte in the bakhalf of myn astrelabie, and fond the sercle of the daies, ¶ the which I knowe by the names of the Monthes writen vndur the same Cercle. ¶ Tho leide I my rewle ouer this forseide day, & fond the

point of my rewle in the bordure vp-on the firste degree of aries, A litel with-in the degree / & thus knowe I this conclusioun. ¶ A-nother day, I wolde knowe the degree of my sonne, & this was at Midday in the 13. day of decembre ; I fond the day of the monthe in maner as I seide / tho leide I my rewle vp-on this forseide 13. day, & found the point of my rewle in the bordure vp-on the first degree of capricorne / a lite with-in the degree ¶ & than haddy of this conclusioun the ful experience / & for the more declaracioun, lo her thi figure.

[folio 9b]

2. To knowe the altitude of the sonne, or of othre celestial bodies.

[De altitudine solis & aliorum corporum supra celestium.]

¶ Put the ring of thin Astrelabie vp-on thi riht thowmbe & turne thi lift side a-gayn the light of the sonne/ And rem[e]ue thi rewle vp and down til þat the stremes of the sonne shyne thorgh bothe holes of thi rewle. ¶ loke thanne how Many degrees thi rewle is a-reised fro the litel crois vp-on thin est line, & tak ther the altitude of thi sonne. ¶ & in this same wyse maistow knowe by nyhte the altitude of the Mone, or of brihte sterres / this chapitre is so general euer in on, þat ther nedith no more declaracion; but for-get it nat. ¶ & for the more declaracioun, lo here the figure.

[folio 10]

3. To knowe euery tyme of the day by liht of the sonne, & euery tyme of the nyht by the sterres fixe, & eke to knowe by nyht or by day the degree of any signe þat assendith on the est Orisonte, which þat is cleped communly the assendent or elles oruscupum.

[Ad cognoscendum quidlibet tempus diei per solis indicacionem, & quodlibet tempus noctis per quasdam stellas in celo fixas; ac eciam ad inveniendum & cognoscendum signum super orizontem qui communiter vocatur ascendens.]

¶ Tak the altitude of the sonne whan the list, as I haue said ; ¶ & set the degree of the sonne, in kas þat it be by-forn the Middel of the day, among thin al-my-kanteras on the est side of thin astralabie ; & ȝif it be after the Middel of the day, set the degree of thy sonne vp-on the west side / tak this manere of settyng for a general rewle, ones for euere. ¶ & whan thow hast set the degree of thy sonne vp as many Almykanteras of heyhte as was the altitude of the sonne takyn by thi rewle, ¶ ley ouer thi label, vp-on the degree of the sonne; ¶ & thanne wol the point of thi label sit[t]en in the bordure, vp-on the verrey tid of the day. Ensample as thus / the yer of owre lord 1391, the 12 day of March, I wold knowe the tyd of the day. I tok the altitude of my sonne, ¶ & fond þat it was 25 degrees and 30 of Minutes of heyhte in the bordure on the bak-side. ¶ tho turnede I Myn astrelabie, & by cause that it was by-forn̄ Midday, I turnede Mi riet and sette the degree of the sonne, that is to seyn the .1. degree of Aries / on the riht side of myn Astralabie, vp-on þat 25 degrees & 30 of Minutes of heyhte among myn almy-kanteras / tho leide I my label vp-on the degree of my sonne, & fond the poynte [folio 10b] of my label in the bordure, vp-on a capital lettre þat is cleped an X; tho rekened I alle the capitalles lettres fro the lyne of Midnyght vn-to this forseide lettre X, & fond þat it was 9 of the clokke of the day. tho loked I do[w]n vp-on the Est Orisonte, and fond there the 20 degree of gemynis assending ;

which þat I tok for Myn assendent. & in this wyse hadde I the experience for euer-mo in wich maner I sholde knowe the tyde of the day / & ek myn assendent. ¶ Tho wold I wyte the same nyght folwyng the howr of the nyght / & wrowhte in this wyse / among an hep of sterris fixe, it liked me for to take the altitude of the feire white sterre þat is cleped Alhabor / and fond hir sitting on the west side of the line of Midday, 18 degres of heyhte taken by my rewle on the bak-side. ¶ tho sette I the centre of this Alhabor vp-on 18 degrees among myn Almy-kanteras, vp-on the west side ; by cause þat she was fonden on the west side. tho leide I my label ouer the degree of the sonne þat was descended vnder the weste Orisonte, ¶ & rikened alle the lettres capitals fro the lyne of Midday vn-to þe point of my label in the bordure; ¶ & fond þat it was passed 8 of the clokke the space of 2 degrees / tho loked I doun vp-on myn est orisonte, ¶ & fond ther 23 degrees of libra assending, whom I tok for myn assendent; & thus lerned I to knowe ones for euer in which Manere I shuld come to the howre of the nyht / and to myn assendent; as verreyli as may be taken by so smal [an] instrument / but natheles in general wold I warne the for euere / ne mak the neuere bold to haue take a Iust Ascendent by thin Astrilabie, or elles to haue sette Iustly a clokke, whan any celestial body by which þat thow wenest gouer e thilke thynges ben ney the sowth lyne / for trust wel, whan þat þe sonne is ney the Meridional lyne, the degree of the sonne rennyth so longe consentrik vp-on the almy-kanteras, þat sothly thow shalt erre fro the Iust assendent / the same conclusioun sey I by þe centre of any sterre fix by nyht; and more-ouer, by experience, I wot wel that in owre Orisonte, from .xi. of the clokke vn-to on of the

clokke, in takyng of a Iust assendent in A portatif Astrelabie, hit is to hard to knowe. I mene, from .xi. of the clokke by-forn the howre of noon til on of the clok next folwyng. ¶ & for the more declaracion, lo her thi figure.

[folio 11]

4. Special declaracion of the assendent.

[Specialis declaracio de ascendente.]

¶ The assendent sothly, as wel in alle natiuitez as in questiouns & elecciouns of tymes, is a thing which þat thise Astrologiens gretly obseruen / wher-fore me semeth conuenient, sin þat I speke of the assendent, to make of it special declaracioun / The assendent sothly, to take it at the [largeste], is thilke degree þat assendith at any of thise forseide tymes v[po]n the est Orisonte; & there-for, yif þat any planet assende at þat same tyme in thilke for-seide [degre of] his longitude, Men seyn þat thilke planete is in horoscopo. ¶ but sothly, the hows of the assendent, þat is to seyn, the firste hous or the est Angle, is a thing more brod & large. ¶ For after the statutz of Astrologiens, what celestial body þat is 5 degres a-boue thilk degre þat assendith, or with-in þat nowmbre, þat is to seyn, nere the degree þat assendith / yit rikne thei thilke planet in the Assendent. ¶ And what planete þat is vnder thilke degree þat assendith the space of [25] degrees, ¶ yit sein thei that thilke planete is lyk to him þat is [in] the hows of the assendent / but sothly, yif he passe the bondes of thise forseide spaces, a-boue or by-nethe, they sein þat the planete is failling fro the assendent; / yit sein thise Astrolog[i]ens, that the assendent ¶ & eke the lord of the assendent, may be shapen for to be fortunat or infortunat / as thus / a fortunat assendent clepen they whan þat no wykkid planete, as saturne or Mars, or elles the tail of the dragoun, is in [þe] hows [folio 11b] of the assendent, ne þat no wikked planete haue non aspecte of enemyte vp-on the assendent ; but they wol caste þat thei haue a fortunat planete in hir assendent & ȝit in his felicite, ¶ & than sey they þat it is wel. ¶ fortherouer,

they seyn þat the infortunyng of an assendent is the contrarie of this forseide thinges. ¶ the lord of the assendent sey they þat he is fortunat, whan he is in god place fro the assendent as in angle; or in a succedent, where-as he is in his dignite & conforted with frendly aspectys of planetes & [wel] resceiued, & ek that he may sen the assendent, and þat he be nat retrograd ne combust, ne ioigned with no shrewe in the same signe / ne that he be nat in his des[c]encioun, ne ioigned with no planete in his discencioun, ne haue vp-on him non aspecte infortunat; & [than] sey they þat he is wel. ¶ natheles, theise ben obseruauncez of iudicial matiere & rytes of paiens, in which my spirit ne hath no feith, ne no knowyng of hir horoscopum; for they seyn þat euery signe is departid in 3 euene parties by [10] degrees, & thilke porcioun they clepe a face. ¶ & al-thogh þat a planete haue a latitude fro the Ecliptik, yit sey [some folk] so þat the planete arise in þat same signe wyth any degree of the forseide face in which [h]is longitude is rekned, þat yit is the planete in horoscopo / be it in natiuite or in eleccioun, &c. ¶ & for the more declaracioun, lo here the figure.

5. To knowe the verrey equacioun of the degree of the sonne, yif so be þat it falle by-twixe thin Almykanteras.

[Ad cognoscendum veram equacionem de gradu solis, si contigerit fore in duas Almicanteras.]

[folio 12]

¶ For as moche as the almykanteras in thin astrelabie ben compownet by two & two, ¶ where-as some Almykanteras in sondri Astrelabies ben compownet by on and on, or elles by 2 & 2, it is necessarie to thy lernyng to teche the first to knowe & worke with thin owne Instrument. ¶ where-for, whan þat the degreee of thy sonne falleth by-twixe two Almykanteras / or elles yif thin Almykanteras ben grauen with ouer gret a point of a compas / for bothe thise thinges may causen errour as wel in knowyng of the tid of the day as of the verrey Assendent / thow Most werken in this wise.

¶ Set the degree [of] thy sonne vp-on the heyer Almykanteras of bothe / & waite wel wher as thin Almury towcheth the bordure, & set ther a prikke of ynke ¶ Set down agayn the degree of thy sonne vp-on the nethere Almy-kanteras of bothe / & set ther another prikke. ¶ remewe thanne thin Almury in the bordure euene amiddes bothe prikkes / & this wol lede iustly the degree of thi sonne to sitte by-twixe bothe Almykanteras in his riht place. ¶ ley thanne thy label ouer the degree of thy sonne ; & find in the bordure the verrey tide of the day or of the nyht. ¶ & as verreyly shaltow fynde vp-on thin est orisonte thyn assendent ¶ & for more declaracioun, lo here thi figure.

[folio 12b]

6. To knowe the spring of the dawyng & the ende of the euenyng, the which ben called the two crepusculus :

[Ad cognoscendum ortum solis & eius occasum, que uocatur vulgariter crepusculum.]

¶ Set the nadir of thy sonne vp-on 18 degrees of heyhte / Among thyn Almykanteras on the west side, & ley thy label on þe degre of thy sonne, & thanne shal the poynt of thi label schewe the spryng of day. ¶ Also set the nadir of thy sonne vp-on 18 degres of heyhte a-mong thin Almykanteras on the [est] side, & ley ouer thy label vp-on the degree of the sonne / & with the point of thy label fynd in the bordure the ende of the euenyng, þat is, verrey nyht. the nadir of the sonne is thilke degree þat is opposit to the degree of the sonne, in the 7 signe, as thus / euery degree of aries bi ordre is nadir to euery degree of libra by ordre / & taurus to Scorpion / gemini to Sagittare / Cancer to Capricorne / leo to aquarie / virgo to pisces / & ȝif any degree in thi zodiak be dirk, [h]is nadire shal declare him. ¶ & for the more declaracioun, lo heere thi figure.

7. To knowe the arch of the day, that some folk kallen the day artificial, from the sonne arisyng til hit go to rest[e].

[Ad cognoscendum archum diei, quem vu1gus vocat diem artificialem in hoc ab ortu solis vsque ad occasum.]

¶ Set the degree of thy sonne vp-on thin Est orisonte, & ley thy label on the degree of the sonne, & at the poynt of thy label in the bordure set a prikke. ¶ Turn̄ thanne thi riet aboute til the degree [folio 13] of the sonne sit vp-on the west Orisonte, & ley thi label vp-on the same degree of the sonne, & at the point of thi label set a-nother prikke. ¶ rekne thanne the quantite of tyme in the bordure by-twixe bothe prikkes, & tak ther thin ark of the day. ¶ the remenant of the bordure vnder the Orisonte is the ark of the nyht. ¶ thus maistow rekne bothe arches / or euery porcion, of wheither þat the liketh. ¶ & by this Manere of wyrkyng / Maistow se how longe þat any sterre fix dwellith a-boue the erthe, fro tyme þat he risith til he go to rest . ¶ but the day natural, þat is to seyn 24 houris, is the reuolucioun of the equinoxial with as moche partie of the zodiak as the sonne of his propre Moeuinge passeth in the mene while. ¶ & for the more declaracioun, lo her thi figure.

8. To turn̄ the howres in-equales in howres equales.

[Ad conuertendum horas inequales in horas equales.]

¶ Knowe the nombre of the degrees in the howris in-equales, & departe hem by 15, & tak ther thin howris equales. [¶ & for the more declaracioun, lo here thi figure.]

[folio 13b]

9. To knowe the quantite of the day vulgare, that is to seyen, from spring of the day vn-to verrey nyht.

[Ad cognoscendum qaantitatem diei vulgaris, viz. ab ortu diei vsque ad noctem.]

¶ Know the quantite of thi crepusculis, as I haue tawht in the chapitre by-forn, & adde hem to the arch of thi day artificial / & tak ther the space of alle the hole day vulgar, vn-to verrey nyht. / The same manere maistow worke to knowe the quantite of the vulgar nyht. / & for the more declaracioun, lo here the figure.

10. To knowe the quantite of howres in-equales by day.

[Ad cognoscendum horas inequale[s] in die.]

¶ Vnderstond wel, þat thise howris in-equalis ben cleped howres of planetes, & vnderstond wel þat som tyme ben thei lengere by day [than] by nyht, & som tyme the contrarie. ¶ but vnderstond wel þat euermo generaly þe howr in-equal of the [day with þe howr in-equal of the] nyght contenen [30] degrees of tho bordure, whiche bordure is euer-mo answering to the degrees of the equinoxial ; wherfor departe the arch of the day artificial in 12, & tak ther the quantite of the howr in-equal by day. ¶ & ȝif thow abate the quantite of the howr in-equal by daye owt of 30 / than shal the remenant þat leueth performe the howr inequal by nyght. ¶ & for the more declaracioun, lo here the figure.

[folio 14]

11. To knowe the quantite of howres equales.

[Ad cognoscendum quantitatem horarum inequalium.]

¶ The quantite of howres equales, þat is to seyn, the howres of the clokke / ben departid by 15 degrees al-redy in the bordure

of thin astalabie, as wel by nyht as by day, generaly for euere. ¶ What nedith more declaracioun? ¶ Wher-for, whan the list to know how manye howres of the clokke ben passed, or any part of any of thise howris þat ben passed, ¶ or elles how many howres or partie of howres ben to come, fro swich a tyme to swych a tyme, by day or by nyhte, ¶ knowe the degree of thy sonne, & ley thy label on it / turne thi Riet abowte ioyntly with thy label, & with the point of it rekne in the bordure fro the sonne arise vn-to the same place ther thow desirest, by day as by nyhte / this conclusioun wol I declare in the laste chapitre of the [4] partie of this tretis so openly, þat [þer] shal lakke no worde þat nedith to the declaracioun. ¶ & for the more declaracioun, lo here the figure.

12. Special declarcioun of the howres of planetes.

Specialis declaracio de horis planetarum.]

¶ Vnderstond wel, þat euere-mo fro the arising of [the] sonne til it go to reste / the nader of the sonne shal shewe the howr of the planete / & fro that tyme forward / al the nyht til the sonne arise / than shal the verrey degree of the sonne shewe the howr of the planete. Ensample as thus. ¶ the xiij. day of March fil vp-on a saterday per auenture / & at the arising of the sonne, I fond the secounde degree of aries sitting vp-on myn est Orisonte, al be it þat it was but lite; [folio 14b] than fond I the [2] degree of libra, nadir of my sonne, dessending on my west Orisonte, vp-on which west Orisonte euery day generally, at the sonne ariste, entrith the howr of any planete, after which planete the day berith his name; ¶ & endith in

the nexte strik of the plate vnder the forseide west Orisonte / & euere as the sonne clymbith vppere & vppere, so goth his nadir downere & downere, techyng by swych strikes the howres of planetes by ordre as thei sitten in the heuene. the first howr inequal of euery Satterd[a]y is to Saturne ; ¶ & the secounde to Iupiter; ¶ the 3 to Mars ; the 4 to the sonne ; ¶ the 5 to venus ; ¶ the 6 to Mercurius; ¶ the 7 to the mone ; ¶ & thanne agayn the 8 is to saturne ; ¶ the 9 to Iupiter; ¶ the 10 to Mars ; ¶ the 11 to the sonne; ¶ the 12 to venus ; ¶ And now is my sonne gon to reste as for that setterday. ¶ Thanne shewyth the verrey degree of the sonne the howr of Mercurie entryng vnder my west orisonte at eue; ¶ & next him succedith the Mone ; ¶ & so forth by ordre, planete aftur planete, in howr after howr, a1 the nyht longe til the sonne arise. ¶ now risith the sonne þat Sonday be the morwe ; ¶ & the nadir of the sonne vp-on the west Orizonte shewith me the entring of the howre of the forseide sonne. ¶ & in this maner succedith planete vnder planete, fro saturne vn-to the mone, & fro the mone vp a-gayn to satourne, howre after howre generaly. ¶ & thus know[e] I this conclusioun. ¶ & for the more declaracioun, lo here the figure.

[folio 15]

13. To knowe the altitude of the sonne in Middes of the day, that is cleped the altitude Meridian.

[Ad cognoscendum altitudinem solis in medio diei, que vocatur altitudo meridiana.]

¶ Set the degree of the sonne vp-on the lyne Meridional, & rikene how many degrees of Almykanteras ben by-twyxe thyn est Orisonte & the degree of the sonne. ¶ & tak ther thyn altitude Meridian / this [is] to seyne, the heiest of the sonne as for that day. ¶ So maistow knowe in the same lyne, the heiest cours þat any sterre fix clymbith by nyht ; ¶ this is to seyn, þat w[h]an any sterre fix is passed the lyne Meridional, than by-gynnyth it to descende, & so doth the sonne. ¶ & for the more declaracioun, lo here thi figure.

14. To knowe the degree of the sonne by thy riet, for a maner curiosite, &c.

[Ad cognoscendum gradum solis curiose.]

¶ Sek bysily with thi rewle the heiest of the sonne in Midde of the day ; ¶ turne thanne thyn Astrelabie, & with a prikke of ynk marke the nombre of þat same Altitude in the lyne Meridiona1. turne thanne thy Ryet a-bowte til thow fynde a degree of thi zodiak acording with the prikke, ¶ this is to seyn, sittynge on the prikke ; ¶ & in soth, thow shalt fynde but 2 degrees in a1 the zodiak of that condicioun; ¶ & yit thilke 2 degrees ben in diuerse signes; ¶ than maistow lyhtly by the sesoun of the yere knowe the signe in whiche þat is the sonne. [¶ & for the more declaracioun, lo here thi figure.]

[folio 15b]

15. To know which day is lik to wych day as of lengthe, &c.

[Ad cognoscendum quales dies in longitudine sunt similes.]

¶ Loke whiche degrees ben illik fer fro the heuedes of Cancer & Capricorn̛ ; & lok, whan the sonne is in any of thilke degrees, than ben the dayes ilike of lengthe. ¶ this is to seyn, þat as long is þat day in þat Monthe, as was swych a day in swich a month ¶ ther variet[h] but lite. ¶ Also yif þow take 2 daies naturaly in the yer ilike fer fro eyther pointe of [the] equinoxial in the opposit parties, ¶ than as long is the day artificial of þat on day / as is the nyht of þat othere, & the contrarie. ¶ & for [the] more declaracioun, lo here thi figure.

16.This chapitre is a Maner declaracioun to conclusiouns þat folwen.

[Illud capitulum est quedam declaracio ad certas conclusiones sequentes.]

¶ Vnderstond wel þat thy zodiak is departid in 2 halfe cercles, as fro the heued of capricorne vn-to the heued of Cancer / & agaynward fro the heued of cancer vn-to the heued of Capricorne. ¶ the heued of Capricorne is the lowest point, wher as the sonne goth in wynter; ¶ & the heued of Cancer is the heiest point, in whiche the sonne goth in somer. ¶ & ther-for vnderstond wel, þat any two degrees þat ben ilike fer fro any of thise two heuedes / truste wel þat thilke two degrees ben of il[i]ke declinacioun, be it sowthward or northward ; & the daies of hem ben ilike of lengthe, & the

nyhtes also ; & the shadwes illke, & the Altitudes ilike at Midday for euere. ¶ & for more declaracioun, lo here thi figure.

[folio 16]

17. To knowe the verrey degree of any maner sterre straunge or vnstraunge after his longitude, thow he be indeterminat in thin astralabie; sothly to the trowthe, thus he shal be knowe.

[Ad cognoscendum verum gradum alicuius stelle aliene secundum eius latitudinem (sic), quamvis sit indeterminata in astrolabio; veraciter isto modo.]

¶ Tak the altitude of this sterre whan he is on the Est side of the lyne Meridional, as ney as thow maist gesse ; ¶ & tak an assendent a-non riht by som maner sterre fix which þat þow knowest ¶ & for-get nat the altitude of the firste sterre, ne thyn assendent ; 4 & whan þat this is don / espie diligently whan this same firste sterre passeth any-thing the sowth westward, and hath him a-non riht in the same nowmbre of altitude on the west side of this lyne Meridional ¶ as he was kawht on the est side ; & tak a newe assendent a-non riht by som Maner sterre fixe which þat thow knowest ; & for-get nat this secounde assendent. ¶ and whan þat this is don, rikne thanne how manye degrees ben by-twixe the firste assendent & the seconde assendent / & rikne wel the Middel degree by-twyne bothe Assendentes,

& set thilke Middel degree vp-on thin est Orisonte ; ¶ & waite thanne what degre þat sit vp-on the line Meridional, & tak ther the verrey degre of the Ecliptik in which the sterre stondeth for the tyme. ¶ For in the Ecliptik is the longitude of a celestial body rekened, euene fro the heued of aries vn-to [the] ende of pisces. ¶ & his latitude is Rikned after the quantite of [h]is declinacion, north or sowth to-warde þe poles of this world / as thus. ¶ yif it be of the sonne or of any fix sterre / rekene [h]is latitude or his declinacioun fro thu Equinoxial cercle; ¶ & yif it be of a planete, rekne than the quantite of [h]is latitude fro the Ecliptik lyne. ¶ Al be it so þat fro [the] Equinoxial may the declinacion or the latitude of any body celestial be rikned, after the site north or south, & after the quantite of [h]is declinacion. ¶ & riht so may the latitude or the declinacion of any body celestial, saue only of the sonne, after his site north or south, & after the quantite of his declinacioun, be rekned fro the Ecliptik lyne ; ¶ Fro which lyne alle planetes som tyme declinen north or south, saue only the for-seide sonne. ¶ & for the more declaracioun, lo here thi figure.

[folio 16b]

18. To knowe the degrees of the longitudes of fixe sterres after þat they ben determinat in thin astralabie, yif so be þat they ben trewly set.

[Ad cognoscendum gradus longitudinis de stellis fixis que determinantur in astrolabio, sicut in suis locis recte locentur.]

¶ Set the centre of the sterre vp-on the lyne Meridional, & tak kep of thi zodiak, ¶ & loke what degree of any signe þat sit on the same lyne Meridional at þat same tyme, & tak the degree in which the sterre standith ; ¶ & with that same degree com[e]th þat same sterre vn-to that same lyne fro the Orisonte. ¶ & for more declaracioun, lo here thi figure.

19. To knowe with which degree of the zodiak any sterre fixe in thin Astrelabie arisith vp-on the est Orisonte, Al-they [h]is dwellyng be in a-nother signe.

[Ad cognoscendum cum quibus gradibus zodiaci que stella fyxa in astrolabio ascendit super orizontem orientalem, quamuis eius orizon (sic) sit in alio signo.]

¶ Set the Sentre of the sterre vp-on the est Orisonte, ¶ & loke what degre of any signe þat sit vp- on the same Orisonte at þat same tyme. ¶ And vnderstond wel, þat with þat same degre arisith þat same sterre ; and thys [folio 17] merueyllous arising with a strange de-gree in another signe is by-cause þat the latitude of the sterre fix is either north or sowth fro the equinoxial. ¶ but sothly, the latitudes

of planetes ben comu[n]ly rekned fro the Ecliptik, bi-cause þat non of hem declinet[h] but fewe degrees owt fro the brede of the zodiak. ¶ & tak god kep of this chapitre of arising of the celestial bodies ; for truste wel, þat neyther mone ne sterre as in owre Embelif orisonte arisith with þat same degree of his longitude, saue in O cas; ¶ & that is, whan they haue no latitude fro the Ecliptik lyne. but natheles som tyme is eueriche of thes planetes vnder the same lyne. ¶ & for more declaracioun, lo here thi figure.

20.To knowe the declinacioun of any degree in the zodiak fro the equinoxial cercle, &c.

[Ad cognoscendum declinacionem alicuius gradus [in] zodiaco [a] circulo equinoctiali.]

¶ Set the degree of any signe vp-on the lyne Meridional, & rikne [h]is altitude in Almykanteras fro the Est Orizonte vp to the same degree set in the forseide lyne, & set ther a prikke. ¶ turne vp thanne thy Riet, and set the heued of aries or libra in the same Meridional lyne, & set ther a-nother prikke. ¶ & whan þat this is don, considere the [folio 17b] Altitudes of hem bothe ; for sothly the difference of thilke altitudes is the declinacion of thilke degre fro the equinoxial. ¶ & yif so be þat thilke degree be northward fro the equinoxial, than is his declinacion north ; ¶ yif it be sowthward, than is it sowth. ¶ & for the more declaracioun, lo here thi figure.

21. To knowe for what latitude in any regioun the Almikanteras of any table ben compowned.

[Ad cognoscendum pro qua latitudine in aliqua regione almicantre tabule mee sunt composite.]

¶ Rikne how manie degrees of Almikanteras in the Meridional lyne be fro the cercle equinoxial vn-to the senyth ; ¶ Or elles fro the pool artik vn-to the north Orisonte; & for so gret a latitude or for so smal a latitude is the table compowned. ¶ & for more declaracion, lo here thi figure.

[folio 18]

22. To knowe in special the latitude of owre countray, I mene after the latitude of Oxenford, & the heyhte of owre pol.

[Ad cognoscendum specialiter latitudinem nostri centri (sic), scilicet latitudinem Oxonie, et altitudinem poli nostri.]

Vnderstond wel, þat as fer is the heued of aries or libra in the equinoxial from owre orisonte as is the cenyth fro the pole artik ; ¶ & as hey [is] the pol Artik fro the Orisonte as the Equinoxial is fer fro the senyth. ¶ I proue it thus by the latitude of Oxenford / vnderstond wel, þat the heyhte of owre pool Artik fro owre north Orisonte is 51 degrees & 50 Minutes; than is the cenyth from owre pool Artik 38 degrees & l0 Minutes; than is the equinoxial from owre senyth 51 degrees & 50 Minutes; ¶ than is owre south Orisonte from owre equinoxial 38 degrees & l0 Minutes. ¶ vnderstond wel

this Reknyng. ¶ Also for-get nat þat the cenyth is 90 degrees of heyhte fro the Orisonte, & owre equinoxial is 90 degrees from owre pool Artik. ¶ Also this shorte rewle is soth, þat the latitude of any place in a regioun is the distance fro the senyth vnto the Equinoxial. ¶ & for more declaracioun, lo here þi figure.

23. To proue euidently the latitude of any place in a Regioun, by the preue of the heyhte of the pol Artik in þat same place.

[Ad probandum euidenter latitudinem alicuius loci in aliqua regione, per probacionem altitudinis de polo artico in eodem loco.]

In some wynters nyht, whan the firmament is clere & thikke- sterred / waite a tyme til þat any sterre fix sit lyne-riht perpendiculer ouer [folio 18b] the pol Artik, & clepe þat sterre A. ¶ & wayte a-nother sterre þat sit lyne-riht vnder A, & vnder the pol / & clepe þat sterre F. And vnderstond wel, þat F is nat consideret but only [to] declare þat A sit euene ouere the pool. ¶ tak thanne a-non riht the altitude of A from the Orisonte / & forget it nat. ¶ Lat A & F go farwel til agayns the dawenyng a gret while / & come thanne agayn & Abid til þat A is euene vnder the pol & vnder F ; ¶ for sothly, than wole F sit ouer the pool / & A wol sit vnder the pool. ¶ tak than eft-sones the altitude of A from the Orisonte ¶ & note as wel [h]is secounde altitude as his furste Altitude / & whan þat this is don, ¶ rikne how manye degrees þat the firste altitude of A excedith his seconde altitude, ¶ & tak half thilke porcioun þat is excedit, & adde it to his seconde altitude ; ¶ & tak ther the eleuacioun of thi pool, & eke the latitude of thy regioun ; ¶ for thise two ben of a nombre ; ¶ this is to seyn, as many degrees as thy pool is eleuat / so michel

is the latitude of the Regioun. ¶ Ensample as thus: par auenture the altitude of A in the euenyng is 56 degrees of heyte than wol his seconde altitude or the dawyng be 48 / þat is [8] lasse than 56, þat was his furste altitude at euen. ¶ take thanne the of 8 / & adde it to 48, þat was [h]is seconde altitude, and [than] hastow 52. ¶ now hastow the heyhte of thy pol and the latitude of the regioun ¶ but vnderstond wel þat to proue this conclusioun & many a-nother fair conclusioun, thow most haue a plomet hanging on a lyne heyer than thin heued on a perche ¶ & thilke lyne mot hange euene perpendiculer by-twixe the pool & thin eye / & thanne shal-tow sen yif A sitte euene ouer the pool & ouer F at euene / & also yif F sitte euene ouer the pool & ouer A or day. ¶ & for more declaracion, lo here thi figure.

[folio 19]

24. Another conclusioun to proue the heyhte of the pool Artik fro the orisonte.

[Alia conclusio ad probandum altitudinem de polo artico ab orizonte.]

Tak any sterre fixe þat neuere dissendith vnder the Orisonte in thilke regioun, & considere his heiest altitude & his lowest Altitude fro the Orisonte ; ¶ & make a nombre of bothe thise altitudes ; tak thanne & abate half þat nombre, & tak þer the eleuacioun of the pol Artik in þat same Regioun / & for more declaracioun, lo here thi figure.

25. A-nother conclusioun to proue the latitude of the Regioun, &c.

[Alia conclusio ad probandum latitudinem regionis.]

¶ Vnderstond wel þat the latitude of any place in A Regioun is verreyly the space by-twixe the senythe of hem þat dwellen there & [the] equinoxial cerkle, north or sowthe, takyng the mesure in the Meridional lyne, as shewith in the Almykanteras of thin Astrelabie. ¶ & thilke space is as moche as the pool artik is hey in the same place fro the Orisonte. ¶ And than is the depressioun of the pol antartik, þat is to seyn, than is the pol antartik by-nethe the Orisonte the same quantite of space, neither mor ne lasse. thanne, yif thow desire to knowe this latitude of the Regioun, tak the altitude of the sonne in the Middel of the day, whan the sonne is in the heuedes of aries or of libra / for thanne Moeuyth the sonne in the lyne equinoxial ; ¶ & abate the nombre of that same sonnes Altitude owt of 90, & thanne is the remenaunt [folio 19b] of the noumbre þat leuyth the latitude of the Regioun, as thus : I suppose that the sonne is thilke day at noon 38 degrees And l0 minutes of heyhte. Abate thanne thees degrees And minutes owt of 90 ; so leueth there 51 degrees and 50 minutes, the latitude. ¶ I sey nat this but for ensample ; for wel I wot the latitude of Oxenforde is certein minutes lasse, as y myght proue. ¶ Now yif so be þat the semith to long a tarienge, to abide til þat [þe] sonne be in the heuedes of aries or of libra, thanne whaite whan the sonne is in any other degree of the zodiak, & considere the degree of [h]is declinacion fro the equinoxial lyne ; ¶ & yif it so be þat the sonnes declinacion be northward fro the equinoxial, abate thanne fro the sonnes altitude at noon the nombre

of his declinacion, ¶ & thanne hastow the heyhte of the heuedes of aries & libra ; as thus / My sonne is, par Auenture, in þe firste degre of leoun, 58 degrees and 10 Minutes of heyhte at noon / & his declinacion is almost 20 degrees northward fro the equinoxial ; abate thanne thilke 20 degrees of declinacion owt of the altitude at noon, than leueth the 38 degrees and odde Minutes ; lo ther the heued of aries or libra, & thin equinoxial in that Regioun. ¶ Also yif so be þat the sonnes declinacioun be sowthward fro the Equinoxial, ¶ Adde thanne thilke declinacion to the altitude of the sonne at noon / and tak ther the heuedes of aries & libra & thin Equinoxial. ¶ abate thanne the heyhte of the Equinoxial owt of 90 degrees, & thanne leuyth there þe distans of the pole, 51 degrees & 50 Minutes, of that regioun fro the Equinoxial. ¶ Or elles yif the lest, take the haiest altitude fro the equinoxial of any sterre fix that thow knowest, & tak his nethere elongacioun lengthing fro the same equinoxial lyne, & wirke in the maner forseid. ¶ & for more declaracion, lo here thi figure.

[folio 20]

26. Declaracioun of the assensioun of signes, &c.

[Declaracio de ascensione signorum.]

The excellence of the spere solide, amonges other noble conclusiouns, shewyth Manifeste the diuerse assenciouns of signes in diuerse places, as wel in the rihte cercle as in the Embelif cercle. ¶ thise Auctours writen þat thilke signe is clept of riht Ascensioun, with which more part of the cercle Equinoxial & lasse part of the zodiak ascendith / & thilke signe assendith Embelif, with whiche lasse part of the Equinoxial and more part of the zodiak assendith.

[Ferther ouer 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 poles of this worlde, thilke folke han this right cercle and the right orisonte;] ¶ & euere mo the Arch of the day & the arch of the nyht is ther ylike long, & the sonne twyes euery yer passinge thorow the cenyth of her heued; & 2 someres & 2 wynteres in a yer han this forseide poeple. ¶ And the Almykanteras in her Astrolabies ben streyhte as a lyne / so as shewyth in this figure. ¶ The vtilite to knowe the Assenciouns in the rihte cercle is this / truste wel þat by mediacioun of thilke assenciouns thise Astrologiens by hir tables &

hir instrumentz knowen verreyly the Assencioun of euery degree & Mynut in al the zodiak, as shal be shewyd. ¶ And nota, þat this forseid rihte orisonte, þat is clepid orison rectum / diuideth the equinoxial in-to riht Angles ; & the embelif orisonte, wher as the pol is enhawsed vp-on the orisonte, ouerkeruyth the equinoxial in Embelif Angles, as shewith in the figure. ¶ & for the more declaracioun, lo here the figure.

27.This is the conclusioun to knowe the Assenciouns of signes in the riht cercle, þat is, circulus directus, &c.

[Ad cognoscendum ascenciones signorum in recto circulo, qui vocatur circulus directus.]

[folio 20b]

Set the heued of what signe the liste to knowe his Assending in the riht cercle / vp-on [the] lyne Meridional, ¶ & waite wher thin Almury towchiet[h] the bordure, & set ther a prikke/ turne thanne thy riet westward til þat the ende of the forseide signe sitte vp-on the Meridional lyne / & eft-sones waite wher thin almury towchith the bordure, & set ther Another prikke. Rikne thanne the nombre of degrees in the bordure by-twyxe bothe prikkes, ¶ & tak the Assencioun of the signe in the riht cercle. And thus maistow wyrke with euery porcioun of thy zodiak, &c. ¶ & for the more declaracioun, lo her thi figure.

28.To knowe the assencions of signes in the Embelif cercle in euery regioun, I Mene, in circulo obliquo.

[Ad cognoscendum ascenciones signorum in recto (sic!) circulo in omni regione, hoc est, in circulo obliquo.]

¶ Set the heued of the signe which as the list to knowe his Ascensioun

vp-on the est Orisonte, ¶ & waite wher thyn Almury towchith the bordure, & [set] ther a prikke. ¶ turne thanne thy riet vpward til þat the ende of the same signe sitte vp-on the Est Orisonte / and waite eft-sones wher as thin almury towcheth the bordure, & set ther a-nother prikke. ¶ Rikne thanne the nowmbre of degrees in the bordure by-twyxe bothe prikkes, & tak ther the Assencioun of the signe in the Embelif cercle. ¶ & vnderstond wel, þat alle signes in thy zodiak fro the heued of aries vnto the ende of virgo ben cleped signes of the north fro the Equinox[i]al, ¶ & the[se] signes arisen by-twyxe the verrey est & the verrey north in owre Orisonte generaly for euere ; & alle signes fro the heued of libra vn-to þe ende of pisces ben cleped signes of the sowth fro [folio 21] the Equinoxial ; ¶ & thise signes arisen euer-mo by-twyxe the verrey est & the verrey sowth in owre orisonte. ¶ Also euery signe by-twixe the heued of capricorne vn-to the ende of geminis ariseth on owre Orisonte in lasse than 2 howres equales; ¶ & thise same signes, fro the heued of capricorne vn-to the ende of geminis, ben cleped tortuos signes or kroked signes / for they arisen embelif on oure Orisonte; ¶ & thise crokede signes ben obedient to the signes þat ben of riht Assencioun. ¶ The signes of riht assencioun ben fro the heued of cancer to þe [ende] of sagittare; ¶ & thise signes arisen more vpriht, & they ben called eke souereyn signes ; ¶ & euerich of hem ariseth in mor space than in to howres. ¶ Of which

signes gemini obeieth to Cancer, ¶ & taurus to leo / Aries to virgo / pisces to libra, ¶ Aquarius to Scorpioun, and Capricorne to Sagittare. ¶ & thus euermo 2 signes that ben illike fer fro the heued of capricorne / obeien euerich of hem til other. ¶ & for more declaracioun, lo here the figure.

29.To knowe Iustly the 4 quarters of the world, as est, west, north, & sowth.

[Ad cognoscendum euidenter quatuor partes mundi, scilicet, orientem, austrum, aquilonem, & occidentem.]

¶ Take the altitude of thy sonne whan the list / & note wel the quarter of the world in which the sonne is for the tyme by the Azymutz. ¶ turne thanne thin Astrolabie / & set the degree of the sonne in the Almykanteras of his altitude on thilke side þat the sonne stant / as is the manere in takyng of howres ; ¶ & ley thy label on the degree of the sonne, And rikene how many degres of the bordure ben by-twixe the lyne Meridional & the point of thy label; & note wel þat nowmbre. ¶ [folio 21b] Turne thanne a-gayn thyn Astralabie, & set the point of thy gret Rewle ther thow takest thyne Altitudes / vp-on as many degrees in his bordure fro his Meridional as was the point of thy label fro the lyne Meridional on the wombe-side. ¶ tak thanne thyn Astrolabie with bothe handes sadly & slely, & lat the sonne shyne thorow bothe holes of thy rewle; ¶ & sleyly in thilke shynynge lat thyn Astrelabie kowch adown euene vp- on a smothe grond, & thanne wol the verrey lyne Merydional of thyn

Astrolabie lye euene sowth, & the est lyne wole lie est, & the west lyne west, & north lyne north, so þat thow werke softly & avisely in the cowchyng ; & thus hastow the 4 quarters of the firmament. ¶ & for the more declaracioun, lo here the figure.

30. To knowe the Altitude of planetes fro the wey of the sonne, whether so they be north or sowth fro the forseide wey.

[Ad cognoscendum altitudinem planetarum a cursu solis, utrum sint in parte australi vel boreali a cursu supra dicto.]

¶ Lok whan þat a planete is in the lyne Meridional, yif þat hir altitude be of the same heyhte þat is the degree of the sonne for þat day, & than is the planete in the verrey wey of the sonne, ¶ & hath no latitude. ¶ & yif the altitude of the planete be heyere than the degree of the sonne, þan is the planete north fro the wey of the sonne swych a quantite of latitude as [shewith] by thyn Almykanteras. & ȝif the altitude of the planete be lasse than the degree of the sonne / thanne [folio 22] is the planete sowth fro the wey of the sonne swich a quantite of latitude as [shewith] by thin almykanteras ; ¶ This is to seyn, fro the wey wher as the sonne wente thilke day / but nat from the wey of the sonne in euery place of the zodiak. ¶ & for the more declaracioun, lo here the figure.

31. To knowe the senyth of the arysing of the sonne, this is to seyn, the partie of the Orisonte in which þat the sonne arisith.

[Ad cognoscendum signum de ortu solis, scilicet, illam partem orientis in qua oritur sol.]

¶ Thow most first considere þat the sonne ariseth nat al-wey verrey est, but some tyme by north the est, and som tyme by sowthe

the est / Sothly the sonne ariseth neuer-mo verrey est in owere Orisonte, ¶ but he be in the heued of aries or libra. now is thin Orisonte departed in 24 parties by thi azymutz, in significacion of 24 partiez of the world; al be it so þat shipmen rikne thilke partiez in 32 / thanne is ther no more but waite in which azymut þat thi sonne entreth at [h]is arisyng / & take ther the senyth of the arising of the sonne. ¶ the manere of the deuisioun of thin Astralabie is this / I Mene as in this cas. ¶ First is it deuided in 4 plages principalx with the lyne þat goth from est to west, ¶ & than with a-nother lyne þat goth fro so[w]th to north. ¶ than is it deuided in smale partiez of Azymutz, as est, and est by sowthe, whereas is the firste Azimut aboue the est lyne ; ¶ & so forth fro partie to partie / til þat thow come agayn vn-to the est lyne / thus maistow vnderstond also the senyth of any sterre, in which partie he riseth, &c. ¶ & for the more declaracion, lo here the figure.

[folio 22b]

32. To knowe in which partie of the firmament is the coniunccioun.

[Ad cognoscendum in qua parte firmamenti sunt coniuncciones solis & lune.]

¶ Considere the tyme of the coniuncc[i]on by thy kalender / as thus ; lok how many howres thilke coniunccion is fro the Midday of

the day precedent, as shewith by the canoun of thi kalender; ¶ rikne thanne thilke nombre of howres in the bordure of thyn Astralabie / as thow art wont to do in knowyng of the howres of the day or of the nyht; ¶ & ley thy label ouer the degree of the sonne; ¶ & thanne wol the point of thy label sitte vp-on the hour of the con- iunccion. ¶ loke thanne in which Azymut the degree of thy sonne sittith, & in that partie of the firmament is the coniunccioun. ¶ & for the more declaracioun, lo here thy figure.

[folio 23]

33. To knowe the senyth of the Altitude of the sonne, &c.

[Ad cognoscendum signa de altitudine solis.]

This is no mor to seyn but any tyme of the day tak the altitude of the sonne, & by the Azymut in which he stondith, ¶ Maistou sen in which partie of the firmament he is ¶ & [in] the same wyse maistou sen, by the nyht, of any sterre, wheither the sterre sitte est or west or north, or any partie by-twene, aftur the name of the Azimut in which is the sterre. ¶ & for the more declaracioun, lo here the figure.

34. To knowe sothly the degree of the longitude of the mone, or of any planete þat hath no latitude for the tyme fro the Ecliptik lyne.

[Ad cognoscendum veraciter gradum de longitudine lune, vel alicuius planete qui non habet longitudinem pro tempore causante (sic) linea ecliptica.]

¶ Tak the altitude of the mone, & rikne thin altitude vp among thyne Almykanteras on which side that the Mone stande, & set there a prikke. ¶ Tak thenne anon riht, vp-on the mones side, the Altitude of any sterre fix which þat thow knowest, & set his Centre vp-on his altitude Among thin Almykanteras ther the sterre is fownde. ¶ Waite thanne which degree of the zodiak [towchith] the prikke of the altitude of the mone, & tak ther the degree in which the mone standith. ¶ this conclusioun is verrey soth, yif the sterres in thin Astrolabie stonden aftur [folio 23b] the trowthe ; of comune, tretis of Astralabie ne make non excepcioun wheyth[er] the mone haue latitude, or non / ne on wheither side of the mone the Altitude of the sterre fix be taken. ¶ And nota, þat yif the Mone [shewe] himself by liht of day, than maistow wyrke this same conclusioun by the sonne, as wel as by the fix sterre. ¶ & for the more declaracioun, lo here thy figure.

35. This is the workinge of the conclusioun, to knowe yif þat any planete be directe or retrograde.

[Hec conclusio operatur ad cognoscendum si aliqua planeta sit directa uel retrograda.]

¶ Tak the altitude of any sterre þat is cleped a planete, ¶ & note it wel. ¶ & tak ek anon the altitude of any sterre fix that thow

knowest, & note it wel also. ¶ Come thanne agayn the thridde or the ferthe nyht next folwyng ; for thanne shaltow aperceyue wel the Moeuyng of a planete, wheither so he Moeue forthward or bakward. ¶ Awaite wel thanne w[h]an þat thi sterre fix is in the same altitude þat she was w[h]an thow toke hir firste altitude ; ¶ and tak than eftsones the Altitude of the forseide planete, & note it wel. ¶ for trust wel, yif so be þat the planete be on the riht side of the Meridional lyne, so þat his seconde altitude be lasse than [h]is firste altitude was, thanne is the planete directe. ¶ And yif he be on the west side in that condicion / thanne is he retrograd. ¶ And yif so be þat this planete be vp-on the Est side whan [h]is altitude is [folio 24] taken, so þat his secounde altitude be more than [h]is firste altitude, thanne is he retrograde, & yif he be on the west side, than is he directe. ¶ but the contrarie of this parties is of the cours of the Moone ; for [sothly] the Moone Moeuyth the contrarie from othere planetes as in hire Episicle, but in non other manere. ¶ & for the more declaracioun, lo here thi figure.

36. The conclusiouns of equaciouns of howses, after the astralabie, &c.

[Conclusio de equacione domorum.]

Set the by-gynnyng of the degree þat assendith vp-on the ende of the 8 howre inequal ; thanne wol the by-gynnyng of the 2 hows sitte vp-on the lyne of Midnyht. ¶ rem[e]ue thanne the degree þat assendith, & set him on the ende of the 10 howr inequal; & thanne

wol the by-gynnyng of the 3 howis sitte vp-on the Midnyht lyne. ¶ bryng vp agayn the same degree þat assendith first / & set him vp-on the Orisonte / & thanne wol the be-gynnyng of the 4 howys sitte vp-on the lyne of Midnyht. ¶ tak thanne the nadir of the degree þat first Assendith / & set him on the ende of the 2 howre inequal / & thanne wol the by-gynnyng of the 5 howys sitte vp-on the lyne of Midnyth ; set thanne the nadir of the assendent on the ende of the 4 howre, þan wol the bygynnyng of the 6 house sitte on the Midnyht lyne. ¶ þe bygynnyng of the 7 hows is nadir of the Assendent / & the bygynnyng of the 8 hows is nadir of the 2; & þe by-gynnyng of the 9 hous is nadir of the 3 ; & þe by-gynnyng of þe 10 hows is the nadir of the 4 ; & þe bygynnyng of the 11 howys is nader of the 5 ; & the bygynnyng of the 12 hows is nadir of the 6. ¶ & for the more declaracion, lo here the figure.

[folio 24b]

37. A-nother manere of equaciouns of howses by the Astrelabie.

[De aliqua forma equacionis domorum secundum astrolabium.]

¶ Tak thin assendent, & thanne hastow thi 4 Angles; for wel thow wost þat the opposit of thin assendent, þat is to seyn, thy by-gynnyng of the 7 howis, sit vp-on the west orizonte ; ¶ & the bygynnyng of the 10 howis sit vp-on the lyne Meridional ; ¶ & his opposit vp- on the lyne of Mydnyht. ¶ Thanne ley thi label ouer

the degree þat assendet[h] / & rekne fro the point of thy label alle the degrees in the bordure, til thow come to the Meridional lyne / & departe alle thilke degrees in 3 euene parties, & take the euene equacion of 3 ; for ley thy label ouer euerich of 3 parties, & [than] maistow se by thy label in which degree of the zodiak [is] the by- gynnyng of euerich of thise same howses fro the assendent / þat is to seyn, the begynyng of the [12] howse nex[t] aboue thin assendent / And [thanne] the begynnyng of the 11 howse, & thanne the 10 vp-on the Meridional lyne / as I first seide. ¶ The same wyse wyrke thow fro the assendent down to the lyne of Mydnyht / & thanne thus hastow other 3 howses, þat is to seyn, the bygynnyng of the 2 & the 3 And the 4 howses ; thanne is [the] nader of thise 3 howsez the by-gynnyng of the 3 howses þat folwen. ¶ & for the more declaracioun, lo here thi figure.

[folio 25]

38. To fynde the lyne Merydional to dwelle fix in any certein place.

[Ad inueniendum lineam meridionalem per subtiles operaciones.]

Tak a rond plate of metal, for [warpyng] the brodere the bettre ; ¶ & make ther-vpon [a] Iust compas, a lite with-in the bordure / & ley this ronde plate vp-on an euene grond or on a[n] euene ston or on a[n] euene stok fix in the gronde / & ley it euen bi a leuel ¶ & in centre of the compas stike an euene pyn or a whir vp-riht / the smallere þe betere ¶ set thy pyn by a plom-rewle euene vpryht ¶ & let this pyn be no lengere than a quarter of the diametre of thi compas, fro the centre. ¶ & waite bisily aboute 10 or 11 of the clokke, & whan the

sonne shynyth, whan the shadwe of the pyn entreth any-thyng with-in the cercle of thi plate an her-mele, ¶ & mark ther a prikke with inke. Abide thanne stille waityng on the sonne aftur 1 of the clokke, til that the schadwe of the wyr or of the pyn passe ony-thyng owt of the cercle of the compas, be it neuer so lite / & set ther a-nother prikke of ynke. ¶ take than a compas, and mesure euene the Middel by-twixe bothe prikkes, & set þer a prikke. ¶ take thanne a rewle / & draw a strike, euene alyne fro the pyn vn-to the Middel prikke; ¶ & tak ther thy lyne Meridional for euere-mo, as in that same place. ¶ & yif thow drawe a cros-lyne ouer-thwart the compas Iustly ouer the lyne Meridional, than hastow est and west & sowth / &, par consequence, than the nader of the sowth lyne is the north lyne. ¶ & for more declaracioun, lo here thi figure.

[folio 25b]

39. Descripcion of the Meridional lyne, of longitudes, & latitudes of Citees and townes from on to a-no[t]her of clymatz.

This lyne Meridional ys but a Maner descripcion [of lyne] ymagined, that passeth vpon the pooles of þis world And by the cenyth of owre heued / And hit is [ycleped the] lyne Meridional / for in what place þat any maner man [ys at] any tyme of the yer / whan that the sonne [by moeuyng] of the firmament cometh to his verrey [meridian] place , than is hit verrey Midday, þat we clepen owre noon, ¶ As to thilke man ; ¶ And therfore ys it clepid þe lyne of

Midday. ¶ And nota, for euermo, of [2 citees] or of 2 Townes, of whiche þat o town aprochith [more] towarde the Est þan doth þat other town, ¶ Truste wel that thylke townes han diuerse Meridians. ¶ Nota also, that the Arch of the Equinoxial that is [conteyned] or bownded by-twyxe the 2 Meridians ys cleped þe longitude of the town. ¶ And [yf] so be þat two townes haue illike Meridian, or on Meridian, ¶ Than is the distance of hem bothe ylike fer fro the Est / & the contrarie. And in this Manere they chaunge nat her Meridian, ¶ But sothly they chaungen here Almikanteras, For the enhausyng of the pool and the distance of the sonne. ¶ The longitude of a clymat ys a lyne ymagined fro Est to west, illike distant by-twene them alle. ¶ þe latitude of a climat is a lyne ymagined from north to south þe space of the erthe, fro the byginnyng [folio 26] of the firste clymat vnto to the verrey ende of the [same] climat, euene directe agayns [þe poole Artik.] ¶ Thus seyn some Auctours / And somme of hem seyn þat yif men clepen þe latitude, thay mene the arch meridian þat is contiened or [inter]cept by-twixe the cenyth and the eqninoxial. Thanne sey þey that the distaunce fro the equinoxial vnto þe ende of a clymat, euene agayns þe pool artyk, ys the latitude of a climat for sothe. ¶ & for more declaracioun, lo here thi figure.

40.To knowe with which degree of the zodiak þat any planete Assendith on the Orisonte, wheyther so that his latitude be north or sowth.

¶ Knowe be thin almenak the degree of the Ecliptik of any signe in which þat the planete is rekned for to be / & that is cleped the degree of his longitude; & knowe Also the degree of his latitude fro the Ecliptik, north or sowth. ¶ And by this samples folwynge in special / maistow wyrke for [sothe] in euery signe of the zodiak. the degree of [longitude] par auenture, of venus or of another planete was 6 of Capricorne, & the latitude of him was northward 2 degrees fro the Ecliptik lyne. I tok a subtil compas, & cleped þat on poynt of my compas A, & þat other poynt F. ¶ Than [tok] I the point of A, & set it in [the] Ecliptik line euene in my zodiak, in the degree of the longitude of venus / þat is to seyn, in the 6 degree of Capricorne ¶ & thanne set I the point of F vpward in the same [folio 26b] signe, bycause þat the latitude was north, vpon the latitude of venus, that is to seyn, in the 6 degree fro the heued of capricorne; & thus hauy 2 degrees by-twixe my to prikkes; than leide I down softely my compas, ¶ & sette the degree of the longitude vp-on the Orisonte / tho tok I & wexede my label in Maner of a peyre tables to resceyue distynctly the prikkes of my compas. ¶ Tho tok I this forseide label, & leide it fix ouer the degree of my longitude / tho tok I vp my compas, ¶ & sette the point of A in the wex on my label, as euene as y kowde gesse ouer the Ecliptik lyne, in the ende of [the] longitude / & sette the point of F endlang in my label vp-on the space of the latitude, inwarde & ouer the zodiak, that

is to seyn, north-ward fro the Ecliptik // than leide I down my compas & lokede wel in the wey vpon the prikke of A & of F; tho turned I my Riet til þat the prikke of F sat vp-on the Orisonte / than saw I wel þat the body of venus, in hir latitude of [2] degrees septentrionalis, assendid, in the ende of the 6 degree, in the heued of capricorne. ¶ And nota, þat in the same maner maistow wyrke with any latitude septentrional [in alle] signes ; but sothly the latitude Meridional of a planete in Capricorne may not be take, by cause of the litel space by-twixe the Ecliptik / & the bordure of the Astrelabie; but sothly, in alle other [signes] it May.

[folio 27]

¶ Also the degree, par auenture, of Iuppiter or of a-nother planete, was in the furst degree of pisces in longitude / & his latitude was 3 degrees Meridional; tho tok I the point of A / & set it in the firste degree of pisces on the Ecliptik / & thanne set I the point of F downward in the same signe, by cause þat the latitude was sowth 3 degrees / þat is to seyn̄, fro the heued of pisces / & thus hauy 3 degrees by-twixe bothe prikkes ; thanne sette I the degree of the longitude vp-on the Orisonte; tho tok I my label / & leide it fix vp-on the degree of the longitude; tho sette I the point of A on my label, euene ouer the Ecliptik lyne in the ende euene of the degree of the longitude / & set the point of [F endlang] in my label the space [of] 3 [degrees] of the latitude fro the zodiak, this is to seyn, sowthward fro the Ecliptik, toward the bordure; and turned my

Riet [til] the prikke of F sat vp-on the Orisonte; thanne [saw] I wel þat the body of Iuppiter, in his latitude of 3 degrees Meridional, ascendit with 14 degrees of pisces in horoscopo / & in this Maner maistow wyrke with any latitude Meridional, as I first seide, saue in Capricorne / And yif thow wolt pleie this craft with the arisyng of the Mone, loke thow rekne wel her cours howre by howre; for she ne dwellith nat in a degree of [hire] longitude but [a] litel while, as thow wel knowest / but natheles, yif thow rekne hir verreye Moeuyng by thy tables howre after howre——[þou shalt do wel ynow.

Explicit tractatus de Conclusionibus Astrolabii compilatus per Galfridum Chauciers ad Filium suum Lodewicum scolarem tunc temporis Oxonie ac sub tutela illius nobilissimi Philosophi Magistri N. Strode, &c.

41. Vmbra Recta.

Ȝif it so be þat þou wylt werke be vmbra recta, & þou may come to þe bas of þe towre, in þis maner þou schalt werke. Tak þe altitude of þe tour be boþe holes, so þat þi rewle ligge euyn in a poynt. Ensample as þus : y see hym þorw at þe poynt of 4; þan mete y þe space be-twen me & þe tour, & y fynde yt 20 feet; þan be-holde y how 4 ys to 12, riȝt so is the space be[-twen] þe & þe tour to þe altitude of þe tour. [For] 4 is þe [þ]ridde part of 12, so is þe space be-twen þe & þe tour þe þridde part of þe altitude of þe tour; þan þries 20 feet ys þe heyȝte of þe tour, wiþ addyng of þyn owne persone to þyn eye; & þis rewle is so general in vmbra recta, fro þe poyn[t] of oon to 12. And ȝif þi rewle falle vppon 5, þan is 5 12-partyes of þe heyȝt þe space be-twen þe & þe towre; wyþ addyng of þyn owne heyȝth.

42. Vmbra Versa.

Anoþer maner of werkynge, be vmbra versa. Ȝif so be þat þou may nat come to þe bas of þe tour, y [see] hym þorw þe nombre of 1 ; y sette þer a prikke [folio 32b] at my foote; þan goo [y] ner to þe tour, & y see hym þorw at þe poynt of 2, & þere y sette a-noþer prikke; &

y be-holde how 1 hath hym to 12, & þer fynde y þat yt hath hym twelfe sithes ; þan be-holde y how 2 hath hym to 12, & þou schalt fynde it sexe syþes; þan þou schalt fynde þat [as] 12 [above] 6 [is þe] numbre of 6, Ryȝt so is þe space be-twen þi too prikkis þe space of 6 tymes þyn altitude. & note, þat at þe ferste altitude of 1, þou settest a prikke, & aftyrward, whan þou [seest] hym at 2, þer þou settest an-oþer prikke, þan þou fyndest betwen too prikkys [60] fett; þan þou schalt fynde þat [10 is þe 6-party of 60. And þen is 10 fete] þe altitude of þe tour. [For] oþer poyntis, ȝif yt fylle in vmbra versa, as þus: y sette caas it fill vppon [2], & at þe secunde vppon [3]; þan schalt þou fynde þat [2] is [6] partyes of 12; [and 3 is 4 partyes of 12]; þan passeþ 6 4, be nombre of 2; so ys þe space be[twen] too prikkes twyes þe heyȝte of þe tour. & ȝif þe differens were þries, þan schulde it be [þre] tymes; & þus mayst þou werke fro 2 to 12; & ȝif yt [folio 33] be 4, 4 tymes; or 5, 5 tymes, & sic de ceteris.

43. Vmbra [Recta].

An oþer maner of wyrkyng be vmbra [recta]. Ȝif it so be þat þou mayst nat come to þe baas of þe tour, yn þis maner þou schalt werke. Sette þi Rewle vppon [1] till þou see þe altitude, & sette at þi foot a prikke. þan sette þi Rewle vppon 2, & be-holde what ys þe diff[e]rense be-twen 1 and 2, & þou shalt fynde þat it is 1. þan mete þe space be-twen too prikkes, & þat ys þe 12 partie of þe altitude of þe tour; & ȝif þer were 2, yt were þe 6 partye; & ȝif þer were 3, þe 4 partye, & sic deinceps. And note, ȝif it were 5, yt were þe 5 party of 12 ; & 7, 7 party of 12 ; and note, at þe altitude of þi conclusioun, adde þe stature of þyn heythe.

44. Another maner conclusion, to knowe the mene mote & þe argumentis of any planete. To know the mene mote & the argumentis of euery planete fro ȝere to ȝere, from day to day, from owre to owre, And from smale fraccionis infinite.

[Ad cognoscendum medios motus & argumenta de hora in horam cuiuslibet planete, de anno in annum, de die in diem.]

In this maner shalt þou worche: consider thy rote furst, [folio 106] the wyche is made the begynning of the tabelis fro the ȝere of owre lord 1397, & entere hit in-to thy slate for the laste merydye of December; and þan consider þe ȝere of ovre lord, what is þe date, & be-hold wheþer thy date be more or lasse þan þe ȝere 1397. And yf hit so be þat hit be more, loke how many [ȝeris] hit passith, & with so many entere into thy tabelis in þe furst lyne þer as is wreten anni collecti & expansi. And loke [where] the same planet is wreten in the hede of thy tabele, and than [loke] what þou findest in directe of the same ȝere of owre lord wyche is passid, be hit 8, or 9, or 10, [or what nombre þat euere it be, tyl þe tyme þat þou come to 20, or] 40, or 60. And that þou fyndest in directe [wryte] in thy slate vnder thy rote, & adde hit [to-geder], and þat is thy mene mote, for the laste meridian of the december, for the same ȝere wyche þat þou [hast] purposid. And yf hit so be [þat] hit passe 20, consider welle þat fro [1] to 20 ben anni expansi, And fro 20 to 3000 ben anni collecti; and yf thy nombere passe 20, þan take þat þou findest in directe of 20, & yf hit be more, as 6 or 18, than take þat þou findist in directe there-of, that is to sayen, signes, degreis, Minutes, & secundis, and adde [to-gedere] vn-to thy rote; and thus to make rotes; and note,

þat yf hit [folio 106b] so be [þat] the ȝere of ovre lord be [lasse] than the rote, wyche is the ȝere of ovre lord 1397, than shalt þou write in the same wyse furst thy rote in thy slate, and after entere in-to thy table in the same ȝere [þat] be lasse, as I tauȝth be-fore; and þan consider how many signes, degrees, Minutes, & secundis thyne entrynge conteynith. And so be that [þer] be 2 entres, than adde hem togeder, & after with-drawe hem from the rote, the ȝere of ovre lord 1397; and the residue þat lewyth is thy mene mote fro the laste mer[y]die of December, the wyche þou haste purposid; and yf hit so be þat þou wolt weten thy mene mote [for] eny day, or [for] ony fraccion of day, in þis maner þou shalt worche. make thy rote fro the laste day of Decembere in þe maner as I thaȝthe, and afterward behold how many monythis, dayes, & howris ben passid from [þe] merydye of Decembere & with that entere [with þe] laste moneth þat is ful passid, and take þat þou findest in directe of hym, & wryte hit in thy slate; & entere with as mony dayes as be more, and wryte þat þou findest in directe of the same planete þat þou worchyst fore; and in þe same wyse in-to þe table of howris, for hovris þat ben passid, and adde alle these to thy rote; and the [folio 107] residue is the mene mote for the same day & þe same hovre.

45. Another manere to knowe the mene mote.

Whan þou wolte make the mene mote of eny planete to be by arsechieles tables, take thy rote, the wyche is for the ȝere of ovre lord 1397; and yf so be that thy ȝere be passid the date, wryte that date / and than write that nombere of the ȝeris. þan wyth-drawe þe ȝeris oute of the ȝeris that ben passid that rote. Ensampulle as thus : the ȝere of ovre lord 1400, I-wryton precise, my rote; þan wrote I

furst 1400. And vnder that nombere I wrote a 1397; þan withdrowe I the laste nombere owte of þat, and þan fond I þe residue was 3 ȝere; I wyst þat 3 ȝere was passid fro the rote, þe wyche was wreten in my tabelis. Than after-ward soȝth I in my tabelis þe annis col1ectis & expansis, & amonge myne expanse ȝeris fond I 3 ȝere. þan toke I alle þe signes, degreis, & minutes, þat I fond directe vnder þe same planete þat I wroȝth fore, & wrote so many signes degreis, & Minutes in my slate, & after-ward added I too signes, degreis, Minutes, & Secundis, þe wiche I fond in my rote the ȝere of owre lord 1397; And kepte the residue; & þan had I the mene mote for þe laste day of Decembere. And yf þou woldest wete þe mene mote ofany planete in March, Aprile, or may, oþer in any oþer tyme or monyth of the ȝere, loke how many monethes & dayes [folio 107b] ben passid from þe laste day of Decembere, the ȝere of owre lord 1400; and soe with monithis & dayes entere in-to þy table þer þou findist thy mene mote I-wreten in monethis & dayes, and take alle þe signes, degrees, Minutes, & secundis þat þou findest I-wrete in directe of thy monethis, and [adde] to signes, degreis, Minutes, & secundis þat þou findest with thy rote þe ȝere of ovre lord 1400, and the residue þat leuyth is þe mene mote for that same day. And note yf hit so be that þou woldest [wete þe] mene mote in ony ȝere þat is lasse þan thy rote, with-drawe þe nombere of so many ȝeris as hit is lasse þan þe ȝere of ovre lord a 1397, & kepe þe residue; & so many ȝeris, monythis, & dayes entere in-to thy tabelis of thy mene mote. And take alle the signes, degreis, and Minutes, [and] Secundis, þat þou findest in directe of alle þe ȝeris, monythis, & dayes, & wryte hem in þy slate; and abowe þilke nombere write þe signes, degreis, Minutes, & secundis, þe wyche þou findest with thy rote þe ȝere of ovre lord a l397; & with-drawe alle þe nethere signis & degreis fro þe signes & degrees, Minutes, & Secundis of oþer signes with thy rote, and thy residue þat lewyth is thy mene mote for þat day.

4la. Vmbra Recta.

[folio 34b]

Ȝif þi rewle falle vppon þe 8 poynt on riȝt schadwe, þan make þi figure of 8; þan loke how moche space of feet ys be-twen þe & þe tour, & multiplie þat be 12, & whan þou [hast] multiplied it, þan diuide yt be þe same nombre of 8, & kepe þe residue, & adde þerto 4 vp to þyn eye to þe residue, & þat schal be þe verry heyȝt of þe tour. & þus mayst þou werke on þe same wyse, fro 1 to 12.

41b. Vmbra Recta.

An-oþer maner of werkyng vppon þe same syde. Loke vppon whych poynt þi Rewle falliþ whan þou seest þe top of þe tour þorow too litil holes, & mete þan þe space fro þi foot to þe baas of þe tour; & ryȝt [folio 36] as the nombre of þy poynt hath hym-self to 12, ryȝt so þe mesure be-twen þe & þe tour haþ hym-self to þe heiȝte of þe same tour. Ensample : y sette caas þi rewle falle vpon 8, þan ys 8 to-þridd partyes of 12; so þe space ys þe too-þridd partyes of þe tour.

42a. Vmbra Versa.

To knowe þe [heyth by þy] poyntes of umbra versa. Ȝif þy rewle falle vppon 3, whan þou seest þe top of þe tour / sett a prikke þere-as þi foot stont; & goo ner tyl þou mayst see þe same top at þe poynt of 4, & sette þer anoþer lyk prikke / þan mete how many foot ben be-twen þe too prikkis, & adde þe lengþe vp to þyn eye þer-to ; & þat schal be þe heyȝte of þe tour. And note, þat 3 ys fourþe party of 12, & 4 is þe þridde party of 12. Now passeþ 4 þe nombre of 3 be þe distaunce of 1; þerfore þe same space, wyþ þyn heyȝt to

þyn eye, ys þe heyȝt of þe tour. & ȝif it so be þat þer be 2 or 3 distaunce in þe nombres, so schulde þe mesures be-twen þe prikkes be twyes or þries þe heyȝte of þe tour.

43a. Ad cognoscendum altitudinem alicuius rei per vmbram [rectam].

[folio 36b]

To knowe þe heyȝte of þynges, ȝif þou mayst [nat] come to þe bas of a þyng. sette þy rewle vppon what þou wylt, so þat þou may see þe topp of þe þyng þorw þe too holes, & make a marke þer þy foot standeþ; and goo neer or forþer / till þou mayst see þorw anoþer poynt, & marke þer a-noþer marke; & loke þan what ys þe differense be-twen þe too poyntes in þe scale; & riȝt as þat difference haþ hym to 12, riȝt so þe space be-twen þe & þe too markys haþ hym to þe heyȝte of þe þyng. Ensample : y set caas þou seest it þorw a poynt of 4 ; aftyr, at þe poynt of 3. Now passiþ þe nombre of 4 þe nombre of 3 be þe difference of 1, and riȝt as þis difference 1 haþ hym-self to 12, riȝt so þe mesure be-twen þe too markis haþ hym to þe heyȝte of þe þyng, puttyng to þe heyȝte of þi-self to þyn eye ; & þus mayst þou werke fro 1 to 12.

42b. Per vmbram versam.

Furþermore, ȝif þou wilt knowe in vmbra versa / be þe craft of vmbra recta, y suppose þou take þe altitude at þe poynt of 4, & makest a marke, & þou goost neer tyl þou hast yt at þe poynt of 3, & þan makyst [folio 37] þou þer an-noþer mark. þan muste þou deuide 144 be eche of þe poyntes be-fornseyd, [as] þus : ȝif þou deuide 144

be [4,] & þe nombre þat comeþ þer-of schal be 36, & ȝif þou deuide 144 be 3, & þe nombre þat comeþ þer-of schal be 48, þanne loke what ys þe difference be-twen 36 & 48, & þer schalt þou fynde 12; and ryȝt as 12 haþ hym to 12, ryȝt so þe space be-twen too prikkes haþ hym to þe altitude of þe þyng.

46. For to knowe at what houre of þe day, or of the night, shal be Flode or ebbe.

First wite thou certeinly, how that haven stondith, that thou list to werke fore ; þat is to say in whiche place of the firmament the mone beyng, makiþ fulle see. Than awayte þou redily in what degree of þe zodiak þat þe mone at þat tyme is ynne. Bringe furth than þe labelle, & sett the point therof in þat same cost þat the mone makiþ flode, and sett þou þere þe degre of þe mone according wiþ þe egge of þe label. Than afterward awayte where is than þe degre of the sonne, at þat tyme. Remeue þou than þe label fro the mone, & bringe & sette [it] iustly vpon þe degre of þe sonne. And þe point of þe label shal þan declare to þe, at what houre of þe day or of þe night shal be flode. And þere also maist þou wite by þe same point of þe label, wheþir it be, at þat same, flode or ebbe, or half flode, or quarter flode, or ebbe, or half or quarter ebbe ; or ellis at what houre it was last, or shalbe next by night or by day, þou þan [maist] esely

knowe, etc. Furþermore if it so be þat thou happe to worke for þis matere aboute þe tyme of coniunccioun, bringe furþe þe degre of þe mone wiþ þe labelle to þat coste as it is before seyde. but than þou shalt vnderstonde þat þou may not bringe furþe þe label fro þe degre of þe mone as þou dide before; For-why the sonne is þan in þe same degre with the mone. And so þou may at þat tyme by þe point of the labelle vnremevid knowe þe houre of þe flode or of þe ebbe as it is before seyd, &c. And euermore as þou findest þe mone passe fro þe sonne, so remeve þou þe labelle þan fro þe degre of þe mone, and bringe it to the degre of þe sonne. And worke þou þan as þou dide before, etc. Or ellis knowe þou what houre it is þat þou art inne, by þin instrument. Than bringe þou furthe fro thennes þe labelle and ley it vpon þe degre of þe mone, and þerby may þou wite also whan it was flode, or whan it wol be next, be it nyght or day; &c.