PART II.

Here biginnen the Conclusions of the Astrolabie.

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

[Hic incipiunt Conclusiones Astrolabii; et prima est ad inveniendum gradus solis in quibus singulis diebus secundum cursum sol est existens.]

Rekene and knowe which is the day of thy monthe; and ley

thy rewle up that same day; and thanne wol the verray point of

thy rewle sitten in the bordure, up-on the degree of thy sonne.

Ensample as thus; the yeer of oure lord 1391, the 12 day of

March at midday, I wolde knowe the degree of the sonne. I

soughte in the bak-half of myn Astrolabie, and fond the cercle of

the dayes, the which I knowe by the names of the monthes writen

under the same cercle. Tho leide I my rewle over this forseide

day, and fond the point of my rewle in the bordure up-on the

firste degree of Aries, a litel with-in the degree; and thus knowe

I this conclusioun. Another day, I wolde knowe the degree of

my sonne, and 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 up-on this forseide 13 day, and fond the point of my rewle

in the bordure up-on the first degree of Capricorne, a lite with-in

the degree; and than hadde I of this conclusioun the ful

experience. And for the more declaracioun, lo here thy figure.

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

[De altitudine solis et aliorum corporum supra celestium.]

Put the ring of thyn Astrolabie up-on thy right thoumbe, and

turne thy lift syde agayn the light of the sonne. And remeve

thy rewle up and doun, til that the stremes of the sonne shyne

thorgh bothe holes of thy rewle. Loke thanne how many degrees

thy rewle is areised fro the litel crois up-on thyn est line, and tak

ther the altitude of thy sonne. And in this same wyse maistow

knowe by nighte the altitude of the mone, or of brighte sterres.

This chapitre is so general ever in oon, that ther nedith no more

declaracion; but forget it nat. And for the more declaracioun,

lo here the figure.

[3.] To knowe every tyme of the day by light of the sonne, and every tyme of the night by the sterres fixe, and eke to knowe by night or by day the degree of any signe that assendeth on the Est Orisonte, which that is cleped communly the Assendent, or elles Oruscupum.

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

Tak the altitude of the sonne whan thee list, as I have said; and

set the degree of the sonne, in cas that it be by-forn the middel of

the day, among thyn almikanteras on the est side of thyn

Astrolabie; and yif it be after the middel of the day, set the degree

of thy sonne up-on the west side; tak this manere of setting for a

general rewle, ones for evere. And whan thou hast set the degree

of thy sonne up as many almikanteras of heyghte as was the

altitude of the sonne taken by thy rewle, ley over thy label, up-on

the degree of the sonne; and thanne wol the point of thy label

sitten in the bordure, up-on the verrey tyd of the day. Ensample

as thus: the yeer of oure lord 1391, the 12 day of March, I wold

knowe the tyd of the day. I took the altitude of my sonne, and

fond that it was 25 degrees and 30 of minutes of heyghte in the

bordure on the bak-syde. Tho turnede I myn Astrolabie, and by-cause

that it was by-forn midday, I turnede my riet, and sette the

degree of the sonne, that is to seyn, the 1 degree of Aries, on the

right syde of myn Astrolabie, up-on that 25 degrees and 30 of

minutes of heyghte among myn almikanteras; tho leide I my label

up-on the degree of my sonne, and fond the poynte of my label in

the bordure, up-on a capital lettre that is cleped an X; tho rekened

I alle the capitalles lettres fro the lyne of midnight un-to this forseide

lettre X, and fond that it was 9 of the clokke of the day.

Tho loked I down up-on the est orisonte, and fond there the 20

degree of Geminis assending; which that I tok for myn assendent.

And in this wyse hadde I the experience for ever-mo in which

maner I sholde knowe the tyd of the day, and eek myn [assendent].

Tho wolde I wite the same night folwing the hour of the

night, and wroughte in this wyse. Among an heep of sterris fixe,

it lyked me for to take the altitude of the feire white sterre that is

cleped [Alhabor]; and fond hir sitting on the west side of the lyne

of midday, 18 degres of heighte taken by my rewle on the bak-syde.

Tho sette I the centre of this Alhabor up-on 18 degrees among

myn almikanteras, up-on the west syde; by-cause that she was

founden on the west syde. Tho leide I my label over the degree

of the sonne that was descended under the weste orisonte, and

rikened alle the lettres capitals fro the lyne of midday un-to the

point of my label in the bordure; and fond that it was passed 8 of

the clokke the space of 2 degrees. Tho loked I doun up-on myn

est orisonte, and fond ther 23 degrees of Libra assending, whom I

tok for myn assendent; and thus lerned I to knowe ones for ever

in which manere I shuld come to the houre of the night and to

myn assendent; as verreyly as may be taken by so smal an instrument.

But natheles, in general, wolde I warne thee for evere, ne

mak thee nevere bold to have take a iust ascendent by thyn

Astrolabie, or elles to have set iustly a clokke, whan any celestial

body by which that thow wenest governe thilke thinges ben ney

the south lyne; for trust wel, whan that the sonne is ney the

meridional lyne, the degree of the sonne renneth so longe consentrik

up-on the almikanteras, that sothly thou shalt erre fro the iust

assendent. The same conclusioun sey I by the centre of any

sterre fix by night; and more-over, by experience, I wot wel that

in oure orisonte, from 11 of the clokke un-to oon of the clokke,

in taking of a iust assendent in a portatif Astrolabie, hit is to hard

to knowe. I mene, from 11 of the clokke biforn the houre of

noon til oon of the clok next folwing. And for the more declaracion,

lo here thy figure.

[4.] Special declaracion of the [assendent].

[Specialis declaracio de ascendente.]

The assendent sothly, as wel in alle nativitez as in questiouns

and elecciouns of tymes, is a thing which that thise astrologiens

gretly observen; wher-fore me semeth convenient, sin that I

speke of the assendent, to make of it special declaracioun. The

assendent sothly, to take it at the largeste, is thilke degree that

assendeth at any of thise forseide tymes upon the est orisonte;

and there-for, yif that any planet assende at that same tyme in

thilke for-seide degree of his longitude, men seyn that thilke

planete is in horoscopo. But sothly, the hous of the assendent,

that is to seyn, the firste hous or the est angle, is a thing more

brood and large. For after the statutz of astrologiens, what

celestial body that is 5 degres above thilk degree that assendeth,

or with-in that noumbre, that is to seyn, nere the degree that

assendeth, yit rikne they thilke planet in the assendent. And

what planete that is under thilke degree that assendith the space

of 25 degrees, yit seyn they that thilke planete is lyk to him that

is in the hous of the assendent; but sothly, yif he passe the

bondes of thise forseide spaces, above or bynethe, they seyn

that the planete is failling fro the assendent. Yit sein thise

astrologiens, that the assendent, and eke the lord of the assendent,

may be shapen for to be fortunat or infortunat, [as thus]: a fortunat

assendent clepen they whan that no wykkid planete, as Saturne

or Mars, or elles the Tail of the Dragoun, is in the hous of the

assendent, ne that no wikked planete have non aspecte of enemite

up-on the assendent; but they wol caste that they have a fortunat

planete in hir assendent and yit in his felicitee, and than sey they

that it is wel. Forther-over, they seyn that the infortuning of an

assendent is the contrarie of thise forseide thinges. The lord of

the assendent, sey they, that he is fortunat, whan he is in good

place fro the assendent as in angle; or in a succedent, where-as

he is in his dignitee and conforted with frendly aspectes of planetes

and wel resceived, and eek that he [may seen the assendent], and

that he be nat retrograd ne [combust], ne ioigned with no shrewe

in the same signe; ne that he be nat in his descencioun, ne

ioigned with no planete in his discencioun, ne have up-on him

non aspecte infortunat; and than sey they that he is wel. Natheles,

thise ben observauncez of iudicial matiere and rytes of payens,

in which my spirit ne hath no feith, ne no knowing of hir horoscopum;

for they seyn that every signe is departed in 3 evene

parties by 10 degrees, and thilke porcioun they clepe a [Face].

And al-thogh that a planete have a latitude fro the ecliptik, yit

sey some folk, so that the planete aryse in that same signe with

any degree of the forseide face in which his longitude is rekned,

that yit is the planete in horoscopo, be it in nativite or in eleccioun,

&c. And for the more declaracioun, lo here the figure.

[5.] To knowe the verrey equacioun of the degree of the sonne, yif so be that it falle by-twixe thyn Almikanteras.

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

For as moche as the almikanteras in thyn Astrolabie been

compouned by two and two, where-as some almikanteras in

sondry Astrolabies ben compouned by on and on, or elles by two

and two, it is necessarie to thy lerning to teche thee first to knowe

and worke with thyn owne instrument. Wher-for, whan that the

degree of thy sonne falleth by-twixe two almikanteras, or elles yif

thyn almikanteras ben graven with over gret a point of a compas,

(for bothe thise thinges may causen errour as wel in knowing of

the tyd of the day as of the verrey assendent), thou most werken

in this wyse. Set the degree of thy sonne up-on the heyer

almikanteras of bothe, and waite wel wher as thin almury toucheth

the bordure, and set ther a prikke of inke. Set doun agayn the

degree of thy sonne up-on the nethere almikanteras of bothe, and

set ther another prikke. Remewe thanne thyn almury in the

bordure evene amiddes bothe prikkes, and this wol lede iustly the

degree of thy sonne to sitte by-twixe bothe almikanteras in his

right place. Ley thanne thy label over the degree of thy sonne;

and find in the bordure the verrey tyde of the day or of the night.

And as verreyly shaltow finde up-on thyn est orisonte thyn assendent.

And for more declaracioun, lo here thy figure.

[6.] To knowe the spring of the dawing and the ende of the evening, the which ben called the two crepusculis:

[Ad cognoscendum ortum solis et eius occasum, que vocatur vulgariter crepusculum.]

Set the nadir of thy sonne up-on 18 degrees of heighte among

thyn almikanteras on the west syde, and ley thy label on the degree

of thy sonne, and thanne shal the poynt of thy label schewe the

spring of day. Also set the nadir of thy sonne up-on 18 degrees

of heighte a-mong thyn almikanteras on the est side, and ley over

thy label up-on the degree of the sonne, and with the point of

thy label find in the bordure the ende of the evening, that is,

verrey night. The nadir of the sonne is thilke degree that is

opposit to the degree of the sonne, in the [seventhe] signe, as thus:

every degree of Aries by ordre is nadir to every degree of Libra

by ordre; and Taurus to Scorpion; Gemini to Sagittare; Cancer

to Capricorne; Leo to Aquarie; Virgo to Pisces; and yif any degree

in thy zodiak be dirk, his nadir shal declare him. And for the

more declaracioun, lo here thy figure.

[7.] To knowe the arch of the day, that some folk callen the day artificial, from the sonne arysing til hit go to reste.

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

Set the degree of thy sonne up-on thyn est orisonte, and ley

thy label on the degree of the sonne, and at the poynt of thy

label in the bordure set a prikke. Turn thanne thy riet aboute

til the degree of the sonne sit up-on the west orisonte, and ley

thy label up-on the same degree of the sonne, and at the point of

thy label set a-nother prikke. Rekne thanne the quantitee of

tyme in the bordure by-twixe bothe prikkes, and tak ther thyn ark

of the day. The remenant of the bordure under the orisonte is

the ark of the night. Thus maistow rekne bothe arches, or

every porcion, of whether that thee lyketh. And by this manere

of wyrking maistow see how longe that any sterre fix dwelleth above

the erthe, fro tyme that he ryseth til he go to reste. But

the day natural, that is to seyn 24 houres, is the revolucioun of

the equinoxial with as moche partie of the zodiak as the sonne

of his propre moevinge passeth in the mene whyle. And for the

more declaracioun, lo here thy figure.

[8.] To turn the houres in-equales in houres equales.

[Ad convertendum horas inequales in horas equales.]

Knowe the nombre of the degrees in the houres in-equales, and

departe hem by 15, and tak ther thyn houres equales. And for

the more declaracioun, lo here thy figure.

[9.] To knowe the quantitee of the day vulgare, that is to seyen, from spring of the day un-to verrey night.

[Ad cognoscendum quantitatem diei vulgaris, viz. ab ortu diei usque ad noctem.]

Know the quantitee of thy crepusculis, as I have taught in the

[chapitre bi-forn], and adde hem to the arch of thy day artificial;

and tak ther the space of alle the hole day vulgar, un-to verrey

night. The [same manere] maystow worke, to knowe the quantitee

of the vulgar night. And for the more declaracioun, lo here the

figure.

[10.] To knowe the quantite of houres in-equales by day.

[Ad cognoscendum horas inequales in die.]

Understond wel, that thise houres in-equales ben cleped houres

of planetes, and understond wel that som-tyme ben they lengere

by day than by night, and som-tyme the contrarie. But understond

wel, that evermo, generaly, the hour in-equal of the day

with the houre in-equal of the night contenen 30 degrees of the

bordure, whiche bordure is ever-mo answering to the degrees of

the equinoxial; wher-for departe the arch of the day artificial in

12, and tak ther the quantitee of the houre in-equal by day.

And yif thow abate the quantitee of the houre in-equal by daye

out of 30, than shal the remenant that leveth performe the houre

inequal by night. And for the more declaracioun, lo here the

figure.

[11.] To knowe the quantite of houres equales.

[Ad cognoscendum quantitatem horarum inequalium.]

The quantitee of houres equales, that is to seyn, the houres of

the clokke, ben departed by 15 degrees al-redy in the bordure

of thyn Astrolabie, as wel by night as by day, generaly for evere.

What nedeth more declaracioun? Wher-for, whan thee list to

know how manye houres of the clokke ben passed, or any part of

any of thise houres that ben passed, or elles how many houres or

partie of houres ben to come, fro swich a tyme to swich a tyme,

by day or by nighte, knowe the degree of thy sonne, and ley thy

label on it; turne thy riet aboute ioyntly with thy label, and with

the point of it rekne in the bordure fro the sonne aryse un-to

the same place ther thou desirest, by day as by nighte. This

conclusioun wol I declare in the laste chapitre of the 4 partie of

this tretis so openly, that ther shal lakke no worde that nedeth to

the declaracioun. And for the more declaracioun, lo here the

figure.

[12.] Special declaracioun of the houres of planetes.

[Specialis declaracio de horis planetarum.]

Understond wel, that evere-mo, fro the arysing 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

aryse; than shal the verrey degree of the sonne shewe the houre

of the planete. Ensample as thus. The 13 day of March fil

up-on a Saterday per aventure, and, at the arising of the sonne, I

fond the secounde degree of Aries sitting up-on myn est orisonte,

al-be-it that it was but lite; than fond I the 2 degree of Libra,

nadir of my sonne, dessending on my west orisonte, up-on which

west orisonte every day generally, at the sonne ariste, entreth

the houre of any planete, after which planete the day bereth his

name; and endeth in the nexte stryk of the plate under the

forseide west orisonte; and evere, as the sonne climbeth uppere

and uppere, so goth his nadir dounere and dounere, teching by

swich strykes the houres of planetes by ordre as they sitten in

the hevene. The first houre inequal of every Satterday is to

Saturne; and 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; and 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 sheweth the verrey degree of the sonne the houre of

Mercurie entring under my west orisonte at eve; and next him

succedeth the Mone; and so forth by ordre, planete after

planete, in houre after houre, al the night longe til the sonne

aryse. Now ryseth the sonne that Sonday by the morwe; and

the nadir of the sonne, up-on the west orizonte, sheweth me the

entring of the houre of the forseide sonne. And in this maner

succedeth planete under planete, fro Saturne un-to the Mone,

and fro the Mone up a-gayn to Saturne, houre after houre

generaly. And thus knowe I this conclusioun. And for the

more declaracioun, lo here the figure.

[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 up-on the lyne meridional, and

rikene how many degrees of almikanteras ben by-twixe thyn est

orisonte and the degree of the sonne. And tak ther thyn altitude

meridian; this is to seyne, the heyest of the sonne as for that day.

So maystow knowe in the same lyne, the [heyest cours] that any

sterre fix climbeth by night; this is to seyn, that whan any sterre

fix is passed the lyne meridional, than by-ginneth it to descende,

and so doth the sonne. And for the more declaracioun, lo here

thy figure.

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

[Ad cognoscendum gradum solis curiose.]

Sek bysily with thy rewle the heyest of the sonne in midde of

the day; turne thanne thyn Astrolabie, and with a prikke of ink

marke the nombre of that same altitude in the lyne meridional.

Turne thanne thy riet a-boute til thou fynde a degree of thy

zodiak acording with the prikke, this is to seyn, sittinge on the

prikke; and in sooth, thou shalt finde [but two degrees] in al the

zodiak of that condicioun; and yit thilke two degrees ben in

diverse signes; than maistow lightly by the sesoun of the yere

knowe the signe in whiche that is the sonne. And for the

more declaracioun, lo here thy figure.

[15.] To know which day is lyk to which day as of lengthe, &c.

[Ad cognoscendum quales dies in longitudine sunt similes.]

Loke whiche degrees ben y-lyke fer fro the hevedes of Cancer

and Capricorn; and lok, whan the sonne is in any of thilke

degrees, than ben the dayes y-lyke of lengthe. This is to seyn,

that as long is that day in that monthe, as was swich a day in

swich a month; ther varieth but lite. Also, yif thou take two

dayes naturaly in the yer y-lyke fer fro eyther pointe of the

equinoxial in the opposit parties, than as long is the day artificial

of that on day as is the night of that othere, and the contrarie.

And for the more declaracioun, lo here thy figure.

[16.] This chapitre is a maner declaracioun to conclusiouns that folwen.

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

Understond wel that thy zodiak is departid in two halfe cercles,

as fro the heved of Capricorne un-to the heved of Cancer; and

agaynward fro the heved of Cancer un-to the heved of Capricorne.

The heved of Capricorne is the lowest point, wher-as the sonne

goth in winter; and the heved of Cancer is the heyest point, in

whiche the sonne goth in somer. And ther-for understond wel,

that any two degrees that ben y-lyke fer fro any of thise two

hevedes, truste wel that thilke two degrees ben of y-lyke declinacioun,

be it southward or northward; and the dayes of hem

ben y-lyke of lengthe, and the nightes also; and the shadwes

y-lyke, and the altitudes y-lyke at midday for evere. And for

more declaracioun, lo here thy figure.

[17.] To knowe the verrey degree of any maner sterre straunge or unstraunge after his longitude, though he be indeterminat in thyn Astrolabie; sothly to the trowthe, thus he shal be knowe.

[Ad cognoscendum verum gradum alicuius stelle aliene secundum eius longitudinem, 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 thou mayst gesse; and tak an assendent

a-non right by som maner sterre fix which that thou

knowest; and for-get nat the altitude of the firste sterre, ne thyn

assendent. And whan that this is don, espye diligently whan this

same firste sterre passeth any-thing the south westward, and hath

him a-non right in the same noumbre of altitude on the west side

of this lyne meridional as he was caught on the est side; and tak

a newe assendent a-non right by som maner sterre fixe which that

thou knowest; and for-get nat this secounde assendent. And

whan that this is don, rikne thanne how manye degrees ben by-twixe

the firste assendent and the seconde assendent, and rikne

wel the middel degree by-twene bothe assendentes, and set thilke

middel degree up-on thin est orisonte; and waite thanne what degree

that sit up-on the lyne meridional, and tak ther the verrey degree

of the ecliptik in which the sterre stondeth for the tyme. For in

the ecliptik is the longitude of a celestial body rekened, evene fro

the heved of Aries un-to the ende of Pisces. And his latitude is

rikned after the quantite of his declinacion, north or south to-warde

the poles of this world; as thus. Yif it be of the sonne or of any

fix sterre, rekene his latitude or his declinacioun fro the equinoxial

cercle; and yif it be of a planete, rekne than the quantitee of his

latitude fro the ecliptik lyne. Al-be-it so that fro the equinoxial

may the declinacion or the latitude of any body celestial be rikned,

after the [site] north or south, and after the quantitee of his declinacion.

And right so may the latitude or the declinacion of any

body celestial, save only of the sonne, after his site north or south,

and after the quantitee of his declinacioun, be rekned fro the

ecliptik lyne; fro which lyne alle planetes som tyme declynen

north or south, save only the for-seide sonne. And for the more

declaracioun, lo here thy figure.

[18.] To knowe the degrees of the longitudes of fixe sterres after that they ben determinat in thin Astrolabie, yif so be that 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 up-on the lyne meridional, and tak

keep of thy zodiak, and loke what degree of any signe that sit on

the same lyne meridional at that same tyme, and tak the degree in

which the sterre standeth; and with that same degree comth that

same sterre un-to that same lyne fro the orisonte. And for more

declaracioun, lo here thy figure.

[19.] To knowe with which degree of the zodiak any sterre fixe in thyn Astrolabie aryseth up-on the est orisonte, althogh his dwelling be in a-nother signe.

[Ad cognoscendum cum quibus gradibus zodiaci que stella fixa in astrolabio ascendit super orizontem orientalem, quamvis eius statio sit in alio signo.]

Set the centre of the sterre up-on the est orisonte, and loke

what degree of any signe that sit up-on the same orisonte at that

same tyme. And understond wel, that with that same degree

aryseth that same sterre; and this merveyllous arysing with a

strange degree in another signe is by-cause that the latitude of the

sterre fix is either north or south fro the [equinoxial]. But sothly

the latitudes of planetes ben comunly rekned fro the ecliptik,

bi-cause that non of hem declineth but fewe degrees out fro the

brede of the zodiak. And tak good keep of this chapitre of arysing

of the celestial bodies; for truste wel, that neyther mone ne sterre

as in oure embelif orisonte aryseth with that same degree of his

longitude, save in o cas; and that is, whan they have no latitude

fro the ecliptik lyne. But natheles, som tyme is everiche of thise

planetes under the same lyne. And for more declaracioun, lo

here thy 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 up-on the lyne meridional, and rikne

his altitude in almikanteras fro the est orizonte up to the same

degree set in the forseide lyne, and set ther a prikke. Turne up

thanne thy riet, and set the heved of Aries or Libra in the same

meridional lyne, and set ther a-nother prikke. And whan that

this is don, considere the altitudes of hem bothe; for sothly the

difference of thilke altitudes is the declinacion of thilke degree

fro the equinoxial. And yif so be that thilke degree be northward

fro the equinoxial, than is his declinacion north; yif it be southward,

than is it south. And for the more declaracioun, lo here

thy figure.

[21.] To knowe for what latitude in any regioun the almikanteras of any table ben compouned.

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

Rikne how manye degrees of almikanteras, in the meridional

lyne, be fro the cercle equinoxial un-to the senith; or elles fro the

pool artik un-to the north orisonte; and for so gret a latitude or

for so smal a latitude is the table compouned. And for more

declaracion, lo here thy figure.

[22.] To knowe in special the latitude of oure countray, I mene after the latitude of Oxenford, and the heighte of oure pol.

[Ad cognoscendum specialiter latitudinem nostri regionis, scilicet latitudinem Oxonie, et altitudinem poli nostri.]

Understond wel, that as fer is the heved of Aries or Libra in the

equinoxial from oure orisonte as is the senith from the pole artik;

and as hey is the pol artik fro the orisonte, as the equinoxial is

fer fro the senith. I prove it thus by the latitude of Oxenford.

Understond wel, that the heyghte of oure pool artik fro oure north

orisonte is 51 degrees and 50 minutes; than is the senith from

oure pool artik 38 degrees and 10 minutes; than is the equinoxial

from oure senith 51 degrees and 50 minutes; than is oure south

orisonte from oure equinoxial 38 degrees and 10 minutes. Understond

wel this rekning. Also for-get nat that the senith is 90

degrees of heyghte fro the orisonte, and oure equinoxial is 90

degrees from oure pool artik. Also this shorte rewle is soth, that

the latitude of any [place] in a regioun is the distance fro the senith

unto the equinoxial. And for more declaracioun, lo here thy

figure.

[23.] To prove evidently the latitude of any place in a regioun, by the preve of the heyghte of the pol artik in that same place.

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

In some winters night, whan the firmament is clere and thikke-sterred,

waite a tyme til that any sterre fix sit lyne-right perpendiculer

over the pol artik, and [clepe that sterre A]. And

wayte a-nother sterre that sit lyne-right under A, and under the

pol, and clepe that sterre F. And understond wel, that F is nat

considered but only to declare that A sit evene overe the pool.

Tak thanne a-non right the altitude of A from the orisonte, and

forget it nat. Lat A and F go farwel til agayns the dawening a

gret whyle; and come thanne agayn, and abyd til that A is evene

under the pol and under F; for sothly, than wol F sitte over the pool,

and A wol sitte under the pool. Tak than eft-sones the altitude of

A from the orisonte, and note as wel his secounde altitude as his

firste altitude; and whan that this is don, rikne how manye degrees

that the firste altitude of A excedeth his seconde altitude, and tak

half thilke porcioun that is exceded, and adde it to his seconde

altitude; and tak ther the elevacioun of thy pool, and eke the

latitude of thy regioun. For thise two ben of a nombre; this is

to seyn, as many degrees as thy pool is elevat, so michel is the

latitude of the regioun. Ensample as thus: par aventure, the

altitude of A in the evening is 56 degrees of heyghte. Than

wol his seconde altitude or the dawing be 48; that is 8 lasse than

56, that was his firste altitude at even. Take thanne the half of

8, and adde it to 48, that was his seconde altitude, and than

hastow 52. Now hastow the heyghte of thy pol, and the latitude

of the regioun. But understond wel, that to prove this conclusioun

and many a-nother fair conclusioun, thou most have a plomet

hanging on a lyne heyer than thin heved on a perche; and thilke

lyne mot hange evene perpendiculer by-twixe the pool and thyn

eye; and thanne shaltow seen yif A sitte evene over the pool and

over F at evene; and also yif F sitte evene over the pool and

over A or day. And for more declaracion, lo here thy figure.

[24.] Another conclusioun to prove the heyghte of the pool artik fro the orisonte.

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

Tak any sterre fixe that nevere dissendeth under the orisonte in

thilke regioun, and considere his heyest altitude and his lowest

altitude fro the orisonte; and make a nombre of bothe thise

altitudes. Tak thanne and abate half that nombre, and tak ther

the elevacioun of the pol artik in that same regioun. And for

more declaracioun, lo here thy figure.

[25.] A-nother conclusioun to prove the latitude of the regioun, &c.

[Alia conclusio ad probandum latitudinem regionis.]

Understond wel that the latitude of any place in a regioun is

verreyly the space by-twixe the senith of hem that dwellen there

and the equinoxial cerkle, north or southe, taking the mesure in

the meridional lyne, as sheweth in the almikanteras of thyn

Astrolabie. And 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, that is to seyn, than is the pol antartik by-nethe

the orisonte, the same quantite of space, neither more 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 hevedes of Aries or of Libra; (for thanne moeveth the

sonne in the lyne equinoxial); and abate the nombre of that same

sonnes altitude out of 90, and thanne is the remenaunt of the

noumbre that leveth the latitude of the regioun. As thus: I

suppose that the sonne is thilke day at noon 38 degrees and 10

minutes of heyghte. Abate thanne thise degrees and minutes out

of 90; so leveth 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 I mighte prove. Now yif

so be that thee semeth to long a taryinge, to abyde til that the

sonne be in the hevedes of Aries or of Libra, thanne waite whan

the sonne is in any other degree of the zodiak, and considere the

degree of his declinacion fro the equinoxial lyne; and yif it so be

that the sonnes declinacion be northward fro the equinoxial, abate

thanne fro the sonnes altitude at noon the nombre of his declinacion,

and thanne hastow the heyghte of the hevedes of Aries

and Libra. As thus: my sonne is, par aventure, in the firste

degre of Leoun, 58 degrees and 10 minutes of heyghte at noon

and his declinacion is almost 20 degrees northward fro the

equinoxial; abate thanne thilke 20 degrees of declinacion out of

the altitude at noon, than leveth thee 38 degrees and odde minutes;

lo ther the heved of Aries or Libra, and thyn equinoxial in that

regioun. Also yif so be that the sonnes declinacioun be southward

fro the equinoxial, adde thanne thilke declinacion to the

altitude of the sonne at noon; and tak ther the hevedes of Aries

and Libra, and thyn equinoxial. Abate thanne the heyghte of

the equinoxial out of 90 degrees, and thanne leveth there the

distans of the pole, 51 degrees and 50 minutes, of that regioun

fro the equinoxial. Or elles, yif thee lest, take the heyest altitude

fro the equinoxial of any sterre fix that thou knowest, and tak his

nethere elongacioun lengthing fro the same equinoxial lyne, and

wirke in the maner forseid. And for more declaracion, lo here

thy figure.

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

[Declaracio de ascensione signorum.]

The excellence of the spere solide, amonges other noble conclusiouns,

sheweth manifeste the diverse assenciouns of signes

in diverse places, as wel in the righte cercle as in the embelif

cercle. Thise auctours wryten that thilke signe is cleped of right

ascensioun, with which more part of the cercle equinoxial and

lasse part of the zodiak ascendeth; and thilke signe assendeth

embelif, with whiche lasse part of the equinoxial and more part of

the zodiak assendeth. [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 passing by the poles of this

worlde, thilke folke han this right cercle and the right orisonte;

and evere-mo the arch of the day and the arch of the night is ther

y-like long, and the sonne twyes every yeer passinge thorow the

senith of her heved; and two someres and two winteres in a yeer

han this forseide poeple. And the almikanteras in her Astrolabies

ben streighte as a lyne, so as sheweth in [this figure]. The utilite to

knowe the [assenciouns in the righte cercle] is this: truste wel that

by mediacioun of thilke assenciouns thise astrologiens, by hir

tables and hir instrumentz, knowen verreyly the assencioun of

every degree and minut in al the zodiak, as shal be shewed. And

nota, that this forseid righte orisonte, that is cleped orison rectum,

divydeth the equinoxial in-to right angles; and the embelif orisonte,

wher-as the pol is enhaused up-on the orisonte, overkerveth the

equinoxial in embelif angles, as sheweth in the figure. And for

the more declaracioun, lo here the figure.

[27.] This is the conclusioun to knowe the assenciouns of signes in the right cercle, that is, circulus directus, &c.

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

Set the heved of what signe thee liste to knowe his assending in

the right cercle up-on the lyne meridional; and waite wher thyn

almury toucheth the bordure, and set ther a prikke. Turne

thanne thy riet westward til that the ende of the forseide signe

sitte up-on the meridional lyne; and eft-sones waite wher thyn

almury toucheth the bordure, and set ther another prikke. Rikne

thanne the nombre of degrees in the bordure by-twixe bothe

prikkes, and tak the assencioun of the signe in the right cercle.

And thus maystow wyrke with every porcioun of thy zodiak, &c.

And for the more declaracioun, lo here thy figure.

[28.] To knowe the assencions of signes in the embelif cercle in every regioun, I mene, in circulo obliquo.

[Ad cognoscendum ascenciones signorum in circulo obliquo, in omni regione.]

Set the heved of the signe which as thee list to knowe his

ascensioun up-on the est orisonte, and waite wher thyn almury

toucheth the bordure, and set ther a prikke. Turne thanne thy

riet upward til that the ende of the same signe sitte up-on the est

orisonte, and waite eft-sones wher as thyn almury toucheth the

bordure, and set ther a-nother prikke. Rikne thanne the noumbre

of degrees in the bordure by-twixe bothe prikkes, and tak ther the

assencioun of the signe in the embelif cercle. And understond

wel, that alle signes in thy zodiak, fro the heved of Aries unto the

ende of Virgo, ben cleped signes of the north fro the equinoxial;

and these signes arysen by-twixe the verrey est and the verrey

north in oure orisonte generaly for evere. And alle signes fro the

heved of Libra un-to the ende of Pisces ben cleped signes of the

south fro the equinoxial; and thise signes arysen ever-mo by-twixe

the verrey est and the verrey south in oure orisonte. Also every

signe by-twixe the heved of Capricorne un-to the ende of Geminis

aryseth on oure orisonte in lasse than two houres equales; and

thise same signes, fro the heved of Capricorne un-to the ende of

Geminis, ben cleped 'tortuos signes' or 'croked signes,' for

they arisen embelif on oure orisonte; and thise crokede signes

ben obedient to the signes that ben of right assencioun. The

signes of right assencioun ben fro the heved of Cancer to the

ende of Sagittare; and thise signes arysen more upright, and they

ben called eke sovereyn signes; and everich of hem aryseth in

more space than in two houres. Of which signes, Gemini obeyeth

to Cancer; and Taurus to Leo; Aries to Virgo; Pisces to Libra;

Aquarius to Scorpioun; and Capricorne to Sagittare. And thus

ever-mo two signes, that ben y-lyke fer fro the heved of Capricorne,

obeyen everích of hem til other. And for more declaracioun, lo

here the figure.

[29.] To knowe iustly the foure quarters of the world, as est, west, north, and sowth.

[Ad cognoscendum evidenter quatuor partes mundi, scilicet, orientem, austrum, aquilonem, et occidentem.]

Take the altitude of thy sonne whan thee list, and note wel the

quarter of the world in which the sonne is for the tyme by the

azimutz. Turne thanne thyn Astrolabie, and set the degree of

the sonne in the almikanteras of his altitude, on thilke side that

the sonne stant, as is the manere in taking of houres; and ley thy

label on the degree of the sonne, and rikene how many degrees of

the bordure ben by-twixe the lyne meridional and the point of thy

label; and note wel that noumbre. Turne thanne a-gayn thyn

Astrolabie, and set the point of thy gret rewle, ther thou takest

thyne altitudes, up-on as many degrees in his bordure fro his

meridional as was the point of thy label fro the lyne meridional on

the wombe-syde. Tak thanne thyn Astrolabie with bothe handes

sadly and slely, and lat the sonne shyne thorow bothe holes of thy

rewle; and sleyly, in thilke shyninge, lat thyn Astrolabie couch

adoun evene up-on a smothe grond, and thanne wol the verrey

lyne meridional of thyn Astrolabie lye evene south, and the est

lyne wole lye est, and the west lyne west, and north lyne north, so

that thou werke softly and avisely in the couching; and thus

hastow the 4 quarters of the firmament. And 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 south fro the forseide wey.

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

Lok whan that a planete is in the lyne meridional, yif that hir

altitude be of the same heyghte that is the degree of the sonne for

that day, and than is the planete in the verrey [wey of the sonne],

and hath no latitude. And yif the altitude of the planete be

heyere than the degree of the sonne, than is the planete north fro

the wey of the sonne swich a quantite of latitude as sheweth by

thyn almikanteras. And yif the altitude of the planete be lasse

than the degree of the sonne, thanne is the planete south fro the

wey of the sonne swich a quantite of latitude as sheweth by thyn

almikanteras. This is to seyn, fro the wey wher-as the sonne

wente thilke day, but nat from the wey of the sonne in every place

of the zodiak. And for the more declaracioun, lo here the figure.

[31.] To knowe the senith of the arysing of the sonne, this is to seyn, the partie of the orisonte in which that the sonne aryseth.

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

Thou most first considere that the sonne aryseth nat al-wey

verrey est, but some tyme by north the est, and som tyme by southe

the est. Sothly, the sonne aryseth never-mo verrey est in oure

orisonte, but he be in the heved of Aries or Libra. Now is thyn

orisonte departed in 24 parties by thy azimutz, in significacion of

[24 partiez] of the world; al-be-it so that shipmen rikne thilke

partiez in 32. Thanne is ther no more but waite in which azimut

that thy sonne entreth at his arysing; and take ther the senith of

the arysing of the sonne. The manere of the devisioun of thyn

Astrolabie is this; I mene, as in this cas. First is it devided in

4 plages principalx with the lyne that goth from est to west, and

than with a-nother lyne that goth fro south to north. Than is it

devided in smale partiez of azimutz, as est, and est by southe,

whereas is the firste azimut above the est lyne; and so forth, fro

partie to partie, til that thou come agayn un-to the est lyne.

Thus maistow understond also the senith of any sterre, in which

partie he ryseth, &c. And for the more declaracion, lo here

the figure.

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

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

Considere the tyme of the coniunccion by thy kalender, as thus;

lok how many houres thilke coniunccion is fro the midday of the

day precedent, as sheweth by the canoun of thy kalender. Rikne

thanne thilke nombre of houres in the bordure of thyn Astrolabie,

as thou art wont to do in knowing of the houres of the day or of

the night; and ley thy label over the degree of the sonne; and

thanne wol the point of thy label sitte up-on the hour of the coniunccion.

Loke thanne in which azimut the degree of thy sonne

sitteth, and in that partie of the firmament is the coniunccioun.

And for the more declaracioun, lo here thy figure.

[33.] To knowe the senith of the altitude of the sonne, &c.

[Ad cognoscendum signa de altitudine solis.]

This is no more to seyn but any tyme of the day tak the altitude

of the sonne; and by the azimut in which he stondeth, maystou

seen in which partie of the firmament he is. And in the same

wyse maystou seen, by the night, of any sterre, whether the

sterre sitte est or west or [north], or any partie by-twene, after the

name of the azimut in which is the sterre. And for the more

declaracioun, lo here the figure.

[34.] To knowe sothly the degree of the longitude of the mone, or of any planete that 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 causanto linea ecliptica.]

Tak the altitude of the mone, and rikne thyn altitude up among

thyne almikanteras on which syde that the mone stande; and set

there a prikke. Tak thenne anon-right, [up-on the mones syde],

the altitude of any sterre fix which that thou knowest, and set his

centre up-on his altitude among thyn almikanteras ther the sterre

is founde. Waite thanne which degree of the zodiak toucheth the

prikke of the altitude of the mone, and tak ther the degree in

which the mone standeth. This conclusioun is verrey soth, yif

the sterres in thyn Astrolabie stonden after the trowthe; of

comune, tretis of Astrolabie ne make non excepcioun whether the

mone have latitude, or non; ne on whether syde of the mone the

altitude of the sterre fix be taken. And nota, that yif the mone

shewe himself by light of day, than maystow wyrke this same

conclusioun by the sonne, as wel as by the fix sterre. And for the

more declaracioun, lo here thy figure.

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

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

Tak the altitude of any sterre that is cleped a planete, and note

it wel. And tak eek anon the altitude of any sterre fix that thou

knowest, and note it wel also. Come thanne agayn the thridde or

the ferthe night next folwing; for thanne shaltow aperceyve wel the

moeving of a planete, whether so he moeve forthward or bakward.

Awaite wel thanne whan that thy sterre fix is in the same altitude that

she was whan thou toke hir firste altitude; and tak than eftsones

the altitude of the forseide planete, and note it wel. For trust

wel, yif so be that the planete be on the [right syde] of the meridional

lyne, so that his seconde altitude be lasse than his firste altitude

was, thanne is the planete directe. And yif he be on the west

syde in that condicion, thanne is he retrograd. And yif so be

that this planete be up-on the est syde whan his altitude is taken,

so that his secounde altitude be more than his firste altitude,

thanne is he retrograde, and yif he be on the west syde, than is he

directe. But the contrarie of thise parties is of the cours of the

mone; for sothly, the mone moeveth the contrarie from othere

planetes as in hir [episicle], but in non other manere. And for

the more declaracioun, lo here thy figure.

[36.] The conclusiouns of [equaciouns of houses], after the Astrolabie, &c.

[Conclusio de equacione domorum.]

Set the by-ginning of the degree that assendeth up-on the ende

of the 8 houre inequal; thanne wol the by-ginning of the 2 hous

sitte up-on the lyne of midnight. Remove thanne the degree that

assendeth, and set him on the ende of the 10 hour inequal; and

thanne wol the byginning of the 3 hous sitte up-on the midnight

lyne. Bring up agayn the same degree that assendeth first, and

set him up-on the orisonte; and thanne wol the be-ginning of the

4 hous sitte up-on the lyne of midnight. Tak thanne the nadir of

the degree that first assendeth, and set him on the ende of the 2

houre inequal; and thanne wol the by-ginning of the 5 hous sitte

up-on the lyne of midnight; set thanne the nadir of the assendent

on the ende of the 4 houre, than wol the byginning of the 6 house

sitte on the midnight lyne. The byginning of the 7 hous is nadir

of the assendent, and the byginning of the 8 hous is nadir of the

2; and the by-ginning of the 9 hous is nadir of the 3; and the

by-ginning of the 10 hous is the nadir of the 4; and the byginning

of the 11 hous is nadir of the 5; and the byginning of the 12 hous

is nadir of the 6. And for the more declaracion, lo here the

figure.

[37.] A-nother manere of equaciouns of houses by the Astrolabie.

[De aliqua forma equacionis domorum secundum astrolabium.]

Tak thyn assendent, and thanne hastow thy 4 angles; for wel

thou wost that the opposit of thyn assendent, that is to seyn, thy

by-ginning of the 7 hous, sit up-on the west orizonte; and the

byginning of the 10 hous sit up-on the lyne meridional; and his

opposit up-on the lyne of midnight. Thanne ley thy label over

the degree that assendeth, and rekne fro the point of thy label

alle the degrees in the bordure, til thou come to the meridional

lyne; and departe alle thilke degrees in 3 evene parties, and take

the evene equacion of 3; for ley thy label over everich of 3 parties,

and than maistow see by thy label in which degree of the zodiak is

the by-ginning of everich of thise same houses fro the assendent:

that is to seyn, the beginning of the 12 house next above thyn

assendent; and thanne the beginning of the 11 house; and

thanne the 10, up-on the meridional lyne; as I first seide. The

same wyse wirke thou fro the assendent doun to the lyne of

midnight; and thanne thus hastow other 3 houses, that is to seyn,

the byginning of the 2, and the 3, and the 4 houses; thanne is

the nadir of [thise 3 houses] the by-ginning of the 3 houses that

folwen. And for the more declaracioun, lo here thy figure.

[38.] To finde the lyne merydional to dwelle fix in any certein place.

[Ad inveniendum lineam meridionalem per subtiles operaciones.]

Tak a rond plate of metal; [for warping, the brodere the bettre];

and make ther-upon a iust compas, a lite with-in the bordure; and

ley this ronde plate up-on an evene grond, or on an evene ston, or

on an evene stok fix in the gronde; and ley it even by a level.

And in centre of the compas stike an evene pin or a wyr upright;

the smallere the betere. Set thy pin by a plom-rewle evene

upright; and let this pin be no lengere than a quarter of the

diametre of thy compas, [fro the centre]. And waite bisily, aboute

10 or 11 of the clokke and whan the sonne shyneth, whan the

shadwe of the pin entreth [any-thing] with-in the cercle of thy plate

an heer-mele, and mark ther a prikke with inke. Abyde thanne

stille waiting on the sonne after 1 of the clokke, til that the

schadwe of the wyr or of the pin passe ony-thing out of the cercle

of the compas, be it never so lyte; and set ther a-nother prikke

of inke. Take than a compas, and mesure evene the middel

by-twixe bothe prikkes; and set ther a prikke. Take thanne

a rewle, and draw a stryke, evene a-lyne fro the pin un-to the

middel prikke; and tak ther thy lyne meridional for evere-mo, as

in that same place. And yif thow drawe a cros-lyne over-thwart

the compas, iustly over the lyne meridional, than hastow est and

west and south; and, par consequence, than the nadir of the

south lyne is the north lyne. And for more declaracioun, lo here

thy figure.

[39.] Descripcion of the meridional lyne, of longitudes, and latitudes of citees and townes from on to a-nother of clymatz.

This lyne meridional is but a maner descripcion of lyne

imagined, that passeth upon the poles of this world and by

the senith of oure heved. And hit is y-cleped the lyne meridional;

for in what place that any maner man is at any tyme of the yeer,

whan that the sonne by moeving of the firmament cometh to his

verrey meridian place, than is hit verrey midday, that we clepen

oure noon, as to thilke man; and therfore is it cleped the lyne of

midday. And nota, for evermo, of 2 citees or of 2 tounes, of

whiche that o toun aprocheth more toward the est than doth

that other toun, truste wel that thilke tounes ban diverse meridians.

Nota also, that the arch of the equinoxial, that is conteyned

or bounded by-twixe the 2 meridians, is cleped the longitude

of the toun. And yif so be that two tounes have y-lyke

meridian, or oon meridian, than is the distance of hem bothe y-lyke

fer fro the est; and the contrarie. And in this manere they

chaunge nat her meridian, but sothly they chaungen her almikanteras;

for the enhausing of the pool and the distance of the

sonne. The longitude of a clymat is a lyne imagined fro est to

west, y-lyke distant by-twene them alle. [The latitude of a clymat]

is a lyne imagined from north to south the space of the erthe,

fro the byginning of the firste clymat unto the verrey ende of

the same climat, evene directe agayns the pole artik. Thus seyn

some auctours; and somme of hem seyn that yif men clepen the

latitude, thay mene the arch meridian that is contiened or intercept

by-twixe the senith and the equinoxial. Thanne sey they that

the distaunce fro the equinoxial unto the ende of a clymat,

evene agayns the pole artyk, is the latitude of a clymat for sothe.

And for more declaracioun, lo here thy figure.

[40.] To knowe with which degree of the zodiak that any planete assendith on the orisonte, whether so that his latitude be north or south.

Knowe by thyn almenak the degree of the ecliptik of any signe

in which that the planete is rekned for to be, and that is cleped

the degree of his longitude; and knowe also the degree of his

latitude fro the ecliptik, north or south. And by thise samples

folwinge in special, maystow wirke for sothe in every signe of the

zodiak. The degree of the longitude, par aventure, of Venus or

of another planete, was 6 of Capricorne, and the latitude of him

was northward 2 degrees fro the ecliptik lyne. I tok a subtil

compas, and cleped that oon poynt of my compas A, and that

other poynt F. Than tok I the point of A, and set it in the

ecliptik lyne evene in my zodiak, in the degree of the longitude

of Venus, that is to seyn, in the 6 degree of Capricorne; and

thanne [sette I the point of F upward] in the same signe, bycause

that the latitude was north, up-on the latitude of Venus, that is to

seyn, in the 6 degree fro the heved of Capricorne; and thus have

I 2 degrees by-twixe my two prikkes. Than leide I doun softely

my compas, and sette the degree of the longitude up-on the

orisonte; tho tok I and wexede my label in maner of a peyre

tables to resceyve distinctly the prikkes of my compas. Tho tok

I this forseide label, and leide it fix over the degree of my

longitude; tho tok I up my compas, and sette the point of A in

the wex on my label, as evene as I coude gesse over the ecliptik

lyne, in the ende of the longitude; and sette the point of F

endlang in my label up-on the space of the latitude, inwarde and

over the zodiak, that is to seyn, north-ward fro the ecliptik. Than

leide I doun my compas, and lokede wel in the wey upon the

prikke of A and of F; tho turned I my riet til that the prikke of

F sat up-on the orisonte; than saw I wel that the body of Venus,

in hir latitude of 2 degrees septentrionalis, assended, in the ende

of the 6 degree, in the heved of Capricorne. And nota, that in the

same maner maistow wirke 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

and the bordure of the Astrolabie; but sothly, in alle other signes

it may.

Also the degree, par aventure, of Iuppiter or of a-nother planete,

was in the first degree of Pisces in longitude, and his latitude was

3 degrees meridional; tho tok I the point of A, and sette it in

the firste degree of Pisces on the ecliptik, and thanne sette I the

point of F dounward in the same signe, by-cause that the latitude

was south 3 degrees, that is to seyn, fro the heved of Pisces; and

thus have I 3 degrees by-twixe bothe prikkes; thanne sette I the

degree of the longitude up-on the orisonte. Tho tok I my label,

and leide it fix upon the degree of the longitude; tho sette I the

point of A on my label, evene over the ecliptik lyne, in the ende

evene of the degree of the longitude, and sette the point of F

endlang in my label the space of 3 degrees of the latitude fro the

zodiak, this is to seyn, southward fro the ecliptik, toward the

bordure; and turned my riet til the prikke of F sat up-on the

orisonte; thanne saw I wel that the body of Iuppiter, in his

latitude of 3 degrees meridional, ascended with 14 degrees of Pisces

in horoscopo. And in this maner maistow wirke with any latitude

meridional, as I first seide, save in Capricorne. And yif thou wolt

pleye this craft with the arysing of the mone, loke thou rekne wel

hir cours houre by houre; for she ne dwelleth nat in a degree of

hir longitude but a litel whyle, as thou wel knowest; but natheles,

yif thou rekne hir verreye moeving by thy tables houre after houre,

[thou shall do wel y-now].

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, etc.

SUPPLEMENTARY PROPOSITIONS.

[41.] Umbra Recta.

Yif it so be that thou wilt werke by umbra recta, and thou may

come to the bas of the toure, in this maner thou schalt 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 be-tween me and the tour, and I

finde it 20 feet; than be-holde I how 4 is to 12, right so is the space

betwixe thee and the tour to the altitude of the tour. For 4 is the

thridde part of 12, so is the space be-tween thee and the tour the

thridde part of the altitude of the tour; than thryes 20 feet is the

heyghte of the tour, with adding of thyn owne persone to thyn

eye. And this rewle is so 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 be-tween thee and the toure; with adding

of thyn owne heyght.

[42.] Umbra Versa.

Another maner of werkinge, by vmbra versa. Yif so be that

thou may nat come to the bas of the tour, I see him thorw the

nombre of 1; I sette ther a prikke at my fote; than go I neer to

the tour, and I see him thorw at the poynt of 2, and there I sette

a-nother 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 shalt finde it sexe sythes; than thou shalt

finde that as 12 above 6 is 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 an-other

prikke; than thou findest between two prikkys 60 feet; than thou

shalt finde that 10 is the 6-party of 60. And then is 10 feet the

altitude of the tour. 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 2 to 12; and yif it be 4, 4 tymes; or 5, 5 tymes; et sic

de ceteris.

[43.] Umbra Recta.

An-other maner of wyrking be umbra recta. Yif it so be that

thou mayst nat come to the baas of the tour, in this maner thou

schalt werke. Sette thy rewle upon 1 till thou see the altitude,

and sette at thy foot a prikke. Than sette thy rewle upon 2, and

beholde what is the differense be-tween 1 and 2, and thou shalt

finde that it is 1. Than mete the space be-tween two prikkes, and

that is the 12 partie 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 conclusioun,

adde the stature of thyn heyghte to thyn eye.

[44.] Another maner conclusion, to knowe the mene mote and the argumentis of any planete. To know the mene mote and the argumentis of every planete fro yere to yere, from day to day, from houre to houre, and from smale fraccionis infinite.

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

In this maner shall thou worche: consider thy rote first, the

whiche is made the beginning of the tables fro the yere of oure

lord 1397, and entere hit in-to thy slate for the laste meridie of

December; and than consider the yere of oure lord, what is the

date, and be-hold whether thy date be more or lasse than the yere

1397. And yf hit so be that hit be more, loke how many yeres

hit passeth, and with so many entere into thy tables in the first

lyne ther-as is writen anni collecti et expansi. And loke where the

same planet is writen in the hede of thy table, and than loke

what thou findest in directe of the same yere of oure lord whiche

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 directe wryte in thy slate under thy rote, and adde hit

to-geder, and that is thy mene mote, for the laste meridian of the

December, for the same yere whiche 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

nombere passe 20, than take that thou findest in directe of 20, and

if hit be more, as 6 or 18, than take that thou findest in directe

there-of, that is to sayen, signes, degrees, minutes, and secoundes,

and adde to-gedere un-to thy rote; and thus to make rotes; and

note, that if hit so be that the yere of oure lord be lasse than the

rote, whiche is the yere of oure lord 1397, than shalt thou wryte in

the same wyse furst thy rote in thy slate, and after entere in-to thy

table in the same yere that be lasse, as I taught be-fore; 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, and after with-drawe hem from the

rote, the yere of oure lord 1397; and the residue that leveth

is thy mene mote fro the laste meridie of December, the whiche

thou hast purposed; and if hit so be that thou wolt weten 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 Decembere in the maner as I have taught, and afterward

behold how many monethis, dayes, and houres ben passid from

the meridie of Decembere, and with that entere with the laste

moneth that is ful passed, and take that thou findest in directe

of him, and wryte hit in thy slate; and entere with as mony

dayes as be more, and wryte that thou findest in directe 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 mene mote for the same day

and the same houre.

[45.] Another manere to knowe the mene mote.

Whan thou wolt make the mene mote of eny planete to be by

Arsechieles tables, take thy rote, the whiche is for the yere of oure

lord 1397; and if so be that thy yere be passid the date, wryte

that date, and than wryte the nombere of the yeres. Than withdrawe

the yeres out of the yeres that ben passed that rote.

Ensampul as thus: the yere of oure lord 1400, I wolde witen,

precise, my rote; than wroot I furst 1400. And under that

nombere I wrote a 1397; than withdraw I the laste nombere

out of that, and than fond I the residue was 3 yere; I wiste

that 3 yere was passed fro the rote, the whiche was writen in

my tables. Than after-ward soghte I in my tables the annis

collectis et expansis, and amonge myn expanse yeres fond I

3 yeer. Than tok I alle the signes, degrees, and minutes, that

I fond directe under the same planete that I wroghte for, and

wroot 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 yere of oure lord 1397;

and kepte the residue; and than had I the mene mote for

the laste day of Decembere. And if thou woldest wete the

mene mote of any planete in March, Aprile, or May, other

in any other tyme or moneth of the yere, loke how many

monethes and dayes ben passed from the laste day of Decembere,

the yere of oure lord 1400; and so with monethes

and dayes entere in-to thy table ther thou findest thy mene

mote y-writen in monethes and dayes, and take alle the signes,

degrees, minutes, and secoundes that thou findest y-write in

directe of thy monethes, and adde to signes, degrees, minutes,

and secoundes that thou findest with thy rote the yere of

oure lord 1400, and the residue that leveth is the mene mote

for that same day. And note, if hit so be that thou woldest

wete the mene mote in ony yere that is lasse than thy rote, withdrawe

the nombere of so many yeres as hit is lasse than the

yere of oure lord a 1397, and kepe the residue; and so many

yeres, monethes, and dayes entere in-to thy tabelis of thy mene

mote. And take alle the signes, degrees, and minutes, and

secoundes, that thou findest in directe of alle the yeris, monethes,

and dayes, and wryte hem in thy slate; and above thilke nombere

wryte the signes, degrees, minutes, and secoundes, the whiche

thou findest with thy rote the yere of oure lord a 1397; and

with-drawe 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.

[46.] For to knowe at what houre of the day, or of the night, shal be flode or ebbe.

First wite thou certeinly, how that haven stondeth, that thou

list to werke for; that is to say in whiche place of the firmament

the mone being, maketh fulle see. Than awayte thou redily in

what degree of the zodiak that the mone at that tyme is inne.

Bringe furth than the labelle, and set the point therof in that

same cost that the mone maketh flode, and set thou there the

degree of the mone according 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 bringe and

sette it iustly 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 flode. And there also maist thou wite by the

same point of the label, whether it be, at that same tyme, 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 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

coniunccioun, bringe furthe the degree of the mone with the

labelle to that coste as it is before seyd. But than thou shalt

understonde that thou may not bringe furthe the label fro the

degree of the mone 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 labelle unremeved knowe the houre of

the flode 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

labelle than fro the degree of the mone, and bringe it to the

degree of the sonne. And worke thou than as thou dide before,

&c. Or elles knowe thou what houre it is that thou art inne, by

thyn instrument. Than bringe thou furth fro thennes the labelle

and ley it upon the degree of the mone, and therby may thou wite

also whan it was flode, or whan it wol be next, be it night or

day; &c.

[The following sections are spurious; they are numbered so as to shew what propositions they repeat.]

[41a.] Umbra Recta.

Yif thy rewle falle upon the 8 poynt on right schadwe, than make

thy figure of 8; than loke how moche space of feet is be-tween thee

and the tour, and multiplye that be 12, and whan thou hast multiplied

it, than divyde it be the same nombre of 8, and kepe the residue; and

adde therto up to thyn eye to the residue, and that shal be the verry

heyght of the tour. And thus mayst thou werke on the same wyse, fro

1 to 12.

[41b.] Umbra Recta.

An-other maner of werking upon the same syde. Loke upon which

poynt thy rewle falleth whan thou seest the top of the tour thorow two

litil holes; and mete than the space fro thy foot to the baas of the

tour; and right as the nombre of thy poynt hath him-self to 12, right

so the mesure be-tween thee and the tour hath him-self to the heighte

of the same tour. Ensample: I sette caas thy rewle falle upon 8;

than is 8 two-thrid partyes of 12; so the space is the two-thrid partyes

of the tour.

[42a.] Umbra Versa.

To knowe the heyghth by thy poyntes of umbra versa. Yif thy

rewle falle upon 3, whan thou seest the top of the tour, set a prikke

there-as thy foot stont; and go ner til thou mayst see the same top at

the poynt of 4, and sette ther another lyk prikke. Than mete how

many foot ben be-tween the two prikkes, and adde the lengthe up to

thyn eye ther-to; and that shal be the heyght of the tour. And note,

that 3 is [the] fourthe party of 12, and 4 is the thridde party of 12.

Now passeth 4 the nombre of 3 be the distaunce of 1; therfore the

same space, with thyn heyght to thyn eye, is the heyght of the tour.

And yif it so be that ther be 2 or 3 distaunce in the nombres, so shulde

the mesures be-tween the prikkes be twyes or thryes the heyghte of

the tour.

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

To knowe the heyghte of thinges, yif thou mayst nat come to the

bas of a thing. Sette thy rewle upon what thou wilt, so that thou may

see the top of the thing thorw the two holes, and make a marke ther

thy foot standeth; and go neer or forther, til thou mayst see thorw

another poynt, and marke ther a-nother marke. And loke than what

is the differense be-twen the two poyntes in the scale; and right as

that difference hath him to 12, right so the space be-tween thee and

the two markes hath him to the heyghte of the thing. Ensample: I

set caas thou seest it thorw a poynt of 4; after, at the poynt of 3.

Now passeth the nombre of 4 the nombre of 3 be the difference of 1;

and right as this difference 1 hath him-self to 12, right so the mesure

be-tween the two markes hath him to the heyghte of the thing, putting

to the heyghte of thy-self to thyn eye; and thus mayst thou werke

fro 1 to 12.

[42b.] Per umbram versam.

Furthermore, yif thou wilt knowe in umbra versa, by the craft of

umbra recta, I suppose thou take the altitude at the poynt of 4, and

makest a marke; and thou goost neer til thou hast it at the poynt of

3, and than makest thou ther a-nother mark. Than muste thou

devyde 144 by eche of the poyntes be-fornseyd, as thus: yif thou

devyde 144 be 4, and the nombre that cometh ther-of schal be 36, and

yif thou devyde 144 be 3, and the nombre that cometh ther-of schal be

48, thanne loke what is the difference be-tween 36 and 48, and ther

shalt thou fynde 12; and right as 12 hath him to 12, right so the space

be-tween two prikkes hath him to the altitude of the thing.

COMMENTARY ("FOOTNOTES").

Little Lewis my son, I perceive that thou wouldst learn the Conclusions of the Astrolabe; wherefore I have given thee an instrument constructed for the latitude of Oxford, and purpose to teach thee some of these conclusions. I say some, for three reasons; (1) because some of them are unknown in this land; (2) because some are uncertain; or else (3) are too hard. This treatise, divided into five parts, I write for thee in English, just as Greeks, Arabians, Jews, and Romans were accustomed to write such things in their own tongue. I pray all to excuse my shortcomings; and thou, Lewis, shouldst thank me if I teach thee as much in English as most common treatises can do in Latin. I have done no more than compile from old writers on the subject, and I have translated it into English solely for thine instruction; and with this sword shall I slay envy.

The first part gives a description of the instrument itself.

The second teaches the practical working of it.

The third shall contain tables of latitudes and longitudes of fixed stars, declinations of the sun, and the longitudes of certain towns.

The fourth shall shew the motions of the heavenly bodies, and especially of the moon.

The fifth shall teach a great part of the general rules of astronomical theory.

Here begins the first part; i.e. the description of the Astrolabe itself.

[1.] The Ring. See [figs. 1] and [2]. The Latin name is Armilla suspensoria; the Arabic name is spelt alhahuacia in MS. Camb. Univ. Ii. 3. 3, but Stöffler says it is Alanthica, Alphantia, or Abalhantica. For the meaning of 'rewle,' see § 13.

[2.] The Turet. This answers nearly to what we call an eye or a swivel. The metal plate, or loop, to which it is fastened, or in which it turns, is called in Latin Ansa or Armilla Reflexa, in Arabic Alhabos.

[3.] The Moder. In Latin, Mater or Rotula. This forms the body of the instrument, the back of which is shewn in [fig. 1], the front in [fig. 2]. The 'large hole' is the wide depression sunk in the front of it, into which the various discs are dropped. In the figure, the 'Rete' is shewn fitted into it.

[4.] See [fig. 1]; Chaucer describes the 'bak-half' of the instrument first. The centre of the 'large hole amydde' is the centre of the instrument, where a smaller hole is pierced completely through. The Southe lyne (marked Meridies in figs. 1 and 2) is also called Linea Meridiei; the North lyne is also named Linea Mediæ Noctis.

[5.] The Est lyne is marked with the word Oriens; the West lyne, with Occidens.

[6.] The rule is the same as in heraldry, the right or dexter side being towards the spectator's left.

[7.] As the 360 degrees answer to 24 hours of time, 15° answer to an hour, and 5° to twenty minutes, or a Mile-way, as it is the average time for walking a mile. So also 1° answers to 4 minutes of time. See the two outermost circles in [fig. 1], and the divisions of the 'border' in [fig. 2].

[8.] See the third and fourth circles (reckoning inwards) in [fig. 1].

[9.] See the fifth and sixth circles in [fig. 1].

[10.] See the seventh, eighth, and ninth circles in [fig. 1]. The names of the months are all Roman. The month formerly called Quinctilis was first called Julius in B.C. 44; that called Sextilis was named Augustus in B.C. 27. It is a mistake to say that Julius and Augustus made the alterations spoken of in the text; what Julius Cæsar really did, was to add 2 days to the months of January, August (Sextilis), and December, and 1 day to April, June, September, and November. February never had more than 28 days till he introduced bissextile years.

[11.] See the two inmost circles in [fig. 1]. The names given are adopted from a comparison of the figures in the Cambridge University and Trinity MSS., neither of which are quite correct. The letters of the 'Abc.' are what we now call the Sunday letters. The festivals marked are those of St. Paul (Jan. 25), The Purification (Feb. 2), The Annunciation (Mar. 25), The Invention of the Holy Cross (May 3), St. John the Baptist (June 24), St. James (July 25), St. Lawrence (Aug. 10), The Nativity of the Blessed Virgin (Sept. 8), St. Luke (Oct. 18), St. Martin of Tours (Nov. 11), and St. Thomas (Dec. 21).

[12.] The 'scale' is in Latin Quadrans, or Scala Altimetra. It is certain that Chaucer has here made a slip, which cannot be fairly laid to the charge of the scribes, as the MSS. agree in transposing versa and recta. The side-parts of the scale are called Umbra versa, the lower part Umbra recta or extensa. This will appear more clearly at the end of Part II. (I here give a corrected text.)

[13.] See fig. 3, [Plate III]. Each plate turns on a hinge, just like the 'sights' of a gun. One is drawn flat down, the other partly elevated. Each plate (tabella vel pinnula) has two holes, the smaller one being the lower. This Rewle is named in Arabic Alhidada or Al´idāda; in Latin Verticulum, from its turning easily on the centre; in Greek Dioptra, as carrying the sights. The straight edge, passing through the centre, is called the Linea Fiduciæ. It is pierced by a hole in the centre, of the same size as that in the Mother.

[14.] See fig. 4, [Plate III]. The Pin is also called Axis or Clavus, in Latin-Arabic Alchitot; it occupies the position of the Arctic or North Pole, passing through the centre of the plates that are required to turn round it. The Wedge is called cuneus, or equus restringens, in Arabic Alfaras or the horse, because it was sometimes cut into the shape of a horse, as shewn in fig. 7, [Plate IV], which is copied from MS. Univ. Camb. Ii. 3. 3.

[15.] See fig. 2, [Plate II]. In the figure, the cross-lines are partly hidden by the Rete, which is separate and removable, and revolves within the border.

[16.] The Border was also called Margilabrum, Margolabrum, or Limbus. It is marked (as explained) with hour-letters and degrees. Each degree contains 4 minutes of time, and each of these minutes contains 60 seconds of time.

[17.] We may place under the Rete any plates we please. If only the Mother be under it, without any plate, we may suppose the Mother marked as in [fig. 2]. The plate or disc (tympanum) which was usually dropped in under the Rete is that shewn in fig. 5, [Plate III], and which Chaucer now describes. Any number of these, marked differently for different latitudes, could be provided for the Astrolabe. The greatest declination of the sun measures the obliquity of the ecliptic, the true value of which is slightly variable, but was about 23° 31′ in Chaucer's time, and about 23° 40′ in the time of Ptolemy, who certainly assigns to it too large a value. The value of it must be known before the three circles can be drawn. The method of finding their relative magnitudes is very simple. Let ABCD (fig. 8, [Pl. IV]) be the tropic of Capricorn, BO the South line, OC the West line. Make the angle EOB equal to the obliquity (say 23½°), and join EA, meeting BO in F. Then OF is the radius of the Equatorial circle, and if GH be drawn parallel to EF, OH is the radius of the Tropic of Cancer. In the phrase angulus primi motus, angulus must be taken to mean angular motion. The 'first moving' (primus motus) has its name of 'moving' (motus) from its denoting motion due to the primum mobile or 'first moveable.' This primum mobile (usually considered as the ninth sphere) causes the rotation of the eighth sphere, or sphæra stellarum fixarum. See the fig. in MS. Camb. Univ. Ii. 3. 3 (copied in fig. 10, [Pl. V]). Some authors make 12 heavens, viz. those of the 7 planets, the firmamentum (stellarum fixarum), the nonum cœlum, decimum cœlum, primum mobile, and cœlum empyræum.

[18.] See fig. 5, [Pl. III]. This is made upon the alt-azimuth system, and the plates are marked according to the latitude. The circles, called in Latin circuli progressionum, in Arabic Almucantarāt, are circles of altitude, the largest imperfect one representing the horizon (horizon obliquus), and the central dot being the zenith, or pole of the horizon. In my figure, they are 'compounded by' 5 and 5, but Chaucer's shewed every second degree, i.e. it possessed 45 such circles. For the method of drawing them, see Stöffler, leaf 5, back.

[19.] Some Astrolabes shew 18 of these azimuthal circles, as in my figure (fig. 5, [Pl. III]). See Stöffler, leaf 13, where will be found also the rules for drawing them.

[20.] If accurately drawn, these embelife or oblique lines should divide the portions of the three circles below the horizon obliquus into twelve equal parts. Thus each arc is determined by having to pass through three known points. They are called arcus horarum inequalium, as they shew the 'houres inequales.'

[21.] In fig. 2, [Pl. II], the Rete is shewn as it appears when dropped into the depression in the front of the instrument. The shape of it varied much, and another drawing of one (copied from Camb. Univ. MS. Ii. 3. 3, fol. 66 b) is given in fig. 9, [Pl. IV]. The positions of the stars are marked by the extreme points of the metal tongues. Fig. 2 is taken from the figures in the Cambridge MSS., but the positions of the stars have been corrected by the list of latitudes and longitudes given by Stöffler, whom I have followed, not because he is correct, but because he probably represents their positions as they were supposed to be in Chaucer's time very nearly indeed. There was not room to inscribe the names of all the stars on the Rete, and to have written them on the plate below would have conveyed a false impression. A list of the stars marked in [fig. 2] is given in the note to § 21, l. 4. The Ecliptic is the circle which crosses the Equinoctial at its East and West points (fig. 2). In Chaucer's description of the zodiac, carefully note the distinction between the Zodiac of the Astrolabe and the Zodiac of Heaven. The former is only six degrees broad, and shews only the northern half of the heavenly zodiac, the breadth of which is imagined to be 12 degrees. Chaucer's zodiac only shewed every other degree in the divisions round its border. This border is divided by help of a table of right ascensions of the various degrees of the ecliptic, which is by no means easily done. See Note on l. 4 of this section. I may add that the Rete is also called Aranea or Volvellum; in Arabic, Al´ancabūt (the spider).

[22.] The Label. See fig. 6, [Pl. III]. The label is more usually used on the front of the instrument, where the Rete and other plates revolve. The rule is used on the back, for taking altitudes by help of the scale.

[23.] The Almury; called also denticulus, ostensor, or 'calculer.' In [fig. 2], it may be seen that the edge of the Rete is cut away near the head of Capricorn, leaving only a small pointed projecting tongue, which is the almury or denticle, or (as we should now say) pointer. As the Rete revolves, it points to the different degrees of the border. See also [fig. 9], where the almury is plainly marked.

Part II, § [1.] [The Latin headings to the propositions are taken from the MS. in St. John's College, Cambridge.] See [fig. 1]. Any straight edge laid across from the centre will shew this at once. Chaucer, reckoning by the old style, differs from us by about eight days. The first degree of Aries, which in his time answered to the 12th of March, now vibrates between the 20th and 21st of that month. This difference of eight days must be carefully borne in mind in calculating Chaucer's dates.

[2.] Here 'thy left side' means the left side of thine own body, and therefore the right or Eastern edge of the Astrolabe. In taking the altitude of the sun, the rays are allowed to shine through the holes; but the stars are observed by looking through them. See [figs. 1] and [3].

[3.] Drop the disc ([fig. 5]) within the border of the mother, and the Rete over it. Take the sun's altitude by § 2, and let it be 25½°. As the altitude was taken by the back of the Astrolabe, turn it over, and then let the Rete revolve westward till the 1st point of Aries is just within the altitude-circle marked 25, allowing for the ½ degree by guess. This will bring the denticle near the letter C, and the first point of Aries near X, which means 9 A.M. At the same time, the 20th degree of Gemini will be on the horizon obliquus. See fig. 11, [Pl. V]. This result can be approximately verified by a common globe thus; elevate the pole nearly 52°; turn the small brass hour-circle so that the figure XII lies on the equinoctial colure; then turn the globe till IX lies under the brass meridian. In the next example, by the Astrolabe, let the height of Alhabor (Sirius) be about 18°. Turn the denticle Eastward till it touches the 58th degree near the letter O, and it will be found that Alhabor is about 18° high among the almicanteras, whilst the first point of Aries points to 32° near the letter H, i.e. to 8 minutes past 8 P.M.; whilst at the same time, the 23rd degree of Libra is almost on the Horizon obliquus on the Eastern side. By the globe, at about 8 minutes past 8 P.M., the altitude of Sirius is very nearly 18°, and the 23rd of Libra is very near the Eastern horizon. See fig. 12, [Pl. V].

[4.] The ascendent at any given moment is that degree of the zodiac which is then seen upon the Eastern horizon. Chaucer says that astrologers reckoned in also 5 degrees of the zodiac above, and 25 below; the object being to extend the planet's influence over a whole 'house,' which is a space of the same length as a sign, viz. 30°. See § 36 below.

[5.] This merely amounts to taking the mean between two results.

[6.] This depends upon the refraction of light by the atmosphere, owing to which light from the sun reaches us whilst he is still 18° below the horizon. The nadir of the sun being 18° high on the W. side, the sun itself is 18° below the Eastern horizon, giving the time of dawn; and if the nadir be 18° high on the E. side, we get the time of the end of the evening twilight. Thus, at the vernal equinox, the sun is 18° high soon after 8 A.M. (roughly speaking), and hence the evening twilight ends soon after 8 P.M., 12 hours later, sunset being at 6 P.M.

[7.] Ex. The sun being in the first point of Cancer on the longest day, its rising will be shewn by the point in [fig. 5] where the horizon obliquus and Tropicus Cancri intersect; this corresponds to a point between P and Q in [fig. 2], or to about a quarter to 4 A.M. So too the sunset is at about a quarter past 8, and the length of the day 16½ hours; hence also, the length of the night is about 7½ hours, neglecting twilight.

[8.] On the same day, the number of degrees in the whole day is about 247½, that being the number through which the Rete is turned in the example to § 7. Divide by 15, and we have 16½ equal hours.

[9.] The 'day vulgar' is the length of the 'artificial day,' with the length of the twilight, both at morn and at eve, added to it.

[10.] If, as in § 7, the day be 16½ hours long, the length of each 'hour inequal' is 1 h. 22½ m.; and the length of each 'hour inequal' of the night is the 12th part of 7½ hours, or 37½ m.; and 1 h. 22½ m., added to 37½ m., will of course make up 2 hours, or 30°.

[11.] This merely repeats that 15° of the border answer to an hour of the clock. The '4 partie of this tretis' was never written.

[12.] This 'hour of the planet' is a mere astrological supposition, involving no point of astronomy. Each hour is an 'hour inequal,' or the 12th part of the artificial day or night. The assumptions are so made that first hour of every day may resemble the name of the day; the first hour of Sunday is the hour of the Sun, and so on. These hours may be easily found by the following method. Let 1 represent both Sunday and the Sun; 2, Monday and the Moon; 3, Tuesday and Mars; 4, Wednesday and Mercury; 5, Thursday and Jupiter; 6, Friday and Venus; 7, Saturday and Saturn. Next, write down the following succession of figures, which will shew the hours at once.

1642753|16427531642753164275316.

Ex. To find the planet of the 10th hour of Tuesday. Tuesday is the third day of the week; begin with 3, to the left of the upright line, and reckon 10 onwards; the 10th figure (counting 3 as the first) is 6, i.e. Venus. So also, the planet of the 24th hour of Friday is the Moon, and Saturday begins with Saturn. It may be observed that this table can be carried in the memory, by simply observing that the numbers are written, beginning with 1, in the reverse order of the spheres, i.e. Sun, Venus, Mercury, Moon; and then (beginning again at the outmost sphere) Saturn, Jupiter, Mars. This is why Chaucer takes a Saturday; that he may begin with the remotest planet, Saturn, and follow the reverse order of the spheres. See fig. 10, [Pl. V]. Here, too, we have the obvious reason for the succession of the names of the days of the week, viz. that the planets being reckoned in this order, we find the Moon in the 25th place or hour from the Sun, and so on.

[13.] The reason of this is obvious from what has gone before. The sun's meridional altitude is at once seen by placing the sun's degree on the South line.

[14.] This is the exact converse of the preceding. It furnishes a method of testing the accuracy of the drawing of the almikanteras.

[15.] This is best done by help of the back of the instrument, [fig. 1]. Thus May 13 (old style), which lies 30° to the W. of the S. line, is nearly of the same length as July 13, which lies 30° to the E. Secondly, the day of April 2 (old style), 20° above the W. line, is nearly of the same length as the night of Oct. 2, 20° below the E. line, in the opposite point of the circle. This is but an approximation, as the divisions on the instrument are rather minute.

[16.] This merely expresses the same thing, with the addition, that on days of the same length, the sun has the same meridional altitude, and the same declination from the equator.

[17.] Here passeth any-thing the south westward means, passes somewhat to the westward of the South line. The problem is, to find the degree of the zodiac which is on the meridian with the star. To do this, find the altitude of the star before it souths, and by help of problem 3, find out the ascending degree of the zodiac; secondly, find the ascending degree at an equal time after it souths, when the star has the same altitude as before, and the mean between these will be the degree that ascends when the star is on the meridian. Set this degree upon the Eastern part of the horizon obliquus, and then the degree which is upon the meridional line souths together with the star. Such is the solution given, but it is but a very rough approximation, and by no means always near to the truth. An example will shew why. Let Arcturus have the same altitude at 10 P.M. as at 2 A.M. In the first case the 4th of Sagittarius is ascending, in the second (with sufficient accuracy for our purpose) the 2nd of Aquarius; and the mean between these is the 3rd of Capricorn. Set this on the Eastern horizon upon a globe, and it will be seen that it is 20 min. past midnight, that 10° of Scorpio is on the meridian, and that Arcturus has past the meridian by 5°. At true midnight, the ascendent is the 29° of Sagittarius. The reason of the error is that right ascension and longitude are here not sufficiently distinguished. By observing the degrees of the equinoctial, instead of the ecliptic, upon the Eastern horizon, we have at the first observation 272°, at the second 332°, and the mean of these is 302°; from this subtract 90°, and the result, 212°, gives the right ascension of Arcturus very nearly, corresponding to which is the beginning of the 5° of Scorpio, which souths along with it. This latter method is correct, because it assumes the motion to take place round the axis of the equator. The error of Chaucer's method is that it identifies the motion of the equator with that of the ecliptic. The amount of the error varies considerably, and may be rather large. But it can easily be diminished, (and no doubt was so in practice), by taking the observations as near the south line as possible. Curiously enough, the rest of the section explains the difference between the two methods of reckoning. The modern method is to call the co-ordinates right ascension and declination, if reckoned from the equator, and longitude and latitude, if from the ecliptic. Motion in longitude is not the same thing as motion in right ascension.

[18.] The 'centre' of the star is the technical name for the extremity of the metal tongue representing it. The 'degree in which the star standeth' is considered to be that degree of the zodiac which souths along with it. Thus Sirius or Alhabor has its true longitude nearly equal to that of 12° of Cancer, but, as it souths with the 9th degree, it would be said to stand in that degree. This may serve for an example; but it must be remembered that its longitude was different in the time of Chaucer.

[19.] Also it rises with the 19th degree of Leo, as it is at some distance from the zodiac in latitude. The same 'marvellous arising in a strange sign' is hardly because of the latitude being north or south from the equinoctial, but rather because it is north or south of the ecliptic. For example, Regulus (α Leonis) is on the ecliptic, and of course rises with that very degree in which it is. Hence the reading equinoctial leaves the case in doubt, and we find a more correct statement just below, where we have 'whan they have no latitude fro the ecliptik lyne.' At all places, however, upon the earth's equator, the stars will rise with the degrees of the zodiac in which they stand.]

[20.] Here the disc ([fig. 5]) is supposed to be placed beneath the Rete ([fig. 2]). The proposition merely tells us that the difference between the meridian altitudes of the given degree of the zodiac and of the 1st point of Aries is the declination of that degree, which follows from the very definition of the term. There is hardly any necessity for setting the second prick, as it is sufficiently marked by being the point where the equinoctial circle crosses the south line. If the given degree lie outside this circle, the declination is south; if inside, it is north.

[21.] In [fig. 5], the almicanteras, if accurately drawn, ought to shew as many degrees between the south point of the equinoctial circle and the zenith as are equal to the latitude of the place for which they are described. The number of degrees from the pole to the northern point of the horizon obliquus is of course the same. The latitude of the place for which the disc is constructed is thus determined by inspection.

[22.] In the first place where 'orisonte' occurs, it means the South point of the horizon; in the second place, the North point. By referring to fig. 13, [Plate V], it is clear that the arc ♈S, representing the distance between the equinoctial and the S. point, is equal to the arc ZP, which measures the distance from the pole to the zenith; since PO♈ and ZOS are both right angles. Hence also Chaucer's second statement, that the arcs PN and ♈Z are equal. In his numerical example, PN is 51° 50′; and therefore ZP is the complement, or 38° 10′. So also ♈Z is 51° 50′; and ♈S is 38° 10′. Briefly, ♈Z measures the latitude.

[23.] Here the altitude of a star (A) is to be taken twice; firstly, when it is on the meridian in the most southern point of its course, and secondly, when on the meridian in the most northern point, which would be the case twelve hours later. The mean of these altitudes is the altitude of the pole, or the latitude of the place. In the example given, the star A is only 4° from the pole, which shews that it is the Pole-star, then farther from the Pole than it is now. The star F is, according to Chaucer, any convenient star having a right ascension differing from that of the Pole-star by 180°; though one having the same right ascension would serve as well. If then, at the first observation, the altitude of A be 56, and at the second be 48, the altitude of the pole must be 52. See fig. 13, [Plate V].

[24.] This comes to much the same thing. The lowest or northern altitude of Dubhe (α Ursæ Majoris) may be supposed to be observed to be 25°, and his highest or southern altitude to be 79°. Add these; the sum is 104; 'abate' or subtract half of that number, and the result is 52°; the latitude.

[25.] Here, as in § 22, Chaucer says that the latitude can be measured by the arc Z♈ or PN; he adds that the depression of the Antarctic pole, viz. the arc SP′ (where P′ is the S. pole), is another measure of the latitude. He explains that an obvious way of finding the latitude is by finding the altitude of the sun at noon at the time of an equinox. If this altitude be 38° 10′, then the latitude is the complement, or 51° 50′. But this observation can only be made on two days in the year. If then this seems to be too long a tarrying, observe his midday altitude, and allow for his declination. Thus, if the sun's altitude be 58° 10′ at noon when he is in the first degree of Leo, subtract his declination, viz. 20°, and the result is 38° 10′, the complement of the latitude. If, however, the sun's declination be south, the amount of it must be added instead of subtracted. Or else we may find ♈A′, the highest altitude of a star A′ above the equinoctial, and also ♈A, its nether elongation extending from the same, and take the mean of the two.

[26.] The 'Sphere Solid' answers nearly to what we now call a globe. By help of a globe it is easy to find the ascensions of signs for any latitude, whereas by the astrolabe we can only tell them for those latitudes for which the plates bearing the almicanteras are constructed. The signs which Chaucer calls 'of right (i.e. direct) ascension' are those signs of the zodiac which rise more directly, i.e. at a greater angle to the horizon than the rest. In latitude 52°, Libra rises so directly that the whole sign takes more than 2¾ hours before it is wholly above the horizon, during which time nearly 43° of the equinoctial circle have arisen; or, in Chaucer's words, 'the more part' (i.e. a larger portion) of the equinoctial ascends with it. On the other hand, the sign of Aries ascends so obliquely that the whole of it appears above the horizon in less than an hour, so that a 'less part' (a smaller portion) of the equinoctial ascends with it. The following is a rough table of Direct and Oblique Signs, shewing approximately how long each sign takes to ascend, and how many degrees of the equinoctial ascend with it, in lat. 52°.

Oblique Signs.	Degrees of the Equinoctial.	Time of ascending.	Direct Signs.	Degrees of the Equinoctial.	Time of ascending.
Capricornus	26°	1 h. 44 m.	Cancer	39°	2 h. 36 m.
Aquarius	16°	1 h. 4 m.	Leo	42°	2 h. 48 m.
Pisces	14°	0 h. 56 m.	Virgo	43°	2 h. 52 m.
Aries	14°	0 h. 56 m.	Libra	43°	2 h. 52 m.
Taurus	16°	1 h. 4 m.	Scorpio	42°	2 h. 48 m.
Gemini	26°	1 h. 44 m.	Sagittarius	39°	2 h. 36 m.

These numbers are sufficiently accurate for the present purpose.

In ll. 8-11, there is a gap in the sense in nearly all the MSS., but the Bodley MS. 619 fortunately supplies what is wanting, to the effect that, at places situated on the equator, the poles are in the horizon. At such places, the days and nights are always equal. Chaucer's next statement is true for all places within the tropics, the peculiarity of them being that they have the sun vertical twice in a year. The statement about the 'two summer and winters' is best explained by the following. 'In the tropical climates, ... seasons are caused more by the effect of the winds (which are very regular, and depend mainly on the sun's position) than by changes in the direct action of the sun's light and heat. The seasons are not a summer and winter, so much as recurrences of wet and dry periods, two in each year.'—English Cyclopædia; Seasons, Change of. Lastly, Chaucer reverts to places on the equator, where the stars all seem to move in vertical circles, and the almicanteras are therefore straight lines. The line marked Horizon Rectus is shewn in [fig. 5], where the Horizon Obliquus is also shewn, cutting the equinoctial circle obliquely.

[27.] The real object in this section is to find how many degrees of the equinoctial circle pass the meridian together with a given zodiacal sign. Without even turning the rete, it is clear that the sign Aries, for instance, extends through 28° of the equinoctial; for a line drawn from the centre, in [fig. 2], through the end of Aries will (if the figure be correct) pass through the end of the 28th degree below the word Oriens.

[28.] To do this accurately requires a very carefully marked Astrolabe, on as large a scale as is convenient. It is done by observing where the ends of the given sign, estimated along the outer rim of the zodiacal circle in [fig. 2], cross the horizon obliquus as the rete is turned about. Thus, the beginning of Aries lies on the horizon obliquus, and as the rete revolves to the right, the end of it, on the outer rim, will at last lie exactly on the same curved line. When this is the case, the rete ought to have moved through an angle of about 14°, as explained in § 26. By far the best way is to tabulate the results once for all, as I have there done. It is readily seen, from [fig. 2], that the signs from Aries to Virgo are northern, and from Libra to Pisces are southern signs. The signs from Capricorn to Gemini are the oblique signs, or as Chaucer calls them, 'tortuous,' and ascend in less than 2 hours; whilst the direct signs, from Cancer to Sagittarius, take more than 2 hours to ascend; as shewn in the table on p. [209]. The eastern signs in fig. 2 are said to obey to the corresponding western ones.

[29.] Here both sides of the Astrolabe are used, the 'rewle' being made to revolve at the back, and the 'label' in front, as usual. First, by the back of the instrument and the 'rewle,' take the sun's altitude. Turn the Astrolabe round, and set the sun's degree at the right altitude among the almicanteras, and then observe, by help of the label, how far the sun is from the meridian. Again turn the instrument round, and set the 'rewle' as far from the meridian as the label was. Then, holding the instrument as near the ground and as horizontal as possible, let the sun shine through the holes of the 'rewle,' and immediately after lay the Astrolabe down, without altering the azimuthal direction of the meridional line. It is clear that this line will then point southwards, and the other points of the compass will also be known.

[30.] This turns upon the definition of the phrase 'the wey of the sonne.' It does not mean the zodiacal circle, but the sun's apparent path on a given day of the year. The sun's altitude changes but little in one day, and is supposed here to remain the same throughout the time that he is, on that day, visible. Thus, if the sun's altitude be 61½°, the way of the sun is a small circle, viz. the tropic of Cancer. If the planet be then on the zodiac, in the 1st degree of Capricorn, it is 47° S. from the way of the sun, and so on.

[31.] The word 'senith' is here used in a peculiar sense; it does not mean, as it should, the zenith point, or point directly overhead, but is made to imply the point on the horizon, (either falling upon an azimuthal line, or lying between two azimuths), which denotes the point of sunrise. In the Latin rubric, it is called signum. This point is found by actual observation of the sun at the time of rising. Chaucer's azimuths divide the horizon into 24 parts; but it is interesting to observe his remark, that 'shipmen' divide the horizon into 32 parts, exactly as a compass is divided now-a-days. The reason for the division into 32 parts is obviously because this is the easiest way of reckoning the direction of the wind. For this purpose, the horizon is first divided into 4 parts; each of these is halved, and each half-part is halved again. It is easy to observe if the wind lies half-way between S. and E., or half-way between S. and S.E., or again half-way between S. and S.S.E.; but the division into 24 parts would be unsuitable, because third-parts are much more difficult to estimate.

[32.] The Latin rubric interprets the conjunction to mean that of the sun and moon. The time of this conjunction is to be ascertained from a calendar. If, e.g. the calendar indicates 9 A.M. as the time of conjunction on the 12th day of March, when the sun is in the first point of Aries, as in § 3, the number of hours after the preceding midday is 21, which answers to the letter X in the border ([fig. 2]). Turn the rete till the first point of Aries lies under the label, which is made to point to X, and the label shews at the same moment that the degree of the sun is very nearly at the point where the equinoctial circle crosses the azimuthal circle which lies 50° to the E. of the meridian. Hence the conjunction takes place at a point of which the azimuth is 50° to the E. of the S. point, or 5° to the eastward of the S.E. point. The proposition merely amounts to finding the sun's azimuth at a given time. [Fig. 11] shews the position of the rete in this case.

[33.] Here 'senyth' is again used to mean azimuth, and the proposition is, to find the sun's azimuth by taking his altitude, and setting his degree at the right altitude on the almicanteras. Of course the two co-ordinates, altitude and azimuth, readily indicate the sun's exact position; and the same for any star or planet.

[34.] The moon's latitude is never more than 5¼° from the ecliptic, and this small distance is, 'in common treatises of Astrolabie,' altogether neglected; so that it is supposed to move in the ecliptic. First, then, take the moon's altitude, say 30°. Next take the altitude of some bright star 'on the moon's side,' i.e. nearly in the same azimuth as the moon, taking care to choose a star which is represented upon the Rete by a pointed tongue. Bring this tongue's point to the right altitude among the almicanteras, and then see which degree of the ecliptic lies on the almicantera which denotes an altitude of 30°. This will give the moon's place, 'if the stars in the Astrolabe be set after the truth,' i.e. if the point of the tongue is exactly where it should be.

[35.] The motion of a planet is called direct, when it moves in the direction of the succession of the zodiacal signs; retrograde, when in the contrary direction. When a planet is on the right or east side of the Meridional line, and is moving forward along the signs, without increase of declination, its altitude will be less on the second occasion than on the first at the moment when the altitude of the fixed star is the same as before. The same is true if the planet be retrograde, and on the western side. The contrary results occur when the second altitude is greater than the first. But the great defect of this method is that it may be rendered fallacious by a change in the planet's declination.

[36.] See fig. 14, [Plate VI]. If the equinoctial circle in this figure be supposed to be superposed upon that in fig. 5, [Plate III], and be further supposed to revolve backwards through an angle of about 60° till the point 1 (fig. 14) rests upon the point where the 8th hour-line crosses the equinoctial, the beginning of the 2nd house will then be found to be on the line of midnight. Similarly, all the other results mentioned follow. For it is easily seen that each 'house' occupies a space equal to 2 hours, so that the bringing of the 3rd house to the midnight line brings 1 to the 10th hour-line, and a similar placing of the 4th house brings 1 to the 12th hour-line, which is the horizon obliquus itself. Moving onward 2 more hours, the point 7 (the nadir of 1) comes to the end of the 2nd hour, whilst the 5th house comes to the north; and lastly, when 7 is at the end of the 4th hour, the 6th house is so placed. To find the nadir of a house, we have only to add 6; so that the 7th, 8th, 9th, 10th, 11th, and 12th houses are the nadirs of the 1st, 2nd, 3rd, 4th, 5th, and 6th houses respectively.

[37.] Again see fig. 14, [Plate VI]. Here the 10th house is at once seen to be on the meridional line. In the quadrant from 1 to 10, the even division of the quadrant into 3 parts shews the 12th and 11th houses. Working downwards from 1, we get the 2nd and 3rd houses, and the 4th house beginning with the north line. The rest are easily found from their nadirs.

[38.] This problem is discussed in arts. 144 and 145 of Hymes's Astronomy, 2nd ed. 1840, p. 84. The words 'for warping' mean 'to prevent the errors which may arise from the plate becoming warped.' The 'broader' of course means 'the larger.' See fig. 15, [Plate VI]. If the shadow of the sun be observed at a time before midday when its extremity just enters within the circle, and again at a time after midday when it is just passing beyond the circle, the altitude of the sun at these two observations must be the same, and the south line must lie half-way between the two shadows. In the figure, S and S′ are the 2 positions of the sun, OT the rod, Ot and Ot′ the shadows, and OR the direction of the south line. Ott′ is the metal disc.

[39.] This begins with an explanation of the terms 'meridian' and 'longitude.' 'They chaungen her Almikanteras' means that they differ in latitude. But, when Chaucer speaks of the longitude and latitude of a 'climate,' he means the length and breadth of it. A 'climate' (clima) is a belt of the earth included between two fixed parallels of latitude. The ancients reckoned seven climates; in the sixteenth century there were nine. The 'latitude of the climate' is the breadth of this belt; the 'longitude' of it he seems to consider as measured along lines lying equidistant between the parallels of latitude of the places from which the climates are named. See Stöffler, fol. 20 b; and Petri Apiani Cosmographia, per Gemmam Phrysium restituta, ed. 1574, fol. 7 b. The seven climates were as follows:—

1. That whose central line passes through Meroë (lat. 17°); from nearly 13° to nearly 20°.

2. Central line, through Syene (lat. 24°); from 20° to 27°, nearly.

3. Central line through Alexandria (lat. 31°); from 27° to 34°, nearly.

4. Central line through Rhodes (lat. 36°); from 34° to 39°, nearly.

5. Central line through Rome (lat. 41°); from 39° to 43°, nearly.

6. Central line through Borysthenes (lat. 45°); from 43° to 47°.

7. Through the Riphæan mountains (lat. 48°); from 47° to 50°. But Chaucer must have included an eighth climate (called ultra Mæotides paludes) from 50° to 56°; and a ninth, from 56° to the pole. The part of the earth to the north of the 7th climate was considered by the ancients to be uninhabitable. A rough drawing of these climates is given in MS. Camb. Univ. Lib. Ii. 3. 3, fol. 33 b.

[40.] The longitude and latitude of a planet being ascertained from an almanac, we can find with what degree it ascends. For example, given that the longitude of Venus is 6° of Capricorn, and her N. latitude 2°. Set the one leg of a compass upon the degree of longitude, and extend the other till the distance between the two legs is 2° of latitude, from that point inward, i.e. northward. The 6th degree of Capricorn is now to be set on the horizon, the label (slightly coated with wax) to be made to point to the same degree, and the north latitude is set off upon the wax by help of the compass. The spot thus marking the planet's position is, by a very slight movement of the Rete, to be brought upon the horizon, and it will be found that the planet (situated 2° N. of the 6th degree) ascends together with the head (or beginning of the sign) of Capricorn. This result, which is not quite exact, is easily tested by a globe. When the latitude of the planet is south, its place cannot well be found when in Capricorn for want of space at the edge of the Astrolabe.

As a second example, it will be found that, when Jupiter's longitude is at the end of 1° of Pisces, and his latitude 3° south, he ascends together with the 14th of Pisces, nearly. This is easily verified by a globe, which solves all such problems very readily.

It is a singular fact that most of the best MSS. leave off at the word 'houre,' leaving the last sentence incomplete. I quote the last five words—'þou shalt do wel y-now'—from the MS. in St. John's College, Cambridge; they also occur in the old editions.

[41.] Sections 41-43 and 41a-42b are from the MS. in St. John's College, Cambridge. For the scale of umbra recta, see fig. 1, [Plate I]. Observe that the umbra recta is used where the angle of elevation of an object is greater than 45°; the umbra versa, where it is less. See also fig. 16, [Plate VI]; where, if AC be the height of the tower, BC the same height minus the height of the observer's eye (supposed to be placed at E), and EB the distance of the observer from the tower, then bc : Eb :: EB : BC. But Eb is reckoned as 12, and if bc be 4, we find that BC is 3 EB, i.e. 60 feet, when EB is 20. Hence AC is 60 feet, plus the height of the observer's eye. The last sentence is to be read thus—'And if thy "rewle" fall upon 5, then are 5-12ths of the height equivalent to the space between thee and the tower (with addition of thine own height).' The MS. reads '5 12-partyes þe heyȝt of þe space,' &c.; but the word of must be transposed, in order to make sense. It is clear that, if bc = 5, then 5 : 12 :: EB : BC, which is the same as saying that EB = 5⁄12 BC. Conversely, BC is 12⁄5 EB = 48, if EB = 20.

[42.] See fig. 1, [Plate I]. See also fig. 17, [Plate VI]. Let Eb = 12, bc = 1; also E′b′ = 12, b′c′ = 2; then EB = 12 BC, E′B = 6 BC; therefore EE′ = 6 BC. If EE′ = 60 feet, then BC = 1⁄6 EE′=10 feet. To get the whole height, add the height of the eye. The last part of the article, beginning 'For other poyntis,' is altogether corrupt in the MS.

[43.] Here versa (in M.) is certainly miswritten for recta, as in L. See fig. 18, [Plate VI]. Here Eb = E′b′ = 12; b′c′ = 1, bc = 2. Hence E′B = 1⁄12 BC, EB = 2⁄12 BC. whence EE′ = 1⁄12 BC. Or again, if bc become = 3, 4, 5, &c., successively, whilst b′c′ remains = 1, then EE′ is successively = 2⁄12 or 1⁄6, 3⁄12 or 1⁄4, 5⁄12, &c. Afterwards, add in the height of E.

[44.] Sections 44 and 45 are from MS. Digby 72. This long explanation of the method of finding a planet's place depends upon the tables which were constructed for that purpose from observation. The general idea is this. The figures shewing a planet's position for the last day of December, 1397, give what is called the root, and afford us, in fact, a starting-point from which to measure. An 'argument' is the angle upon which the tabulated quantity depends; for example, a very important 'argument' is the planet's longitude, upon which its declination may be made to depend, so as to admit of tabulation. The planet's longitude for the given above-mentioned date being taken as the root, the planet's longitude at a second date can be found from the tables. If this second date be less than 20 years afterwards, the increase of motion is set down separately for each year, viz. so much in 1 year, so much in 2 years, and so on. These separate years are called anni expansi. But when the increase during a large round number of years (such as 20, 40, or 60 years at once) is allowed for, such years are called anni collecti. For example, a period of 27 years includes 20 years taken together, and 7 separate or expanse years. The mean motion during smaller periods of time, such as months, days, and hours, is added in afterwards.

[45.] Here the author enters a little more into particulars. If the mean motion be required for the year 1400, 3 years later than the starting-point, look for 3 in the table of expanse years, and add the result to the number already corresponding to the 'root,' which is calculated for the last day of December, 1397. Allow for months and days afterwards. For a date earlier than 1397 the process is just reversed, involving subtraction instead of addition.

[46.] This article is probably not Chaucer's. It is found in MS. Bodley 619, and in MS. Addit. 29250. The text is from the former of these, collated with the latter. What it asserts comes to this. Suppose it be noted, that at a given place, there is a full flood when the moon is in a certain quarter; say, e.g. when the moon is due east. And suppose that, at the time of observation, the moon's actual longitude is such that it is in the first point of Cancer. Make the label point due east; then bring the first point of Cancer to the east by turning the Rete a quarter of the way round. Let the sun at the time be in the first point of Leo, and bring the label over this point by the motion of the label only, keeping the Rete fixed. The label then points nearly to the 32nd degree near the letter Q, or about S.E. by E.; shewing that the sun is S.E. by E. (and the moon consequently due E.) at about 4 A.M. In fact, the article merely asserts that the moon's place in the sky is known from the sun's place, if the difference of their longitudes be known. At the time of conjunction, the moon and sun are together, and the difference of their longitudes is zero, which much simplifies the problem. If there is a flood tide when the moon is in the E., there is another when it comes to the W., so that there is high water twice a day. It may be doubted whether this proposition is of much practical utility.

[41a]: This comes to precisely the same as Art. 41, but is expressed with a slight difference. See [fig. 16], where, if bc = 8, then BC = 12⁄8 EB.

[41b]: Merely another repetition of Art. 41. It is hard to see why it should be thus repeated in almost the same words. If bc = 8 in [fig. 16], then EB = 8⁄12 BC = 2⁄3 BC. The only difference is that it inverts the equation in the last article.]

[42a] This is only a particular case of Art. 42. If we can get bc = 3, and b′c′ = 4, the equations become EB = 4BC, E′B = 3BC; whence EE′ = BC, a very convenient result. See [fig. 17].]

[43a]: The reading versam (as in the MS.) is absurd. We must also read 'nat come,' as, if the base were approachable, no such trouble need be taken; see Art. 41. In fact, the present article is a mere repetition of Art. 43, with different numbers, and with a slight difference in the method of expressing the result. In [fig. 18], if b′c′ = 3, bc = 4, we have E′B = 3⁄12 BC, EB = 4⁄12 BC; or, subtracting, EE′ = (4-3)/12 BC; or BC = 12 EE′. Then add the height of E, viz. Ea, which = AB.

[42b.]: Here, 'by the craft of Umbra Recta' signifies, by a method similar to that in the last article, for which purpose the numbers must be adapted for computation by the umbra recta. Moreover, it is clear, from [fig. 17], that the numbers 4 and 3 (in lines 2 and 4) must be transposed. If the side parallel to bE be called nm, and mn, Ec be produced to meet in o, then mo : mE :: bE : bc; or mo : 12 :: 12 : bc; or mo = 144, divided by bc (= 3) = 48. Similarly, m′o′ = 144, divided by b′c′ (= 4) = 36. And, as in the last article, the difference of these is to 12, as the space EE′ is to the altitude. This is nothing but Art. 42 in a rather clumsier shape.

Hence it appears that there are here but 3 independent propositions, viz. those in articles 41, 42, and 43, corresponding to figs. 16, 17, and 18 respectively. Arts. 41a and 41b are mere repetitions of 41; 42a and 42b, of 42; and 43a, of 43.

CRITICAL NOTES.

As, in the preceding pages which contain the text, the lower portion of each page is occupied with a running commentary, such Critical Notes upon the text as seem to be most necessary are here subjoined.

Title. Tractatus, &c.; adopted from the colophon. MS. F has 'tractatus astrolabii.' A second title, 'Bred and mylk for childeren,' is in MSS. B. and E.

[The MSS. are as follows:—A. Cambridge Univ. Lib. Dd. 3. 53.—B. Bodley, E Museo 54.—C. Rawlinson 1370.—D. Ashmole 391.—E. Bodley 619.—F. Corpus 424.—G. Trin. Coll. Cam. R. 15. 18.—H. Sloane 314.—I. Sloane 261.—K. Rawlinson Misc. 3.—L. Addit. 23002. (B. M.)—M. St. John's Coll. Cam.—N. Digby 72.—O. Ashmole 360.—P. Camb. Univ. Lib. Dd. 12. 51.—Q. Ashmole 393.—R. Egerton 2622 (B. M.).—S. Addit. 29250 (B. M.) See the descriptions of them in the Introduction.]

Prologue. l. 26. thise B; þese C; miswritten this A; see above, ll. 21, 22.

32. curious BC; miswritten curios A.

Many similar very slight alterations of spelling have been silently made in the text, and are not worth specifying here. A complete list of them is given in my edition of this treatise for the Early English Text Society. I give, however, the real variations of reading. Thus, in l. 58, A. has som for sonne; and in l. 64 omits the second the.

Part I. § 1, l. 3. wol B; wolde AC.

§ 2, l. 2. Rowm is here an adjective, meaning large, ample. It is the right reading; we find Rowm AB rowme C; rvm M.

§ 3, l. 1. AB omit the.

§ 9, l. 3. nombre AB; noumbre C; but nombres in old editions.

§ 12, l. 5. The MSS. all[^[60]] read—'vmbra recta or elles vmbra extensa, & the nether partie is cleped the vmbra versa.' This is certainly wrong.

§ 13, l. 2. a certein] so in AB; CM omit a. But Chaucer certainly uses the phrase 'a certain'; cf. 'of unces a certain,' C. T., G 776; and see G 1024.

§ 14, ll. 2, 5. The word halt for holdeth, and the expression to-hepe, together, both occur in Troil. iii. 1764:—

'And lost were al, that Love halt now to-hepe.'

§ 17, l. 1. principal C; tropikal AB; M om. The reading tropikal is absurd, because there are but two such; besides which, see l. 34 below.

17. the nyht (over an erasure) B; thee nyht (over an erasure) A; þe niȝtes C; þe nyȝtes M.

§ 20, l. 4. figure; here (and sometimes elsewhere) miswritten vigur A. Throughout the whole treatise, the scribe has commonly written 'vigur'; in many places, it has been corrected to 'figure.'

§ 21, l. 15. the (before sterres) supplied from BC.

27. where as C; wher AB.

56. ouerkeruyd A; ouerkerued B; ouerkerueth (the latter part of the word over an erasure) C; first time only.

Part II. § 2, l. 8. euer M; euere C; euery (wrongly) AB.

§ 3, ll. 31, 32. A has 12 degres, corrected to 18 degres; B. has 12 degrees; C has 18. The numbers in the MSS. in these propositions are somewhat uncertain; it seems probable that some alteration was made by Chaucer himself.

The readings in MS. B give one set of calculations, which are no doubt the original ones; for in MS. A the same set is again found, but altered throughout, by the scribe who drew the diagrams. The sets of readings are these:—

Ll. 31, 32. 12 degrees B; so in A, but altered to 18; C has 18.

37. passed 9 of the clokke the space of 10 degrees B; so in A, with 9 altered to 8, and 10 altered to 2; C has ij for 9, but agrees with A in the reading 2.

39. fond ther 10 degrees of taurus B; so in A originally, but 10 has been corrected to 23, and libra is written over an erasure. C agrees with neither, having 20 for 10, but agreeing with A as to libra. The later MSS. sometimes vary from all these.

42. an supplied from C; AB omit.

§ 4, l. 5. largest C; largesse AB.

6. upon C; vn (!) AB.

8. forseide degree of his longitude] forseyde same degre of hys longitude C; forseid same gre of his longitude P; forseyde latitude his longitude (sic!) AB.

9. planete ys C; miswritten planetes AB, but is is added in margin of A.

16. For '25 degrees,' all the MSS. have '15 degrees.' The mistake is probably Chaucer's own; the correction was made by Mr. Brae, who remarks that it is a mere translation from the Latin version of Ptolemy's Tetrabiblos, which has—'Signum ascendentis, quod est a quinque gradibus qui super horizontem ante ipsum ascenderant usque ad viginti quinque qui ad ascendentem remanserint'; Lib. iii. c. 10. In fact, it is clear that 25 must be added to 5 to make up the extent of a 'house,' which was 30 degrees.

16. ys like C; is lik P; miswritten illyk AB.

17. in is supplied from GM; ABC omit it.

23. second the supplied from CP; AB omit.

32. wel supplied from CPM; AB omit.

36. than] þan CM; þenne P; AB omit.

40. The number 10 is supplied from C; AB omit.

42. some folk supplied from CPG; AB omit.

44. yit is] AB wrongly have yit it is; but CPGM omit it.

§ 5, l. 3. by 2 and 2 ACG; by 3 and 3 P; left blank in B. Either reading makes sense, but it is clear that divisions representing three degrees each must have been very awkward.

10. of supplied from CPGM: AB omit.

§ 6, l. 5. est C; west A (which is absurd); west (corrected to est) B.

9. signe CGP; signes ABM.

§ 10, l. 3. than B; þan C; A has & by nyht, which is absurd.

4, 5. A omits day with the howr inequal of the, which is supplied from BCP; the number 30 is also supplied from BCM, as A has a blank space here; see l. 10.

§ 11, l. 12. The number 4 is from CP; AB omit; old edd. fourthe.

13. ther supplied from PM; þere C; AB omit.

§ 12, l. 1. the supplied from BC; A omits.

8. The figure 2 is from BCP; G has secunde; A omits.

§ 14, l. 9, 10. The last clause supplied from B.

§ 15, l. 6. pointe] point P; pointes A; pointz B; poyntes C; but grammar requires the singular.

9. the supplied from CP; AB omit.

§ 16, l. 5. AB wrongly insert the before Cancer; CP omit it.

8. y-lyke] Ilyke G; ilik P; y-like C; ilke AB; see l. 7.

§ 17. Latin rubric; for latitudinem (as in M) read longitudinem. l. 18. heued B; hed ACP; see sect. 16, l. 3. The word 'the' (rightly placed in BCMP) is, in A, wrongly placed before 'Aries' instead of before 'ende.'

23. second the] þe C; AB omit.

§ 19. Latin Rubric; for orizon (as in M) read statio.

§ 20. Latin Rubric; the MS. (M) transposes the words in and a, having a zodiaco in circulo, which contradicts the sense.

§ 22. Latin Rubric; for centri (as in M) read regionis.

§ 23, l. 21. The figure '8' is omitted in AB.

23. than] A omits; thanne inserted afterwards in B.

§ 25, l. 3. first the] supplied from B; AC omit.

15. CP om. and 10 minutes.

16. CP om. and minutes out. For 51 degrees and 50 minutes, C has 52, þan is 52 degrees; and P has 52. Þenne is .52. grees.

19. CP om. as I mighte prove.

20. the supplied from CP; AB om.

27. the firste degree] 10 degrees C; 10 gree P.

28. 58 degrees and 10 minutes] almost 56 C (meaning 56 degrees); almost .56. grees P.

29. almost 20] almost 18 C.

31. thee] C om. and odde Minutes] CP om.

It thus appears that there is a second set of readings, involving a different calculation. The second set supposes the Sun to be in the 10th degree of Leo, his altitude to be 56°, and his declination 18°; the difference, viz. 38°, is the complement of the latitude. Either set of readings suits the sense, but the one in the text agrees best with the former latitude, viz. 51°. 50′.

37. After there, C inserts 38 grees, þat is; and omits the words of the pole, 51 degrees and 50 minutes. But this is a mere repetition of the 'height of the Equinoctial,' and is obviously wrong. After pole, in l. 38, A inserts an that, which is unmeaning, and omitted in B.

§ 26, l. 8. Nearly all the MSS. omit from Fertherover down to right orisonte. The missing clause appears in MS. Bodley 619; I have not found it elsewhere. It is obviously correct, and agrees sufficiently closely with the conjectural addition by Mr. Brae, in his edition of Chaucer's Astrolabe, p. 48.

§ 27, l. 2. second the] supplied from BCPM; A om.

§ 28. Latin Rubric. MS. has in recto circulo; read obliquo.

3. set] sett C; sete P; AB omit.

11. these] þese C; thise B; the A.

23. ende] heed A; heued C. In fact, heed, heued, or hed seems to be the reading of all the MSS. and printed copies, and may have been a slip of the pen in the first instance. The reading ende is, however, amply justified by its previous occurrence, four times over, in lines 10, 13, 16, 18. We thus have

Six Northern signs. From head of Aries to end of Virgo.

Six Southern signs. From head of Libra to end of Pisces.

Six Tortuous signs. From head of Capricorn to end of Gemini.

Six Direct signs. From head of Cancer to end of Sagittarius.

Opposite 'sagittare' is written 'sagittarie' in the margin of A, probably as a correction; but it is left uncorrected in l. 27.

§ 29, l. 3. Turne thanne] Turne þan C; turne the thanne AB.

9. thou] þou C; two AB.

14. rewle] rule CP; miswritten rewles AB; see l. 9.

§ 30. l. 11. wey A; place C. After zodiak C inserts—for on þe morowe wol þe sonne be in a-noþer degre þan þan, et cetera; P inserts—For yn þe morowe wol þe sonne be yn an oþer gree, & norþer or souþer par aventure. Nothing can be plainer than that 'the way of the sun' in this passage means the small circle formed by the sun's apparent path during a day; the text says expressly—'the wey wher as the sonne wente thilke day.' We need not argue about the impossibility of a planet being found in 'the way of the Sun' at midnight at the time of the Summer solstice, because Chaucer makes no assertion whatever here about the relative positions of the sun and planet; indeed, he carefully repeats 'if' three times. He is only concerned with defining the phrase—'the latitude of a planet from the way of the sun'; and in every possible case, it is clear that a planet can be either (1) situate in the small circle called in the Latin rubric cursus solis, or (2) to the north of such a circle, or (3) to the south of such a circle. About this there need be no difficulty at all. It is all copied from Messahala.

§ 31, l. 7. azimut] azymutz ABC; cf. sect. 32, l. 8.

§ 33, l. 2. Azimut] Azymutz ABC; minutis P; the same error as in sect. 31, l. 7; but see sect. 32, l. 8.

3. second in] yn P; ABC omit.

4. the night] so in AB; CP om. the.

§ 34. English Rubric; latitude for] so in CP; latitude and for AB.

6. toucheth] touchiþ P; to which (sic) ABC; see sect. 27, l. 6.

§ 35, l. 15. After west side, AB add & yf he be on the est syde, a mere superfluous repetition; see l. 11.

17. sothly] soþly CP; miswritten he settes (!) AB.

18. hir Episicle] so in CP; by an odd mistake, AB put hire after manere, instead of before Episicle.

§ 37, l. 10. than] þan C; AB omit. is] AS omit; but it is obviously wanted; C varies here.

12. 12 house next] 12 hous next C; howses nex (sic) AB.

13. thanne] þan C; A omits. howse] hous C; howses AB.

17. AB absurdly insert fro before the byginning.

18. first the] þe C; AB omit.

§ 38, l. 1. warpyng MP; werpynge C; weripinge (sic) A.

2. first a CP; AB omit.

3, 4. an euene C; a enene AB (twice).

8. fro the centre; i.e. above the centre. The length of the pin, measured from the centre in which it is inserted, is to be not more than a quarter of the diameter, or half the radius. This would make the ratio of the gnomon to the shadow (or radius) to be one-half, corresponding to an altitude a, where tan a = ½; i.e. to an altitude of about 26½°. As Chaucer talks about the sun's altitude being 25½° at about 9 o'clock, at the time of the equinoxes (sect. 3), there is nothing that is particularly absurd in the text of this section. For Mr. Brae's conjectural emendations, see p. 56 of his edition.

16. tak thanne] so in P; tak me thanne AB; take me þan C. But there seems no sufficient reason for thus inserting me here.

§ 39. At this point MS. A, which has so far, in spite of occasional errors of the scribe, afforded a very fair text, begins to break down; probably because the corrector's hand has not touched the two concluding sections, although section 40 is much less corrupt. The result is worth recording, as it shews what we may expect to find, even in good MSS. of the Astrolabe. The section commences thus (the obvious misreadings being printed in italics):—

'This lyne Meridional ys but a Maner descripcion or the ymagined, that passeth vpon the pooles of þis the world And by the cenyth of owre heued / And hit is the same lyne Meridional / for in what place þat any maner man [omission] any tyme of the yer / whan that the sonne schyneth ony thing of the firmament cometh to his verrey Middel lyne of the place / than is hit verrey Midday, þat we clepen owre noon,' &c.

It seems clear that this apparent trash was produced by a careless scribe, who had a good copy before him; it is therefore not necessary to reject it all as unworthy of consideration, but it is very necessary to correct it by collation with other copies. And this is what I have done.

MS. B has almost exactly the same words; but the section is considerably better, in general sense, in MSS. C and P, for which reason I here quote from the former the whole section.

[Rawl. MS. Misc. 1370, fol. 40 b.]

Descripcioun of þe meridional lyne, of þe longitudes and latitudes of Citees and townes, as wel as of a (sic) clymatz.

39. conclusio. This lyne meridional is but a maner discripcion̄ or lyne ymagyned, þat passeþ upon þe pooles of þis worlde, and by þe Cenith of oure heued. ¶ And yt is cleped þe lyne meridional, for in what place þat any man ys at any time of þe ȝere, whan þat þe sonne by menynge of þe firmament come to his uerrey meridian place / þan is it þe uerrey mydday þat we clepe none, as to þilke man. And þerefore is yt cleped þe lyne of mydday. And nota, þat euermo of any .2. citees or of 2 townes, of which þat oo towne a-procheþ neer þe est þan doþ þe oþer towne, trust wel þat þilke townes han diuerse meridians. Nota also, þat þe arche of þe equinoxial, þat is contened or bownded by-twixe þe two meridians, is cleped þe longitude of þe towne. ¶ & ȝif so be / þat two townes haue I-like meridian or one merydian, ¶ Than ys þe distaunce of hem boþe I-like fer from þe est, & þe contrarye. And in þis maner þei chaunge not her meridyan, but soþly, þei chaungen her almykanteras, For þe enhaunsynge of þe pool / and þe distaunce of þe sonne. ¶ The longitude of a clymate ys a lyne ymagyned fro þe est to þe west, I-like distaunte fro þe equinoxial. ¶ The latitude of a clymat may be cleped þe space of þe erþe fro þe by-gynnynge of þe first clymat unto þe ende of þe same clymat / euene-directe a-ȝens þe pool artyke. ¶ Thus seyn somme auctours / and somme clerkes seyn / þat ȝif men clepen þe latitude of a contrey[^[61]], þe arche merdian þat is contened or intercept by-twixe þe Cenyth & þe equinoxial; þan sey þei þat þe distaunce fro þe equinoxial unto þe ende of a clymat, euene[^[62]] a-gaynes þe pool artik, is þe latitude off þat climat[^[62]] forsoþe.

The corrections made in this section are here fully described.

1. of lyne P; of a line I; or lyne C; or the AB.

2. this] þis the AB, absurdly; CP omit the, rightly.

3. ycleped the] y-clupid þe P; cleped þe C; the same (sic) AB.

4. is at; supplied from PCI; AB omit.

5. by moeving] by meuynge C; by mevyng PI; schyneth ony thing (sic) A; schyned eny thing B; for the spelling moeving, see sect. 35, l. 5.

6. meridian CP; meridianale I; Middel lyne of the (sic) AB.

8. 2 citees CI; too citees P; any lynes (sic) AB.

9. aprocheth] a-procheþ C; aprochiþ P; miswritten aprochid AB.

more toward] neer C; ner P; neerer I; thoward AB.

11. conteyned I; conteynyd P; contened C; consideered (sic) A; contined B.

13. yf P; ȝif C; if it I; AB omit. N.B. It is best to use the spelling yif, as the word is commonly so spelt in A.

22. same CPI; seconde AB. The reading same is right; for the 'latitude of a climate' means the breadth of a zone of the earth, and the latitude of the first climate (here chosen by way of example) is the breadth as measured along a great circle perpendicular to the equator, from the beginning of the said first climate to the end of the same. The words 'evene-directe agayns the poole Artik' mean in the direction of the North pole; i.e. the latitude of a climate is reckoned from its beginning, or southernmost boundary-line, towards the end of the same, viz. its northern boundary-line.

22. þe poole Artik P; þe pool artyke C; the pole artike I; from north to south AB. Observe that this singular error in A, 'euene directe agayns from north to south,' probably arose from a confusion of the text 'euene directe agayns þe poole Artik' with a gloss upon it, which was 'from north to south.' It is important as throwing light on the meaning of the phrase, and proving that the interpretation of it given above (note to l. 22) is correct.

24. intercept CP; intercepte I; except (over an erasure) AB.

The only reading about which there is any doubt is that in line 18, which may be either 'illike distant by-twene them alle' (A), or 'I-like distaunte fro þe equinoxial' (C). But it is immaterial which reading be adopted, since Illike-distant is here used merely in the sense of parallel, and the boundaries of the climates are parallel both to one another, and to the equinoctial. The climates themselves were of different breadths.

§ 40, l. 4. this samples AB; þese ensamples C.

5. for sothe] miswritten for sonne AB; in general C; yn special P; the reading sonne points to sothe, and makes it very probable that for sothe is the true reading.

6. the longitude] þe longitude C; latitude AB (absurdly); see l. 11.

7. planete; miswritten that A, but corrected to planete in the margin; C has planete, correctly. The figure 6 is omitted in C; so are all the other figures further on. him] hir C.

8. I tok] Than toke I C. 8, 16. 2 degrees A; 3 degrees B.

10. Than tok I] Than toke I C; for tok AB wrongly have stykke, afterwards altered to stokke in A. second the] supplied from C, which has þe; AB omit.

23. the] þe C; AB omit.

27. prikke] prickes C; perhaps prikkes would be a better reading.

29. AB omit the figure 2; but see l. 8.

31. in alle] in al C; A has septentrionalle, an obvious mistake for septentrional in alle, by confusion of the syllable 'al' in the former with 'al' in the latter word; B has septentrional, omitting in alle.

34. signes C] tymes AB (wrongly); see l. 32.

46. Perhaps evene before of should be omitted, as in C. AB have in the ende euene ouer of thee, where euene ouer is repeated from the former part of the line.

47. F endlang] F endlonge C; A euene AB; but see ll. 23, 24.

A omits of and degrees, yet both are required; BC omit of 3 degrees altogether.

49. til] tyl þat C; tho AB (absurdly).

50. saw] sey C; may AB; see l. 28.

56. hir] his ABC. a] ABC omit.

57. At the word houre four of the best MSS. break off, viz. MSS. ABCE, although E adds one more section, viz. sect. 46; others come to a sudden end even sooner, viz. MSS. DFGHK. But MS. P carries us on to the end of sect. 43, and supplies the words—þu shalt do wel ynow, as in the old editions.

§ 41. 7. betwixe] be M (wrongly); betwixe R; by-twyx L.

M inserts & before to þe altitude; a mere slip. For; miswritten Fro M.

8. thridde; miswritten ridde M; þrydde R.

13. LM wrongly place of after the heyȝt instead of before it.

§ 42, l. 2. see] so in LR; miswritten sette M; see sect. 41, l. 4.

3. second I] so L; y R; M omits.

8. M omits as, above, and is þe; L has 12 passethe 6 the.

11. seest] so in LR; miswritten settest M.

12. 60] so in LNR; sexe M.

13. M omits from 10 is to 10 feet, which is supplied from NLPR.

14. For] so in LNR; fro M.

15. For 2, M has 6; so also R. For 3, M has 4.

16. For 2, M has 6; for 6, M has 2; and the words and 3 is 4 partyes of 12 are omitted, though L has—& 4 is the thrid partye of 12.

17. betwen R] by-twene L; bitwixe P; miswritten be M; cf. sect. 41, 7.

19. thre R] 3 LP; miswritten þe M.

§ 43. Rubric in M, Umbra Versa; obviously a mistake for Recta. The error is repeated in l. 1. LPR rightly read Recta.

3. M omits 1, which is supplied from LPR; see l. 5.

11. After heythe (as in M), LNR add to thyn eye. In place of lines 9-11, P has—& so of alle oþer, &c.

§ 44. From MS. Digby 72 (N). Also in LMOR.

2. fro] so in LO; for M.

3. into] so in L; in M. for] so in O; fro M.

6. ȝeris M; LNO omit.

7. tabelis NO; table M; tables L.

8. where L; qwere O; wheþer N.

9. loke LM; N omits.

11, 2. NM omit from or what to or; supplied from O, which has—or qwat nombre þat euere it be, tyl þe tyme þat þou come to 20, or 40, or 60. I have merely turned qwat into what, as in L, which also has this insertion.

13. wreten N; the alteration to wryte is my own; see l. 23.

under] so in L; vndirneþe M.

14. to-geder] too-geder M; miswritten to 2 degreis N; to the 2 degrees L.

15. hast M; miswritten laste N; last L.

16. that (1); supplied from M; LN omit. For 1 (as in M) LN have 10.

21. to-gedere M; to the degreis N; 2 grees O; to degrees L.

22. that (2); supplied from M; LNO omit.

lasse] passid LNO; M omits. Of course passid is wrong, and equally of course lasse is right; see ll. 5, 6 above, and l. 25 below.

25. that] so in L; þat MO; if hit N.

27. entringe] entre M; entre L. ther] so in M; miswritten the ȝere N; the ȝeer L.

30. merydie LM; merdie N.

32. for LM; fro N (twice).

34. thaȝthe N; have tauȝt M; have tawȝt O; haue tauht L.

36. the (1); supplied from M; LNO omit.

with the] so in M; wyche N; see l. 36.

40. in (2)] in-to N; yn M.

§ 45. From MS. Digby 72 (N); also in LOR; but not in M.

4. that N; the L; þe O (after wryte in l. 3).

6. wrytoun O; Iwyton N. But L has I wold wyttyn; read—I wolde witen precise my rote; cf. ll. 19, 30.

8. 1397] miswritten 1391 LN; O has 1391, corrected to 1397; see l. 3.

11. soȝth N; sowte O; sowthe L; read soghte.

14. vnder N; vndyr-nethe O; vndre-nethe L.

20, 1. oþer in any oþer tyme or monyth N; or any oder tymys or monthys O; or in eny other moneth L.

27. adde] supplied from L; NO omit. There is no doubt about it, for see l. 16.

31. wete the] so in O; wete thi L; miswritten with thy N; see l. 19.

35. and (3)] supplied from LO; N omits.

§ 46, 5, 6. þat same E; þe same S.

10. it S; E omits.

13. þat same (om. tyme) E; þe same tyme S.

16. þou þan esely E; than shallt thou easly S.

17. tyme of E; tyme of the S.

20. S meve (for bringe furþe).

§ 41a. This and the remaining sections are certainly spurious. They occur in LMNR, the first being also found in O. The text of 41a-42b is from M.

3. hast] supplied from LR; M omits.

§ 42a, 1. heyth by þy N; heyth by the L; heythe bi þi R; M om.

4. lyk] lykk M; L. omits. mete] mette M; mett L.

9. is L; miswritten bys M.

§ 43a, 1. nat] not R; nott L; M omits; see the footnote. In the rubric, M has versam; but L has the rubric—Vmbra Recta.

§ 42b, 5. as] so in LR; miswritten & M.

6. 4 is supplied from LR; M omits.

NOTES TO THE HOUSE OF FAME.