Chaucer's Works (ed. Skeat) Vol. III/Treatise on the Astrolabe

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[ 175 ]

A TREATISE ON THE ASTROLABE.


PROLOGUE.

Litell Lowis my sone, I have perceived wel by certeyne
evidences thyn abilite to lerne sciencez touchinge noumbres
and proporciouns; and as wel considere I thy bisy preyere in
special to lerne the Tretis of the Astrolabie. Than, for as mechel
as a philosofre seith, 'he wrappeth him in his frend, that condescendeth       5
to the rightful preyers of his frend,' ther-for have I
geven thee a suffisaunt Astrolabie as for oure orizonte, compowned
after the latitude of Oxenford; up-on which, by mediacion of this
litel tretis, I purpose to teche thee a certein nombre of conclusions
apertening to the same instrument. I seye a certein of conclusiouns,       10
for three causes. The furste cause is this: truste wel that alle the
conclusiouns that han ben founde, or elles possibly mighten be
founde in so noble an instrument as an Astrolabie, ben un-knowe
perfitly to any mortal man in this regioun, as I suppose. A-nother
cause is this; that sothly, in any tretis of the Astrolabie that I have       15
seyn, there ben some conclusions that wole nat in alle thinges
performen hir bihestes; and some of hem ben to harde to thy
tendre age of ten yeer to conseyve. This tretis, divided in fyve
[ 176a ]parties, wole I shewe thee under ful lighte rewles and naked
wordes in English; for Latin ne canstow yit but smal, my lyte       20
sone. But natheles, suffyse to thee thise trewe conclusiouns in
English, as wel as suffyseth to thise noble clerkes Grekes thise same
conclusiouns in Greek, and to Arabiens in Arabik, and to Iewes in
Ebrew, and to the Latin folk in Latin; whiche Latin folk han hem
furst out of othre diverse langages, and writen in hir owne tonge,       25
that is to sein, in Latin. And god wot, that in alle thise langages,
and in many mo, han thise conclusiouns ben suffisantly lerned and
taught, and yit by diverse rewles, right as diverse pathes leden
diverse folk the righte wey to Rome. Now wol I prey meekly
every discret persone that redeth or hereth this litel tretis, to have       30
my rewde endyting for excused, and my superfluite of wordes, for
two causes. The firste cause is, for that curious endyting and hard
sentence is ful hevy atones for swich a child to lerne. And the
seconde cause is this, that sothly me semeth betre to wryten un-to
a child twyes a good sentence, than he for-gete it ones. And       35
Lowis, yif so be that I shewe thee in my lighte English as trewe
conclusiouns touching this matere, and naught only as trewe but
as many and as subtil conclusiouns as ben shewed in Latin in any
commune tretis of the Astrolabie, con me the more thank; and
preye god save the king, that is lord of this langage, and alle that       40
him feyth bereth and obeyeth, everech in his degree, the more and
the lasse. But considere wel, that I ne usurpe nat to have founde
this werk of my labour or of myn engin. I nam but a lewd compilatour
of the labour of olde Astrologiens, and have hit translated
in myn English only for thy doctrine; and with this swerd shal I       45
sleen envye.

I. The firste partie of this tretis shal reherse the figures and the
membres of thyn Astrolabie, bi-cause that thou shalt han the
grettre knowing of thyn owne instrument.

[ 177a ]II. The second partie shal teche thee werken the verrey       50
practik of the forseide conclusiouns, as ferforth and as narwe
as may be shewed in so smal an instrument portatif aboute.
For wel wot every astrologien that smalest fraccions ne wol
nat ben shewed in so smal an instrument, as in subtil tables
calculed for a cause.       55

III. The thridde partie shal contienen diverse tables of
longitudes and latitudes of sterres fixe for the Astrolabie, and
tables of declinacions of the sonne, and tables of longitudes
of citeez and of townes; and as wel for the governance of a
clokke as for to finde the altitude meridian; and many another       60
notable conclusioun, after the kalendres of the reverent clerkes,
frere I. Somer and frere N. Lenne.

IV. The ferthe partie shal ben a theorik to declare the
moevinge of the celestial bodies with the causes. The whiche
ferthe partie in special shal shewen a table of the verray       65
moeving of the mone from houre to houre, every day and in
every signe, after thyn almenak; upon which table ther folwith
a canon, suffisant to teche as wel the maner of the wyrking of
that same conclusioun, as to knowe in oure orizonte with which
degree of the zodiac that the mone ariseth in any latitude;       70
and the arising of any planete after his latitude fro the ecliptik
lyne.

V. The fifte partie shal ben an introductorie after the statutz
of oure doctours, in which thou maist lerne a gret part of the
general rewles of theorik in astrologie. In which fifte partie       75
shaltow finde tables of equacions of houses aftur the latitude of
Oxenford; and tables of dignetes of planetes, and other noteful
thinges, yif god wol vouche-sauf and his modur the mayde, mo
than I be-hete, &c.


[ 178a ]

PART I.

Here biginneth the descripcion of the Astrolabie.

1. Thyn Astrolabie hath a ring to putten on the thoumbe of
thy right hand in taking the heighte of thinges. And tak keep, for
from hennes-forthward, I wol clepe the heighte of any thing that
is taken by thy rewle, the altitude, with-oute mo wordes.

2. This ring renneth in a maner turet, fast to the moder of
thyn Astrolabie, in so rowm a space that hit desturbeth nat the
instrument to hangen after his righte centre.

3. The Moder of thyn Astrolabie is the thikkeste plate, perced
with a large hole, that resseyveth in hir wombe the thinne plates
compowned for diverse clymatz, and thy riet shapen in manere
of a net or of a webbe of a loppe; and for the more declaracioun,
lo here the figure.       5

4. This moder is devyded on the bak-half with a lyne, that
cometh dessendinge fro the ring down to the nethereste bordure.
The whiche lyne, fro the for-seide ring un-to the centre of the
large hole amidde, is cleped the south lyne, or elles the lyne
meridional. And the remenant of this lyne downe to the bordure       5
is cleped the north lyne, or elles the lyne of midnight. And for
the more declaracioun, lo here the figure.

[ 179a ]5. Over-thwart this for-seide longe lyne, ther crosseth him
another lyne of the same lengthe from est to west. Of the
whiche lyne, from a litel croys + in the bordure un-to the centre
of the large hole, is cleped the Est lyne, or elles the lyne Orientale;
and the remenant of this lyne fro the forseide + un-to the bordure,       5
is cleped the West lyne, or the lyne Occidentale. Now hastow
here the foure quarters of thin Astrolabie, devyded after the foure
principals plages or quarters of the firmament. And for the more
declaracioun, lo here thy figure.

6. The est side of thyn Astrolabie is cleped the right side, and
the west side is cleped the left side. Forget nat this, litel Lowis.
Put the ring of thyn Astrolabie upon the thoumbe of thy right
hand, and thanne wole his right syde be toward thy left syde, and
his left syde wol be toward thy right syde; tak this rewle general,       5
as wel on the bak as on the wombe-side. Upon the ende of this
est lyne, as I first seide, is marked a litel +, wher-as evere-mo
generaly is considered the entring of the first degree in which the
sonne aryseth. And for the more declaracioun, lo here the
figure.       10

7. Fro this litel + up to the ende of the lyne meridional, under
the ring, shaltow finden the bordure devyded with 90 degrees;
and by that same proporcioun is every quarter of thin Astrolabie
devyded. Over the whiche degrees ther ben noumbres of augrim,
that devyden thilke same degrees fro fyve to fyve, as sheweth by       5
longe strykes by-twene. Of whiche longe strykes the space by-twene
contienith a mile-wey. And every degree of the bordure
contieneth foure minutes, that is to seyn, minutes of an houre.
And for more declaracioun, lo here the figure.

8. Under the compas of thilke degrees ben writen the names of
the Twelve Signes, as Aries, Taurus, Gemini, Cancer, Leo, Virgo,
[ 180a ]Libra, Scorpio, Sagittarius, Capricornus, Aquarius, Pisces; and
the nombres of the degrees of tho signes ben writen in augrim
above, and with longe devisiouns, fro fyve to fyve; devyded fro       5
tyme that the signe entreth un-to the laste ende. But understond
wel, that thise degrees of signes ben everich of hem considered
of 60 minutes, and every minute of 60 secondes, and so
forth in-to smale fraccions infinit, as seith Alkabucius. And
ther-for, know wel, that a degree of the bordure contieneth foure       10
minutes, and a degree of a signe contieneth 60 minutes, and
have this in minde. And for the more declaracioun, lo here
thy figure.

9. Next this folweth the Cercle of the Dayes, that ben figured
in maner of degrees, that contienen in noumbre 365; divyded
also with longe strykes fro fyve to fyve, and the nombres in
augrim writen under that cercle. And for more declaracioun, lo
here thy figure.

10. Next the Cercle of the Dayes, folweth the Cercle of the
names of the Monthes; that is to seyen, Ianuare, Februare,
Marcius, Aprile, Mayus, Iuin, Iulius, Augustus, Septembre,
October, Novembre, Decembre. The names of thise monthes
were cleped in Arabiens, somme for hir propretees, and some by       5
statutz of lordes, some by other lordes of Rome. Eek of thise
monthes, as lyked to Iulius Cesar and to Cesar Augustus, some
were compowned of diverse nombres of dayes, as Iuil and
August. Thanne hath Ianuare 31 dayes, Februare 28, March
31, Aprille 30, May 31, Iunius 30, Iulius 31, Augustus 31,       10
September 30, Octobre 31, Novembre 30, December 31.
Natheles, al-though that Iulius Cesar took 2 dayes out of Feverer
and put hem in his moneth of Iuille, and Augustus Cesar cleped
the moneth of August after his name, and ordeyned it of 31 dayes,
[ 181a ]yit truste wel, that the sonne dwelleth ther-for nevere the more ne       15
lesse in oon signe than in another.

11. Than folwen the names of the Halidayes in the Kalender,
and next hem the lettres of the Abc. on which they fallen. And
for the more declaracioun, lo here thy figure.

12. Next the forseide Cercle of the Abc., under the cros-lyne,
is marked the scale, in maner of two squyres, or elles in manere
of laddres, that serveth by hise 12 poyntes and his devisiouns of
ful many a subtil conclusioun. Of this forseide scale, fro the
croos-lyne un-to the verre angle, is cleped umbra versa, and the       5
nether partie is cleped the umbra recta, or elles umbra extensa.
And for the more declaracioun, lo here the figure.

13. Thanne hastow a brood Rewle, that hath on either ende a
square plate perced with a certein holes, some more and some
lesse, to resseyven the stremes of the sonne by day, and eek
by mediacioun of thyn eye, to knowe the altitude of sterres by
nighte. And for the more declaracioun, lo here thy figure.       5

14. Thanne is ther a large Pyn, in maner of an extree, that
[ 182a ]goth thorow the hole that halt the tables of the clymates and the
riet in the wombe of the Moder, thorw which Pyn ther goth a
litel wegge which that is cleped 'the hors,' that streyneth alle
thise parties to-hepe; this forseide grete Pyn, in maner of an       5
extree, is imagined to be the Pol Artik in thyn Astrolabie.
And for the more declaracioun, lo here the figure.

15. The wombe-side of thyn Astrolabie is also devyded with a
longe croys in foure quarters from est to west, fro south to north,
fro right syde to left syde, as is the bak-syde. And for the more
declaracioun, lo here thy figure.

16. The bordure of which wombe-side is devyded fro the poynt
of the est lyne un-to the poynt of the south lyne under the ring,
in 90 degres; and by that same proporcioun is every quarter
devyded as is the bak-syde, that amonteth 360 degrees. And
understond wel, that degrees of this bordure ben answering and       5
consentrik to the degrees of the Equinoxial, that is devyded in
the same nombre as every othere cercle is in the heye hevene.
This same bordure is devyded also with 23 lettres capitals and a
smal croys + above the south lyne, that sheweth the 24 houres
equals of the clokke; and, as I have said, 5 of thise degrees       10
maken a mile-wey, and 3 mile-wey maken an houre. And every
degree of this bordure conteneth 4 minutes, and every minut 60
secoundes; now have I told thee twye. And for the more
declaracioun, lo here the figure.

17. The plate under thy riet is descryved with 3 principal
[ 183a ]cercles; of which the leste is cleped the cercle of Cancer, by-cause
that the heved of Cancer turneth evermor consentrik up-on
the same cercle. In this heved of Cancer is the grettest declinacioun
northward of the sonne. And ther-for is he cleped the       5
Solsticioun of Somer; whiche declinacioun, aftur Ptholome, is 23
degrees and 50 minutes, as wel in Cancer as in Capricorne. This
signe of Cancre is cleped the Tropik of Somer, of tropos, that is
to seyn 'agaynward'; for thanne by-ginneth the sonne to passe
fro us-ward. And for the more declaracioun, lo here the figure.       10
The middel cercle in wydnesse, of thise 3, is cleped the Cercle
Equinoxial; up-on whiche turneth evermo the hedes of Aries and
Libra. And understond wel, that evermo this Cercle Equinoxial
turneth iustly fro verrey est to verrey west; as I have shewed thee
in the spere solide. This same cercle is cleped also the Weyere,       15
equator, of the day; for whan the sonne is in the hevedes of
Aries and Libra, than ben the dayes and the nightes ilyke of
lengthe in al the world. And ther-fore ben thise two signes
called the Equinoxies. And alle that moeveth with-in the
hevedes of thise Aries and Libra, his moeving is cleped northward;
and alle that moeveth with-oute thise hevedes, his moeving
[ 184a ]is cleped south-ward as fro the equinoxial. Tak keep of thise
latitudes north and sowth, and forget it nat. By this Cercle
Equinoxial ben considered the 24 houres of the clokke; for
everemo the arysing of 15 degrees of the equinoxial maketh an       25
houre equal of the clokke. This equinoxial is cleped the girdel
of the firste moeving, or elles of the angulus primi motus vel
primi mobilis. And nota, that firste moeving is cleped 'moeving'
of the firste moevable of the 8 spere, whiche moeving is fro est to
west, and eft agayn in-to est; also it is clepid 'girdel' of the first       30
moeving, for it departeth the firste moevable, that is to seyn, the
spere, in two ilyke parties, evene-distantz fro the poles of this
world.

The wydeste of thise three principal cercles is cleped the
Cercle of Capricorne, by-cause that the heved of Capricorne       35
turneth evermo consentrik up-on the same cercle. In the heved
of this for-seide Capricorne is the grettest declinacioun southward
of the sonne, and ther-for is it cleped the Solsticioun of Winter.
This signe of Capricorne is also cleped the Tropik of Winter, for
thanne byginneth the sonne to come agayn to us-ward. And for       40
the more declaracioun, lo here thy figure.

18. Upon this forseide plate ben compassed certein cercles
that highten Almicanteras, of which som of hem semen perfit
cercles, and somme semen inperfit. The centre that standith
a-middes the narwest cercle is cleped the Senith; and the
netherest cercle, or the firste cercle, is clepid the Orisonte, that       5
is to seyn, the cercle that devydeth the two emisperies, that is,
the partie of the hevene a-bove the erthe and the partie be-nethe.
Thise Almicanteras ben compowned by two and two, al-be-it so
that on divers Astrolabies some Almicanteras ben devyded by oon,
and some by two, and somme by three, after the quantite of the       10
Astrolabie. This forseide senith is imagened to ben the verrey
point over the crowne of thyn heved; and also this senith is the
[ 185a ]verrey pool of the orisonte in every regioun. And for the
more declaracioun, lo here thy figure.

19. From this senith, as it semeth, ther come a maner crokede
strykes lyke to the clawes of a loppe, or elles like to the werk of a
womanes calle, in kerving overthwart the Almikanteras. And
thise same strykes or divisiouns ben cleped Azimuthz. And they
devyden the orisonte of thyn Astrolabie in four and twenty       5
devisiouns. And thise Azimutz serven to knowe the costes of the
firmament, and to othre conclusiouns, as for to knowe the cenith
of the sonne and of every sterre. And for more declaracioun, lo
here thy figure.

20. Next thise azimutz, under the Cercle of Cancer, ben ther
twelve devisiouns embelif, moche like to the shap of the azimutes,
that shewen the spaces of the houres of planetes; and for more
declaracioun, lo here thy figure.

21. The Riet of thyn Astrolabie with thy zodiak, shapen in
maner of a net or of a loppe-webbe after the olde descripcioun,
which thow mayst tornen up and doun as thy-self lyketh, conteneth
certein nombre of sterres fixes, with hir longitudes and latitudes
determinat; yif so be that the makere have nat erred. The names       5
of the sterres ben writen in the margin of the riet ther as they sitte;
of whiche sterres the smale poynt is cleped the Centre. And
understond also that alle sterres sittinge with-in the zodiak of thyn
Astrolabie ben cleped 'sterres of the north,' for they arysen by
northe the est lyne. And alle the remenant fixed, out of the       10
zodiak, ben cleped 'sterres of the south;' but I sey nat that they
[ 186a ]arysen alle by southe the est lyne; witnesse on Aldeberan and
Algomeysa. Generally understond this rewle, that thilke sterres
that ben cleped sterres of the north arysen rather than the degree
of hir longitude, and alle the sterres of the south arysen after the       15
degree of hir longitude; this is to seyn, sterres fixed in thyn
Astrolabie. The mesure of this longitude of sterres is taken in the
lyne ecliptik of hevene, under which lyne, whan that the sonne
and the mone ben lyne-right or elles in the superfice of this lyne,
than is the eclips of the sonne or of the mone; as I shal declare,       20
and eek the cause why. But sothly the Ecliptik Lyne of thy
zodiak is the outtereste bordure of thy zodiak, ther the degrees ben
marked.

Thy Zodiak of thyn Astrolabie is shapen as a compas which that
conteneth a large brede, as after the quantite of thyn Astrolabie;       25
in ensample that the zodiak in hevene is imagened to ben a superfice
contening a latitude of twelve degrees, wheras al the remenant
of cercles in the hevene ben imagined verrey lynes with-oute eny
latitude. Amiddes this celestial zodiak ys imagined a lyne, which
that is cleped the Ecliptik Lyne, under which lyne is evermo the       30
wey of the sonne. Thus ben ther six degrees of the zodiak on
that on side of the lyne, and six degrees on that other. This
zodiak is devided in twelve principal devisiouns, that departen the
twelve signes. And, for the streitnes of thin Astrolabie, than is
every smal devisioun in a signe departid by two degrees and two;       35
I mene degrees contening sixty minutes. And this forseide
hevenissh zodiak is cleped the Cercle of the Signes, or the Cercle
of the Bestes; for zodia in langage of Greek sowneth 'bestes' in
Latin tonge; and in the zodiak ben the twelve signes that ban
names of bestes; or elles, for whan the sonne entreth in any of the       40
signes, he taketh the propretee of swich bestes; or elles, for that
the sterres that ben there fixed ben disposed in signes of bestes,
or shape like bestes; or elles, whan the planetes ben under thilke
[ 187a ]signes, they causen us by hir influence operaciouns and effectes
lyk to the operaciouns of bestes. And understonde also, that whan       45
an hot planete cometh in-to an hot signe, than encresseth his hete;
and yif a planete be cold, thanne amenuseth his coldnesse, by-cause
of the hote signe. And by this conclusioun maystow take ensample
in alle the signes, be they moist or drye, or moeble or fix; rekening
the qualitee of the planete as I first seide. And everich of       50
thise twelve signes hath respecte to a certein parcelle of the body
of a man and hath it in governance; as Aries hath thyn heved, and
Taurus thy nekke and thy throte, Gemini thyn armholes and thyn
armes, and so forth; as shal be shewed more pleyn in the fifte
partie of this tretis. This zodiak, which that is part of the eighte       55
spere, over-kerveth the equinoxial; and he over-kerveth him again
in evene parties; and that on half declineth southward, and that
other northward, as pleynly declareth the tretis of the spere. And
for more declaracioun, lo here thy figure.

22. Thanne hastow a label, that is schapen lyk a rewle, save that
it is streit and hath no plates on either ende with holes; but, with
the smale point of the forseide label, shallow calcule thyne
equaciouns in the bordure of thin Astrolabie, as by thyn almury.
And for the more declaracioun, lo here thy figure.       5

23. Thyn Almury is cleped the Denticle of Capricorne, or elles
the Calculer. This same Almury sit fix in the bed of Capricorne,
[ 188a ]and it serveth of many a necessarie conclusioun in equaciouns of
thinges, as shal be shewed; and for the more declaracioun, lo here
thy figure.       5


Here endeth the descripcion of the Astrolabie.


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       5
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       10
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
[ 189a ]in the bordure up-on the first degree of Capricorne, a lite with-in       15
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       5
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.       10

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
[ 190a ]of thy sonne up-on the west side; tak this manere of setting for a       5
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       10
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       15
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       20
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       25
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       30
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
[ 191a ]founden on the west syde. Tho leide I my label over the degree
of the sonne that was descended under the weste orisonte, and       35
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       40
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       45
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       50
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,       55
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       5
[ 192a ]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       10
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       15
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,       20
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       25
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       30
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       35
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.       40
[ 193a ]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.       45

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       5
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       10
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       15
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.       20

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
[ 194a ]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       5
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       10
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       5
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       10
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
[ 195a ]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       15
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       5
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       5
[ 196a ]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       10
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       5
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       10
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.       15

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
[ 197a ]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       5
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       10
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       15
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       20
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       25
aryse. Now ryseth the sonne that Sonday by the morwe; and
[ 198a ]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       30
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       5
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
[ 199a ]zodiak acording with the prikke, this is to seyn, sittinge on the       5
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.       10

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       5
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.
[ 200a ]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       5
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       10
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       5
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
[ 201a ]thou knowest; and for-get nat this secounde assendent. And       10
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       15
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       20
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.       25
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
[ 202a ]ecliptik lyne; fro which lyne alle planetes som tyme declynen
north or south, save only the for-seide sonne. And for the more       30
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       5
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
[ 203a ]strange degree in another signe is by-cause that the latitude of the       5
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       10
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.       15

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       5
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
[ 204a ]fro the equinoxial, than is his declinacion north; yif it be southward,
than is it south. And for the more declaracioun, lo here       10
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.       5

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       5
orisonte is 51 degrees and 50 minutes; than is the senith from
oure pool artik 38 degrees and 10 minutes; than is the equinoxial
[ 205a ]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       10
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.       15

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       5
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,       10
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
[ 206a ]that the firste altitude of A excedeth his seconde altitude, and tak
half thilke porcioun that is exceded, and adde it to his seconde       15
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       20
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       25
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       30
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       5
more declaracioun, lo here thy figure.

[ 207a ]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       5
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       10
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       15
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       20
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,       25
and thanne hastow the heyghte of the hevedes of Aries
and Libra. As thus: my sonne is, par aventure, in the firste
[ 208a ]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       30
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       35
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       40
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       5
lasse part of the zodiak ascendeth; and thilke signe assendeth
embelif, with whiche lasse part of the equinoxial and more part of
[ 209a ]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       10
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       15
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       20
[ 210a ]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.       25

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       5
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.       10

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
[ 211a ]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       5
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;       10
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       15
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       20
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       25
to Cancer; and Taurus to Leo; Aries to Virgo; Pisces to Libra;
Aquarius to Scorpioun; and Capricorne to Sagittare. And thus
[ 212a ]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.       30

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       5
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       10
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       15
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.       20

[ 213a ]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       5
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       10
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
[ 214a ]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       5
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       10
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.       15
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,
[ 215a ]as thou art wont to do in knowing of the houres of the day or of       5
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       5
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
[ 216a ]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       5
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       10
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.       15

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.       5
[ 217a ]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       10
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       15
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       5
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
[ 218a ]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       10
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       15
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       5
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       10
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
[ 219a ]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       15
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;       5
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       10
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       15
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
[ 220a ]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       20
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       5
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.       10
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       15
chaunge nat her meridian, but sothly they chaungen her almikanteras;
for the enhausing of the pool and the distance of the
[ 221a ]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,       20
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       25
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       5
zodiak. The degree of the longitude, par aventure, of Venus or
of another planete, was 6 of Capricorne, and the latitude of him
[ 222a ]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       10
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       15
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       20
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       25
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       30
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.       35

[ 223a ]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       40
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       45
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       50
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       55
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.


[ 224a ]

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       5
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       10
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
[ 225a ]a-nother prikke; and I beholde how 1 hath him to 12, and ther       5
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       10
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;       15
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       20
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       5
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,       10
adde the stature of thyn heyghte to thyn eye.

[ 226a ]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       5
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       10
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.       15
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,       20
and adde to-gedere un-to thy rote; and thus to make rotes; and
[ 227a ]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       25
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       30
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       35
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       40
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.       5
[ 228a ]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       10
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       15
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       20
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,       25
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       30
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       35
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
[ 229a ]with-drawe alle the nethere signes and degrees fro the signes and       40
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       5
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       10
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       15
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       20
[ 230a ]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       25
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       30
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       5
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       5
[ 231a ]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       5
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       10
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       5
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;       10
[ 232a ]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       5
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.       10