SUPPLEMENTARY PROPOSITIONS
Umbra Recta.-->
Yif it so be that thou wilt werke by umbra
recta-->, and
thou may come to the bas of the tour, in this maner shalt thou
werke. Tak the altitude of the tour by bothe holes, so that thy
rewle ligge even in a poynt. Ensample as thus: I see him thorw
at the poynt of 4; than mete I the space betwixe me and the tour,
and I finde it 20 foot; than beholde I how 4 is to 12, right so
is the space betwixe thee and the tour to the altitude of the
tour. For 4 is the thridde part of 12, so is the space between
thee and the tour the thridde part of the altitude of the tour;
than thryes 20 foot is the heyghte of the tour, with adding of
thyn owne persone to thyn eye. And this rewle is general in
umbra recta-->, fro the poynt of oon to 12. And yif thy
rewle falle upon 5, than is 5 12-partyes of the heyght the space
between thee and the tour; with adding of thyn owne heyghte.
Umbra Versa.-->
Another maner of the werkinge, by umbra versa-->. Yif so
be that thou may nat come to the bas of the tour, I see him thorw
at the nombre of 1; I sette ther a prikke at my fot; than go I
neer to the tour, and I see him thorw at the poynt of 2, and
there I sette another prikke; and I beholde how 1 hath him to 12,
and ther finde I that it hath him twelfe sythes; than beholde I
how 2 hath him to 12, and thou shalt finde it sexe sythes; than
thou shalt finde that 12 passith 6 by the numbre of 6; right so
is the space between thy two prikkes the space of 6 tymes thyn
altitude. And note, that at the ferste altitude of 1, thou
settest a prikke; and afterward, whan thou seest him at 2, ther
thou settest another prikke; than thou findest betwyx thes two
prikkys 60 foot; than thou shalt finde that 10 is the 6-party of
60. And then is 10 feet the altitude of the tour. For other
poyntis, yif it fille in umbra versa-->, as thus: I sette
caas it fill upon 2, and at the secunde upon 3; than schalt thou
finde that 2 is 6 partyes of 12; and 3 is 4 partyes of 12; than
passeth 6 4, by nombre of 2; so is the space between two prikkes
twyes the heyghte of the tour. And yif the differens were thryes,
than shulde it be three tymes; and thus mayst
thou werke fro 1 to 12; and yif it be 4, 4 tymes; or 5, 5 tymes;
et sic de ceteris-->.
Umbra Recta.-->
Another maner of wyrking, by umbra recta-->:
Yif it so be that thou mayst nat come to the baas of the tour, in this
maner thou schalt werke. Set thy rewle upon 1 till thou see the
altitude, and set at thy foot a prikke. Than set thy rewle upon
2, and behold what is the differense between 1 and 2, and thou
shalt finde that it is 1. Than mete the space between two
prikkes, and that is the 12 partie of the altitude of the tour.
And yif ther were 2, it were the 6 partye; and yif ther were 3,
the 4 partye; et sic deinceps. And note, yif it were 5,
it were the 5 party of 12; and 7, 7 party of 12; and note, at the
altitude of thy conclusion, adde the stature of thyn heyghte to
thyn eye.
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 yeer to yeer, from day to day,
from houre to houre, and from smale fraccionis infinite.
In this maner shalt thou worche; consider thy rote first, the
whiche is made the beginning of the tables fro the yer of oure
Lord 1397, and enter hit into thy slate for the laste meridie of
December; and than consider the yer of oure Lord, what is the
date, and behold whether thy date be more or lasse than the yer
1397. And yf hit so be that hit he more, loke how many yeres hit
passeth, and with so many enter into thy tables in the first lyne
theras is writen anni collecti et expansi-->. And loke where
the same planet is writen in the hed of thy table, and than loke
what thou findest in direct of the same yer of oure Lord which
is passid, he hit 8, or 9, or 10, or what nombre that evere it
be, til the tyme that thou come to 20, or 40, or 60. And that
thou findest in direct wryt in thy slate under thy rote, and adde
hit togeder, and that is thy mene mote, for the laste meridian
of the December, for the same yer which that thou hast purposed.
And if hit so he that hit passe 20, consider wel that fro 1 to
20 ben anni expansi-->, and fro 20 to
3000 ben
anni collecti-->; and if thy nomber passe 20,
than tak that thou findest in direct of 20, and if hit he more, as 6 or 18, than tak
that thou findest in direct thereof, that is to sayen, signes,
degrees, minutes, and secoundes, and adde togedere unto thy rote;
and thus to make rotes. And note, that if hit so be that the yer
of oure Lord be lasse than the rote, which is the yer of oure
Lord 1397, than shalt thou wryte in the same wyse first thy rote
in thy slate, and after enter into thy table in the same yer that
be lasse, as I taught before; and than consider how many signes,
degrees, minutes, and secoundes thyn entringe conteyneth. And so
be that ther be 2 entrees, than adde hem togeder, and after
withdraw hem from the rote, the yer of oure Lord 1397; and the
residue that leveth is thy mene mote for the laste meridie of
December, the whiche thou hast purposid; and if hit so he that
thou wolt witen thy mene mote for any day, or for any fraccioun
of day, in this maner thou shalt worche. Make thy rote fro the
laste day of December in the maner as I have taught, and
afterward behold how many monethes, dayes, and houres ben passid
from the meridie of December, and with that enter with the laste
moneth that is ful passed, and take that thou findest in direct
of him, and wryt hit in thy slate; and enter with as mony dayes
as be more, and wryt that thou findest in direct of the same
planete that thou worchest for; and in the same wyse in the table
of houres, for houres that ben passed, and adde alle these to thy
rote; and the residue is the mene mote for the same day and the
same houre.
Another manere to knowe the mene mote.
Whan thou wolt make the mene mote of eny planete to be by
Arsechieles tables, tak thy rote, the which is for the yer of
oure Lord 1397; and if so be that thy yer be passid the date,
wryt that date, and than wryt the nomber of the yeres. Than
withdraw the yeres
out of the yeres that ben passed
that rote. Ensampul as thus: the yer of oure Lord 1400, I wolde
wyten, precise, my rote; than wrot I first 1400. And under that
nomber I wrot a 1397; than withdrow I the laste nomber out of
that, and than fond I the residue was 3 yer; I wiste that 3 yer
was passed fro the rote, the which was writen in my tables. Than
afterward soghte I in my tables the
annis
collectis et expansis-->, and among myn expanse yeres fond I 3 yeer. Than tok
I alle the signes, degrees, and minutes, that I fond direct under
the same planete that I wroghte for, and wrot so many signes,
degrees, and minutes in my slate, and afterward added I to
signes, degrees, minutes, and secoundes, the whiche I fond in my
rote the yer of oure Lord 1397; and kepte the residue; and than
had I the mene mote for the laste day of December. And if thou
woldest wete the mene mote of any planete in March, April, or
May, other in any other tyme or moneth of the yer, loke how many
monethes and dayes ben passed from the laste day of December, the
yer of oure Lord 1400; and so with monethis and dayes enter into
thy table ther thou findest thy mene mote iwriten in monethes and
dayes, and tak alle the signes, degrees, minutes, and secoundes
that thou findest ywrite in direct of thy monethes, and adde to
signes, degrees, minutes, and secoundes that thou findest with
thy rote the yer of oure Lord 1400, and the residue that leveth
is the mene mote for that same day. And note, if hit so he that
thou woldest wite the mene mote in any yer that is lasse than thy
rote, withdraw the nomber of so many yeres as hit is lasse than
the yer of oure Lord a 1397, and kep the residue; and so many
yeres, monethes, and dayes enter into thy tables of thy mene
mote. And tak alle the signes, degrees, and minutes, and
secoundes, that thou findest in direct of alle the yeres,
monethes, and dayes, and wryt hem in thy slate; and so above
thilke nomber wryt the signes, degrees, minutes, and secoundes,
the which thou findest with thy rote the yer of oure Lord a 1397;
and withdraw alle the nethere signes and degrees fro the signes
and degrees, minutes, and secoundes of other signes with thy
rote; and thy residue that leveth is thy mene mote for that
day.
For to knowe at what houre of the day, or of the night,
shal be flod or ebbe.
First wite thou certeinly, hou that haven stondeth, that thou
list to werke for; that is to say in which place of the firmament
the mone beyng, makith full see. Than awayte thou redily in what
degree of the zodiak that the mone at that tyme is ynne. Bring
furth than the label, and set the point therof in that same cost
that the mone makith flod, and set thou there the degree of the
mone according with the egge of the label. Than afterward awayte
where is than the degree of the sonne, at that tyme. Remeve thou
than the label fro the mone, and bring and set it justly upon the
degree of the sonne. And the point of the label shal than declare
to thee, at what houre of the day or of the night shal be flod.
And there also maist thou wite by the same point of the label,
whethir it be, at that same tyme, flod or ebbe, or half flod, or
quarter flod, or ebbe, or half or quarter ebbe; or ellis at what
houre it was last, or shal be next by night or by day, thou than
shalt esely knowe, &c. Furthermore, if it so be that thou happe
to worke for this matere aboute the tyme of the conjunccioun,
bring furth the degree of the mone with the label to that coste
as it is before seyd. But than thou shalt understonde that thou
may not bringe furth the label fro the degree of the mone as thou
dide before; for-why the sonne is than in the same degree with
the mone. And so thou may at that tyme by the point of the label
unremevid knowe the houre of the flod or of the ebbe, as it is
before seyd, &c. And evermore as thou findest the mone passe
fro the sonne, so remeve thou the label than fro the degree of
the mone, and bring it to the degree of the sonne. And work thou
than as thou dide before, &c. Or ellis know thou what houre it
is that thou art inne, by thyn instrument. Than bring thou furth
fro thennes the label and ley it upon the degree of the mone, and
therby may thou wite also whan it was flod, or whan it wol be
next, be it night or day; &c.
