Supplementary Propositions
41. ~ Rub Umbra Recta. ~
Yif it so be that thou wilt werke by umbra
recta, and thou may come to the bas of the
tour, in this maner shalt thou werke. Tak the
altitude of the tour by bothe holes, so that
15 thy rewle ligge even in a poynt. Ensample as
thus: I see him thorw at the poynt of 4; than
mete I the space betwixe me and the tour,
and I finde it 20 foot; than beholde I how 4
is to 12, right so is the space betwixe thee
110 and the tour to the altitude of the tour.
For 4 is the thridde part of 12, so is the
space between thee and the tour the thridde
part of the altitude of the tour; than thryes 20
foot is the heyghte of the tour, with adding of
115 thyn owne persone to thyn eye. And this rewle
is general in umbra recta, fro the poynt of
oon to 12. And yif thy rewle falle upon 5, than
is 5 12-partyes of the heyght the space between
thee and the tour; with adding of
120 thyn owne heyghte.
42. ~ 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
15 go I neer to the tour, and I see him thorw at
the poynt of 2, and there I sette another prikke;
and I beholde how 1 hath him to 12, and ther
finde I that it hath him twelfe sythes; than
beholde I how 2 hath him to 12, and thou
110 shalt finde it sexe sythes; than thou shalt
finde that 12 passith 6 by the numbre of
6; right so is the space between thy two prikkes
the space of 6 tymes thyn altitude. And note,
that at the ferste altitude of 1, thou settest a
115 prikke; and afterward, whan thou seest him at
2, ther thou settest another prikke; than thou
findest betwyx thes two prikkys 60 foot; than
thou shalt finde that 10 is the 6-party of 60.
And then is 10 feet the altitude of the tour.
120 For other poyntis, yif it fille in umbra versa,
as thus: I sette caas it fill upon 2, and at
the secunde upon 3; than schalt thou finde
that 2 is 6 partyes of 12; and 3 is 4 partyes of
12; than passeth 6 4, by nombre of 2; so is the
125 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.
43. ~ 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
5 altitude, and set at thy foot a prikke. Than
set thy rewle upon 2, and behold what is the
differense between 1 and 2, and thou shalt
finde that it is 1. Than mete the space between
two prikkes, and that is the 12 partie
10 of the altitude of the tour. And yif ther
were 2, it were the 6 partye; and yif ther
were 3, the 4 partye; et sic deinceps. And
note, yif it were 5, it were the 5 party of 12;
and 7, 7 party of 12; and note, at the altitude
15 of thy conclusion, adde the stature of thyn
heyghte to thyn eye.
44. ~ Another maner conclusion, to knowe
the mene mote and the argumentis of any
planete. To know the mene mote and the argumentis
of every planete fro 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
5 meridie of December; and than consider the
yer of oure Lord, what is the date, and behold
whether thy date be more or lasse than the
yer 1397. And yf hit so be that hit be more,
loke how many yeres hit passeth, and with
10 so many enter into thy tables in the first
lyne theras is writen anni collecti et expansi.
And loke where the same planet is
writen in the hed of thy table, and than loke
what thou findest in direct of the same yer of
15 oure Lord which is passid, be hit 8, or 9, or
10, or what nombre that evere it be, til the
tyme that thou come to 20, or 40, or 60. And
that thou findest in direct wryt in thy slate under
thy rote, and adde hit togeder, and that is
20 thy mene mote, for the laste meridian of
the December, for the same yer which that
thou hast purposed. And if hit so be that hit
passe 20, consider wel that fro 1 to 20 ben
anni expansi, and fro 20 to 3000 ben anni collecti;
25 and if thy nomber passe 20, than tak that
thou findest in direct of 20, and if hit be more,
as 6 or 18, than tak that thou findest in direct
thereof, that is to sayen, signes, degrees, minutes,
and secoundes, and adde togedere
30 unto thy rote; and thus to make rotes. And
note, that if hit so be that the yer of oure
Lord be lasse than the rote, which is the yer
of oure Lord 1397, than shalt thou wryte in
the same wyse first thy rote in thy slate, and
35 after enter into thy table in the same yer that
be lasse, as I taught before; and than consider
how many signes, degrees, minutes, and secoundes
thyn entringe conteyneth. And so be
that ther be 2 entrees, than adde hem togeder,
40 and after withdraw hem from the
rote, the yer of oure Lord 1397; and the
residue that leveth is thy mene mote for the
laste meridie of December, the whiche thou
hast purposid; and if hit so be that thou wolt
45 witen thy mene mote for any day, or for any
fraccioun of day, in this maner thou shalt
worche. Make thy rote fro the laste day of
December in the maner as I have taught,
and afterward behold how many monethes,
50 dayes, and houres ben passid from the
meridie of December, and with that enter
with the laste moneth that is ful passed, and
take that thou findest in direct of him, and
wryt hit in thy slate; and enter with as mony
55 dayes as be more, and wryt that thou findest
in direct of the same planete that thou worchest
for; and in the same wyse in the table of
houres, for houres that ben passed, and adde
alle these to thy rote; and the residue is the
60 mene mote for the same day and the same
houre.
45. ~ 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
5 date, wryt that date, and than wryt the nomber
of the yeres. Than withdraw the yeres
out of the yeres that ben passed that rote.
Ensampul as thus: the yer of oure Lord 1400,
I wolde wyten, precise, my rote; than wrot
10 I first 1400. And under that nomber I
wrot a 1397; than withdrow I the laste
nomber out of that, and than fond I the residue
was 3 yer; I wiste that 3 yer was passed
fro the rote, the which was writen in my
15 tables. Than afterward soghte I in my tables
the annis collectis et expansis, and among myn
expanse yeres fond I 3 yeer. Than tok I alle
the signes, degrees, and minutes, that I fond
direct under the same planete that I
20 wroghte for, and wrot so many signes,
degrees, and minutes in my slate, and afterward
added I to signes, degrees, minutes, and
secoundes, the whiche I fond in my rote the
yer of oure Lord 1397; and kepte the residue;
25 and than had I the mene mote for the laste
day of December. And if thou woldest wete
the mene mote of any planete in March, April,
or May, other in any other tyme or moneth of
the yer, loke how many monethes and
30 dayes ben passed from the laste day of December,
the yer of oure Lord 1400; and so
with monethis and dayes enter into thy table
ther thou findest thy mene mote iwriten in
monethes and dayes, and tak alle the signes,
35 degrees, minutes, and secoundes that thou findest
ywrite in direct of thy monethes, and adde
to signes, degrees, minutes, and secoundes that
thou findest with thy rote the yer of oure
Lord 1400, and the residue that leveth is the
40 mene mote for that same day. And note,
if hit so be that thou woldest wite the mene
mote in any yer that is lasse than thy rote,
withdraw the nomber of so many yeres as hit
is lasse than the yer of oure Lord a 1397, and
45 kep the residue; and so many yeres, monethes,
and dayes enter into thy tables of thy mene
mote. And tak alle the signes, degrees, and
minutes, and secoundes, that thou findest in
direct of alle the yeres, monethes, and
50 dayes, and wryt hem in thy slate; and
above thilke nomber wryt the signes, degrees,
minutes, and secoundes, the which thou
findest with thy rote the yer of oure Lord a
1397; and withdraw alle the nethere signes
55 and degrees fro the signes and degrees, minutes,
and secoundes of other signes with thy
rote; and thy residue that leveth is thy mene
mote for that day.
46. ~ For to knowe at what houre of the day,
or of the night, shal be 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
5 thou redily in what degree of the zodiak that
the mone at that tyme is ynne. Bring furth
than the label, and set the point therof in
that same cost that the mone makith flod, and
set thou there the degree of the mone according
10 with the egge of the label. Than
afterward awayte where is than the degree
of the sonne, at that tyme. Remeve thou than
the label fro the mone, and bring and set it
justly upon the degree of the sonne. And the
15 point of the label shal than declare to thee, at
what houre of the day or of the night shal
be flod. And there also maist thou wite by the
same point of the label, whethir it be, at that
same tyme, flod or ebbe, or half flod, or
20 quarter flod, or ebbe, or half or quarter
ebbe; or ellis at what houre it was last, or
shal be next by night or by day, thou than
shalt esely knowe, &c. Furthermore, if it so
be that thou happe to worke for this matere
25 aboute the tyme of the conjunccioun, bring
furth the degree of the mone with the label
to that coste as it is before seyd. But than thou
shalt understonde that thou may not bringe
furth the label fro the degree of the mone
30 as thou dide before; for-why the sonne is
than in the same degree with the mone.
And so thou may at that tyme by the point of
the label unremevid knowe the houre of the
flod or of the ebbe, as it is before seyd, &c.
35 And evermore as thou findest the mone passe
fro the sonne, so remeve thou the label than
fro the degree of the mone, and bring it to
the degree of the sonne. And work thou than
as thou dide before, &c. Or ellis know
40 thou what houre it is that thou art inne,
by thyn instrument. Than bring thou furth
fro thennes the label and ley it upon the degree
of the mone, and therby may thou wite
also whan it was flod, or whan it wol be next,
45 be it night or day; &c.
