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 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.

 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
 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
 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
 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 flo

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