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de 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
 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

 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.

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
 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

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