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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
 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
 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
 _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
 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

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