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HE CONCLUSIOUN, TO KNOWE YIF THAT ANY
 PLANETE BE DIRECTE OR RETROGRADE.

 [HEC CONCLUSIO OPERATUR AD COGNOSCENDUM SI ALIQUA PLANETA SIT DIRECTA VEL
 RETROGRADA.]

 Tak the altitude of any sterre that is cleped a planete, and note
 it wel. And tak eek anon the altitude of any sterre fix that thou
 knowest, and note it wel also. Come thanne agayn the thridde or
 the ferthe night next folwing; for thanne shaltow aperceyve wel the
 moeving of a planete, whether so he moeve forthward or bakward. 5
 Awaite wel thanne whan that thy sterre fix is in the same altitude that
 she was whan thou toke hir firste altitude; and tak than eftsones
 the altitude of the forseide planete, and note it wel. For trust
 wel, yif so be that the planete be on the right syde of the meridional
 lyne, so that his seconde altitude be lasse than his firste altitude 10
 was, thanne is the planete directe. And yif he be on the west
 syde in that condicion, thanne is he retrograd. And yif so be
 that this planete be up-on the est syde whan his altitude is taken,
 so that his secounde altitude be more than his firste altitude,
 thanne is he retrograde, and yif he be on the west syde, than is he 15
 directe. But the contrarie of thise parties is of the cours of the
 mone; for sothly, the mone moeveth the contrarie from othere
 planetes as in hir episicle, but in non other manere. And for
 the more declaracioun, lo here thy figure.

 36. THE CONCLUSIOUNS OF EQUACIOUNS OF HOUSES, AFTER THE ASTROLABIE, &C.

 [CONCLUSIO DE EQUACIONE DOMORUM.]

 Set the by-ginning of the degree that assendeth up-on the ende
 of the 8 houre inequal; thanne wol the by-ginning of the 2 hous
 sitte up-on the lyne of midnight. Remove thanne the degree that
 assendeth, and set him on the ende of the 10 hour inequal; and
 thanne wol the byginning of the 3 hous sitte up-on the midnight 5
 lyne. Bring up agayn the same degree that assendeth first, and
 set him up-on the orisonte; and thanne wol the be-ginning of the
 4 hous sitte up-on the lyne of midnight. Tak thanne the nadir of
 the degree that first assendeth, and set him on the ende of the 2
 houre inequal; and thanne wol the by-ginning of the 5 hous sitte 10
 up-on the lyne of midnight; set thanne the nadir of the assendent
 on the ende of the 4 houre, than wol the byginning of the 6 house
 sitte on the midnight lyne. The byginning of the 7 hous is nadir
 of the assendent, and the byginning of the 8 hous is nadir of the
 2; and the by-ginning of the 9 hous is nadir of the 3; and the 15
 by-ginning of the 10 hous is the nadir of the 4; and the byginning
 of the 11 hous is nadir of the 5; and the byginning of the 12 hous
 is nadir of the 6. And for the more declaracion, lo here the
 figure.

 37. A-NOTHER MANERE OF EQUACIOUNS OF HOUSES BY THE ASTROLABIE.

 [DE ALIQUA FORMA EQUACIONIS DOMORUM SECUNDUM ASTROLABIUM.]

 Tak thyn assendent, and thanne hastow thy 4 angles; for wel
 thou wost that the opposit of thyn assendent, that is to seyn, thy
 by-ginning of the 7 hous, sit up-on the west orizonte; and the
 byginning of the 10 hous sit up-on the lyne meridional; and his
 opposit up-on the lyne of midnight. Thanne ley thy label over 5
 the degree that assendeth, and rekne fro the point of thy label
 alle the degrees in the bordure, til thou come to the meridional
 lyne; and departe alle thilke degrees in 3 evene parties, and take
 the evene equacion of 3; for ley thy label over everich of 3 parties,
 and than maistow see by thy label in which degree of the zodiak is 10
 the by-ginning of everich of thise same houses fro the assendent:
 that is to seyn, the beginning of the 12 house next above thyn
 assendent; and thanne the beginning of the 11 house; and
 thanne the 10, up-on the meridional lyne; as I first seide. The
 same wyse wirke thou fro the assendent doun to the lyne of 15
 midnight; and thanne thus hastow other 3 houses, that is to seyn,
 the byginning of the 2, and the 3, and the 4 houses; thanne is
 the nadir of thise 3 houses the by-ginning of the 3 houses that
 folwen. And for the more declaracioun, lo here thy figure.

 38. TO FINDE THE LYNE MERYDIONAL TO DWELLE FIX IN ANY CERTEIN PLACE.

 [AD INVENIENDUM LINEAM MERIDIONALEM PER SUBTILES OPERACIONES.]

 Tak a rond plate of metal; for warping, the brodere the bettre;
 and make ther-upon a iust compas, a lite with-in the bordure; and
 ley this ronde plate up-on an evene grond, or on an evene ston, or
 on an evene stok fix in the gronde; and ley it even by a level.
 And in centre of the compas stike an evene pin or a wyr upright; 5
 the smallere the betere. Set thy pin by a plom-rewle evene
 upright; and let this pin be no lengere than a quarter of the
 diametre of thy compas, fro the centre. And waite bisily, aboute
 10 or 11 of the clokke and whan the sonne shyneth, whan the
 shadwe of the pin entreth any-thing with-in the cercle of thy plate 10
 an heer-mele, and mark ther a prikke with inke. Abyde thanne
 stille waiting on the sonne after 1 of the clokke, til that the
 schadwe of the wyr or of the pin passe ony-thing out of the cercle
 of the compas, be it never so lyte; and set ther a-nother prikke
 of inke. Take than a compas, and mesure evene the middel 15
 by-twixe bothe prikkes; and set ther a prikke. Take thanne
 a rewle, and draw a stryke, evene a-lyne fro the pin un-to the
 middel prikke; and tak ther thy lyne meridional for evere-mo, as
 in that same place. And yif thow drawe a cros-lyne over-thwart
 the compas, iustly over the lyne meridional, than hastow est and 20
 west and south; and, par consequence, than the nadir of the
 south lyne is the north lyne. And for more declaracioun, lo here
 thy figure.

 39. DESCRIPCION OF THE MERIDIONAL LYNE, OF LONGITUDES, AND LATITUDES OF
 CITEES AND TOWNES FROM ON TO A-NOTHER OF CLYMATZ.

 This lyne meridional is but a maner descripcion of lyne
 imagined, that passeth upon the poles of this world and by
 the senith of oure heved. And hit is y-cleped the lyne meridional;
 for in what place that any maner man is at any tyme of the yeer,
 whan that the sonne by moeving of the firmament cometh to his 5
 verrey meridian place, than is hit verrey midday, that we clepen
 oure noon, as to thilke man; and therfore is it cleped the lyne of
 midday. And _nota_, for evermo, of 2 citees or of 2 tounes, of
 whiche that o toun aprocheth more toward the est than doth
 that other toun, truste wel that thilke tounes ban diverse meridians. 10
 _Nota_ also, that the arch of the equinoxial, that is conteyned
 or bounded by-twixe the 2 meridians, is cleped the longitude
 of the toun. And yif so be that two tounes have y-lyke
 meridian, or oon meridian, than is the distance of hem bothe y-lyke
 fer fro the est; and the contrarie. And in this manere they 15
 chaunge nat her meridian, but sothly they chaungen her almikanteras;
 for the enhausing of the pool and the distance of the
 sonne. The longitude of a clymat is a lyne imagined fro est to
 west, y-lyke distant by-twene them alle. The latitu
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