|b{A_TREATISE_ON_THE_ASTROLABE;_in}
|b{The_Complete_Works_of_Geoffrey_Chaucer}
|b{ed._Walter_W._Skeat,_2nd_ed.,_vol._3}
|b{Oxford:_Clarendon_Press,_1900,}
|b{pp._175-232.}



|p175


|r[A_TREATISE_ON_THE_ASTROLABE]

PROLOGUE.

|r<b> LITELL Lowis my sone, I have perceived wel by certeyne
          evidences thyn abilite to lerne sciencez touchinge noum_bres 
     and proporciouns, and as wel considere I thy bisy preyere in
     special to lerne the Tretis of the Astrolabie. Than, for as mechel
   5 as a philosofre seith, `he wrappeth him in his frend, that con_descendeth
     to the rightful preyers of his frend,' ther-for have I
     geven thee a suffisaunt Astrolabie as for oure orizonte, compowned
     after the latitude of Oxenford; up-on which, by mediacion of this
     litel tretis, I purpose to teche thee a certein nombre of conclusions,
  10 apertening to the same instrument. I seye a certein of conclusiouns,
     for three causes. The furste cause is this: truste wel that alle the
     conclusiouns that han ben founde, or elles possibly mighten be
     founde in so noble an instrument as an Astrolabie, ben un knowe
     perfitly to any mortal man in this regioun, as I suppose. A-nother
  15 cause is this; that sothly, in any tretis of the Astrolabie that I have
     seyn, there ben some conclusions that wole nat in alle thinges
     performen hir bihestes; and some of hem ben to harde to thy
     tendre age of ten yeer to conseyve. This tretis, divided in fyve



|p176


     parties, wole I shewe thee under ful lighte rewles and naked
  20 wordes in English; for Latin ne canstow yit but smal, my lyte
     sone. But natheles, suffyse to thee thise trewe conclusiouns in
     English, as wel as suffyseth to thise noble clerkes Grekes thise same
     conclusiouns in Greek, and to Arabiens in Arabik; and to Iewes in
     Ebrew, and to the Latin folk in Latin, whiche Latin folk han hem
  25 furst out of othre diverse langages, and writen in hir owne tonge,
     that is to sein, in Latin. And god wot, that in alle thise langages,
     and in many mo, han thise conclusiouns ben suffisantly lerned and
     taught, and yit by diverse rewles, right as diverse pathes leden
     diverse folk the righte wey to Rome. Now wol I prey meekly
  30 every discret persone that redeth or hereth this litel tretis, to have
     my rewde endyting for excused, and my superfluite of wordes, for
     two causes. The firste cause is, for that curious endyting and hard
     sentence is ful hevy atones for swich a child to lerne. And the
     seconde cause is this, that sothly me semeth betre to wryten un-to
  35 a child twyes a good sentence, than he for-gete it ones. And
     Lowis, yif so be that I shewe thee in my lighte English as trewe
     conclusiouns touching this matere, and naught only as trewe but
     as many and as subtil conclusiouns as ben shewed in Latin in any
     commune tretis of the Astrolabie, con me the more thank; and
  40 preye god save the king, that is lord of this langage, and alle that
     him feyth bereth and obeyeth, everech in his degree, the more and
     the lasse. But considere wel, that I ne usurpe nat to have founde
     this werk of my labour or of myn engin. I nam but a lewd com_pilatour 
     of the labour of olde Astrologiens, and have hit translated
  45 in myn English only for thy doctrine; and with this swerd shal I
     sleen envye.
       I. The firste partie of this tretis shal reherse the figures and the
     membres of thyn Astrolabie, bi-cause that thou shalt han the
     grettre knowing of thyn owne instrument.



|p177


       II. The second partie shal teche thee werken the verrey
     practik of the forseide conclusiouns, as ferforth and as narwe
     as may be shewed in so smal an instrument portatif aboute.
     For wel wot every astrologien that smalest fraccions ne wol
     nat ben shewed in so smal an instrument, as in subtil tables
  55 calculed for a cause.
       III. The thridde partie shal contienen diverse tables of
     longitudes and latitudes of sterres fixe for the Astrolabie, and
     tables of declinacions of the sonne, and tables of longitudes
     of citeez and of townes; and as wel for the governance of a
  60 clokke as for to finde the altitude meridian; and many another
     notable conclusioun, after the kalendres  of the reverent clerkes,
     frere I. Somer and frere N. Lenne.
       IV. The ferthe partie shal ben a theorik to declare the
     moevinge of the celestial bodies with the causes. The whiche 
  65 ferthe partie in special shal shewen a table of the verray
     moeving of the mone from houre to houre, every day and in
     every signe, after thyn almenak; upon which table ther folwith
     a canon, suffisant to teche as wel the maner of the wyrking of
     that same conclusioun, as to knowe in oure orizonte with which
  70 degree of the zodiac that the mone ariseth in any latitude;
     and the arising of any planete after his latitude fro the ecliptik
     lyne.
       V. The fifte partie shal ben an introductorie after the statutz
     of oure doctours, in which thou maist lerne a gret part of the
  75 general rewles of theorik in astrologie. In which fifte partie
     shaltow finde tables of equacions of houses aftur the latitude of
     Oxenford; and tables of dignetes of planetes, and other noteful
     thinges, yif god wol vouche-sauf and his modur the mayde, mo
     than I be-hete, &c.



|p178


     PART I.

     HERE BIGINNETH THE DESCRIPCION OF THE ASTROLABIE.

       l. Thyn Astrolabie hath a ring to putten on the thoumbe of
     thy right hand in taking the heighte of thinges. And tak keep, for
     from hennes-forthward, I wol clepe the heighte of any thing that
     is taken by thy rewle, the altitude, with-oute mo wordes.
       2. This ring renneth in a maner turet, fast to the moder of
     thyn Astrolabie, in so rowm a space that hit desturbeth nat the
     instrument to hangen after his righte centre.
       3. The Moder of thyn Astrolabie is the thikkeste plate, perced
     with a large hole, that resseyveth in hir wombe the thinne plates
     compowned for diverse clymatz, and thy riet shapen in manere
     of a net or of a webbe of a loppe; and for the more declaracioun,
   5 lo here the figure.
       4. This moder is devyded on the bak-half with a lyne, that
     cometh dessendinge fro the ring down to the nethereste bordure.
     The whiche lyne, fro the for-seide ring un-to the centre of the
     large hole amidde, is cleped the south lyne, or elles the lyne
   5 meridionaI. And the remenant of this lyne downe to the bordure
     is cleped the north lyne, or elles the lyne of midnight. And for
     the more declaracioun, lo here the figure.



|p179


       5. Over-thwart this for-seide longe lyne, ther crosseth him
     another lyne of the same lengthe from est to west. Of the
     whiche lyne, from a litel croys + in the bordure un-to the centre
     of the large hole, is cleped the Est lyne, or elles the lyne Orientale;
   5 and the remenant of this lyne fro the forseide + un-to the bordure,
     is cleped the West lyne, or the lyne Occidentale. Now hastow
     here the foure quarters of thin Astrolabie, devyded after the foure
     principals plages or quarters of the firmament. And for the more.
     declaracioun, lo here thy figure.
       6. The est side of thyn Astrolabie is cleped the right side, and
     the west side is cleped the left side. Forget nat this, litel Lowis.
     Put the ring of thyn Astrolabie upon the thoumbe of thy right
     hand, and thanne wole his right syde be toward thy left syde, and
   5 his left syde wol be toward thy right syde; tak this rewle general,
     as wel on the bak as on the wombe-side. Upon the ende of this
     est lyne, as I first seide, is marked a litel +, wher-as evere-mo
     generaly is considered the entring of the first degree in which the
     sonne aryseth. And for the more declaracioun; lo here the
  10 figure.
       7. Fro this litel + up to the ende of the lyne meridional, under
     the ring, shaltow finden the bordure devyded with 90 degrees;
     and by that same proporcioun is every quarter of thin Astrolabie
     devyded. Over the whiche degrees ther ben noumbres of augrim,
   5 that devyden thilke same degrees fro fyve to fyve, as sheweth by
     longe strykes by-twene. Of whiche longe strykes the space by_twene 
     contienith a mile-wey. And every degree of the bordure
     contieneth foure minutes, that is to seyn, minutes of an houre.
     And for more declaracioun, lo here the figure.
       8. Under the compas of thilke degrees ben writen the names of
     the Twelve Signes, as Aries, Taurus, Gemini, Cancer, Leo, Virgo,



|p180


     Libra, Scorpio, Sagittarius, Capricornus, Aquarius, Pisces; and
     the nombres of the degrees of tho signes ben writen in augrim
   5 above, and with longe devisiouns, fro fyve to fyve; devyded fro
     tyme that the signe entreth un-to the laste ende. But understond
     wel, that thise degrees of signes ben everich of hem considered
     of 60 minutes, and every minute of 60 secondes, and so
     forth in-to smale fraccions infinit, as seith Alkabucius. And
  10 ther-for, know wel, that a degree of the bordure contieneth foure
     minutes, and a degree of a signe contieneth 60 minutes, and
     have this in minde. And for the more declaracioun, lo here
     thy figure.
       9. Next this folweth the Cercle of the Dayes, that ben figured
     in maner of degrees, that contienen in noumbre 365; divyded
     also with longe strykes fro fyve to fyve, and the nombres in
     augrim writen under that cercle. And for more declaracioun, lo
   5 here thy figure.
       10. Next the Cerle of the Dayes, folweth the Cercle of the
     names of the Monthes; that is to seyen, Ianuare, Februare,
     Marcius, Aprile, Mayus, Iuin, Iulius, Augustus, Septembre,
     October, Novembre, Decembre. The names of thise monthes
   5 were cleped in Arabiens, somme for hir propretees, and some by
     statutz of lordes, some by other lordes of Rome. Eek of thise
     monthes, as lyked to Iulius Cesar and to Cesar Augustus, some
     were compowned of diverse nombres of dayes, as Iuil and
     August. Thanne hath Ianuare 31 dayes, Februare 28, March
  10 31, Aprille 30, May 31, Iunius 30, Iulius 31, Augustus 31,
     September 30, Octobre 31, Novembre 30, December 31.
     Natheles, al-though that Iulius Cesar took 2 dayes out of Feverer
     and put hem in his moneth of Iuille, and Augustus Cesar cleped 
     the moneth of August after his name, and ordeyned it of 31 dayes,



|p181


  15 yit truste wel, that the sonne dwelleth ther-for nevere the more ne
     lesse in oon signe than in another.
       ll. Than folwen the names of the Halidayes in the Kalender,
     and next hem the lettres of the Abc. on which they fallen. And
     for the more declaracioun, lo here thy figure.
       12. Next the forseide Cercle of the Abc., under the cros-lyne,
     is marked the scale, in maner of two squyres, or elles in manere
     of laddres, that serveth by hise 12 poyntes and his devisiouns of
     ful many a subtil conclusioun. Of this forseide scale, fro the
   5 croos-lyne un-to the verre angle, is cleped umbra versa, and the
     nether partie is cleped the umbra recta, or elles umbra extensa.
     And for the more declaracioun, lo here the figure.
       13. Thanne hastow a brood Rewle, that hath on either ende a
     square plate perced with a certein holes, some more and some
     lesse, to resseyven the stremes of the sonne by day, and eek
     by mediacioun of thyn eye, to knowe the altitude of sterres by
   5 nighte. And for the more declaracioun, lo here thy figure.
       14. Thanne is ther a large Pyn, in maner of an extree, that



|p182


     goth thorow the hole that halt the tables of the clymates and the
     riet in the wombe of the Moder, thorw which Pyn ther goth a
     litel wegge which that is cleped `the hors,' that streyneth alle
   5 thise parties to-hepe; this forseide grete Pyn, in maner of an
     extree, is imagined to be the Pol Artik in thyn Astrolabie.
     And for the more declaracioun, lo here the figure.
       l5. The wombe-side of thyn Astrolabie is also devyded with a
     longe croys in foure quarters from est to west, fro south to north,
     fro right syde to left syde, as is the bak-syde. And for the more
     declaracioun, lo here thy figure.
       16. The bordure of which wombe-side is devyded fro the poynt
     of the est lyne un-to the poynt of the south lyne under the ring,
     in 90 degres; and by that same proporcioun is every quarter
     devyded as is the bak-syde, that amonteth 360 degrees. And
  10 understond wel, that degrees of this bordure ben answering and
     consentrik to the degrees of the Equinoxial, that is devyded in
     the same nombre as every othere cercle is in the heye hevene.
     This same bordure is devyded also with 23 lettres capitals and a
     smal croys + above the south lyne, that sheweth the 24 houres
  10 equals of the clokke; and, as I have said, 5 of thise degrees
     maken a mile-wey, and 3 mile-wey maken an houre. And every
     degree of this bordure conteneth 4 minutes, and every minut 
     secondes; now have I told thee twye. And for the more
     declaracioun, lo here the figure.
       17. The plate under thy riet is descryved with 3 principal.



|p183


     cercles; of whiche the leste is cleped the cercle of Cancer, by_cause 
     that the heved of Cancer turneth evermor consentrik up-on
     the same cercle. In this heved of Cancer is the grettest declina_cioun 
   5 northward of the sonne. And ther-for is he cleped the
     Solsticioun of Somer, whiche declinacioun, aftur Ptholome, is 23
     degrees and 50 minutes, as wel in Cancer as in Capricorne. This
     signe of Cancre is cleped the Tropik of Somer, of tropos, that is
     to seyn `agaynward'; for thanne by-ginneth the sonne to passe
  10 fro us-ward. And for the more declaracioun, lo here the figure.
       The middel cercle in wydnesse, of thise 3, is cleped the Cercle
     Equinoxial; up-on whiche turneth evermo the hedes of Aries and
     Libra. And understond wel, that evermo this Cercle Equinoxial
     turneth iustly fro verrey est to verrey west, as I have shewed thee
  15 in the spere solide. This same cercle is cleped also the Weyere,
     equator, of the day; for whan the sonne is in the hevedes of
     Aries and Libra, than ben the dayes and the nightes ilyke of
     lengthe in al the world. And ther-fore ben thise two signes
     called the Equinoxies. And alle that moeveth with-in the
  20 hevedes of thise Aries and Libra, his moeving is cleped north_ward, 
     and alle that moeveth with-oute thise hevedes, his moeving



|p184


     is cleped south-ward as fro the equinoxial. Tak keep of thise
     latitudes north and sowth, and forget it nat. By this Cercle
     Equinoxial ben considered the 24 houres of the clokke; for
  25 everemo the arysing of 15 degrees of the equinoxial maketh an
     houre equal of the clokke. This equinoxial is cleped the girdel
     of the firste moeving, or elles of the angulus primi motus vel
     primi mobilis. And nota, that firste moeving is cleped `moeving'
     of the firste moevable of the 8 spere, whiche moeving is fro est to
  30 west, and eft agayn in-to est; also it is clepid `girdel' of the first
     moeving, for it departeth the firste moevable, that is to seyn, the
     spere, in two ilyke parties, evene-distantz fro the poles of this
     world.
       The wydeste of thise three principal cercles is cleped the
  35 Cercle of Capricorne, by-cause that the heved of Capricorne
     turneth evermo consentrik up-on the same cercle. In the heved
     of this for-seide Capricorne is the grettest declinacioun southward
     of the sonne, and ther-for is it cleped the Solsticioun of Winter.
     This signe of Capricorne is also cleped the Tropik of Winter, for
  40 thanne byginneth the sonne to come agayn to us-ward. And for
     the more declaracioun, lo here thy figure.
       18. Upon this forseide plate ben compassed certein cercles
     that highten Almicanteras, of which som of hem semen perfit
     cercles, and somme semen inperfit. The centre that standith
     a-middes the narwest cercle is cleped the Senith; and the
   5 netherest cercle, or the firste cercle, is clepid the Orisonte, that
     is to seyn, the cercle that devydeth the two emisperies, that is,
     the partie of the hevene a-bove the erthe and the partie be-nethe.
     Thise Almicanteras ben compowned by two and two, al-be-it so
     that on divers Astrolabies some Almicanteras ben devyded by oon,
  10 and some by two, and somme by three, after the quantite of the
     Astrolabie. This forseide senith is imagened to ben the verrey
     point over the crowne of thyn heved; and also this senith is the



|p185


     verrey pool of the orisonte in every regioun. And for the
     more declaracioun, lo here thy figure.
       19. From this senith, as it semeth, ther come a maner crokede
     strykes lyke to the clawes of a loppe, or elles like to the werk of a
     womanes calle, in kerving overthwart the Almikanteras. And
     thise same strykes or divisiouns ben cleped Azimuthz. And they
   5 devyden the orisonte of thyn Astrolabie in four and twenty
     devisiouns. And thise Azimutz serven to knowe the costes of the
     firmament, and to othre conclusiouns, as for to knowe the cenith
     of the sonne and of every sterre. And for more declaracioun, lo
     here thy figure.
       20. Next thise azimutz, under the Cercle of Cancer, ben ther
     twelve devisiouns embelif, moche like to the shap of the azimutes,
     that shewen the spaces of the houres of planetes; and for more
     declaracioun, lo here thy figure.
       21. The Riet of thyn Astrolabie with thy zodiak, shapen in
     maner of a net or of a loppe-webbe after the olde descripcioun,
     which thow mayst tornen up and doun as thy-self lyketh, conteneth
     certein nombre of sterres fixes, with hir longitudes and latitudes
   5 determinat; yif so be that the makere have nat erred. The names
     of the sterres ben writen in the margin of the riet ther as they sitte;
     of whiche sterres the smale poynt is cleped the Centre. And
     understond also that alle sterres sittinge with-in the zodiak of thyn
     Astrolabie ben cleped `sterres of the north,' for they arysen by
  10 northe the est lyne. And alle the remenant fixed, out of the
     zodiak, ben cleped `sterres of the south;' but I sey nat that they



|p186


     arysen alle by southe the est lyne; witnesse on Aldeberan and
     Algomeysa. Generally understond this rewle, that thilke sterres
     that ben cleped sterres of the north arysen rather than the degree
  15 of hir longitude, and alle the sterres of the south arysen after the
     degree of hir longitude; this is to seyn, sterres fixed in thyn
     Astrolabie. The mesure of this longitude of sterres is taken in the
     lyne ecliptik of hevene, under which lyne, whan that the sonne
     and the mone ben lyne-right or elles in the superfice of this lyne,
  20 than is the eclips of the sonne or of the mone; as I shal declare,
     and eek the cause why. But sothly the Ecliptik Lyne of thy
     zodiak is the outtereste bordure of thy zodiak, ther the degrees ben
     marked.
       Thy Zodiak of thyn Astrolabie is shapen as a compas which that
  25 conteneth a large brede, as after the quantite of thyn Asstrolabie;
     in ensample that the zodiak in hevene is imagened to ben a super_fice 
     contening a latitude of twelve degrees, wheras al the remenant
     of cercles in the hevene ben imagined verrey lynes with-oute eny
     latitude. Amiddes this celestial zodiak ys imagined a lyne, which
  30 that is cleped the Ecliptik Lyne, under which lyne is evermo the
     wey of the sonne. Thus ben ther six degrees of the zodiak on
     that on side of the lyne, and six degrees on that other. This
     zodiak is devided in twelve principal devisiouns, that departen the
     twelve signes. And, for the streitnes of thin Astrolabie, than is
  25 every smal devisioun in a signe departid by two degrees and two;
     I mene degrees contening sixty minutes. And this forseide
     hevenissh zodiak is cleped the Cercle of the Signes, or the Cercle
     of the Bestes; for zodia in langage of Greek sowneth `bestes' in
     Latin tonge; and in the zodiak ben the twelve signes that han
  40 names of bestes; or elles, for whan the sonne entreth in any of the
     signes, he taketh the propretee of swich bestes; or elles, for that
     the sterres that ben there fixed ben disposed in signes of bestes,
     or  shape like bestes; or elles, whan the planetes ben under thilke



|p187


     signes, they causen us by hir influence operaciouns and effectes
  45 lyk to the operaciouns of bestes. And understonde also, that whan
     an hot planete cometh in-to an hot signe, than encresseth his hete;
     and yif a planete be cold, thanne amenuseth his coldnesse, by-cause
     of the hote signe. And by this conclusioun maystow take ensample
     in alle the signes, be they moist or drye, or moeble or fix; reken_ing 
  50 the qualitee of the planete as I first seide. And everich of
     thise twelve signes hath respecte to a certein parcelle of the body
     of a man and hath it in governance; as Aries hath thyn heved, and
     Taurus thy nekke and thy throte, Gemini thyn armholes and thyn
     armes, and so forth, as shal be shewed more pleyn in the fifte
  55 partie of this tretis. This zodiak, which that is part of the eighte
     spere, over-kerveth the equinoxial; and he over-kerveth him again
     in evene parties, and that on half declineth southward, and that
     other northward, as pleynly declareth, the tretis of the spere. And
     for more declaracioun, lo here thy figure.
       22. Thanne hastow a label, that is schapen lyk a rewle, save that
     it is streit and hath no plates on either ende with holes; but, with
     the smale point of the forseide label, shaltow calcule thyne
     equaciouns in the bordure of thin Astrolabie, as by thyn almury.
   5 And for the more declaracioun, lo here thy figure.
       23. Thyn Almury is cleped the Denticle of Capricorne, or elles
     the Calculer. This same Almury sit fix in the hed of Capricorne,



|p188


     and it serveth of many a necessarie conclusioun in equaciouns of
     thinges, as shal be shewed, and for the more declaracion, lo here 
   5 thy figure.

     Here endeth the descripcion of the Astrolabie.

      PART II

      HERE BIGINNEN THE CONCLUSIONS OF THE ASTROLABIE.

     1. To fynde the degree in which the sonne is day by day,
      after hir cours a-boute.

     [Hic incipiunt Conclusiones Astrolabii; et prima est ad
     inveniendum gradus solis in quibus singulis diebus
     secundum cursum sol est existens.]

       Rekene and knowe which is the day of thy monthe; and ley
     thy rewle up, that same day, and thanne wol the verray point of
     thy rewle sitten in the bordure, up-on the degree of thy sonne.
     Ensample as thus; the yeer of oure lord 1391, the 12 day of
   5 March at midday, I wolde knowe the degree of the sonne. I
     soughte in the bak-half of myn Astrolabie, and fond the cercle of
     the dayes, the which I knowe by the names of the monthes writen
     under the same cercle. Tho leide I my rewle over this forseide
     day, and fond the point of my rewle in the bordure up-on the
  10 firste degree of Aries, a litel with-in the degree; and thus knowe
     I this conclusioun. Another day, I wolde knowe the degree of
     my sonne, and this was at midday in the 13 day of Decembre; I
     fond the day of the monthe in maner as I seide; tho leide I my
     rewle up-on this forseide 13 day, and fond the point of my rewle



|p189


  15 in the bordure up-on the first degree of Capricorne, a lite with-in
     the degree, and than hadde I of this conclusioun the ful
     experience. And for the more declaracioun, lo here thy figure.

     2. To kowe the altitude of the sonne, or of othre celestial
      bodies.

     [De altitudine solis et aliorum corporum supra celestium.]

       Put the ring of thyn Astrolabie up-on thy right thoumbe, and
     turne thy lift syde agayn the light of the sonne. And remeve
     thy rewle up and doun, til that the stremes of the sonne shyne
     thorgh bothe holes of thy rewle. Loke thanne how many degrees
   5 thy rewle is areised fro the litel crois up-on thyn est line, and tak
     ther the altitude of thy sonne. And in this same wyse maistow
     knowe by nighte the altitude of the mone, or of brighte sterres.
     This chapitre is so general ever in oon, that ther nedith no more
     declaracion; but forget it nat. And for the more declaracioun,
  10 lo here the figure.

     3. To knowe every tyme of the day by light of the sonne,
       and every tyme of the night by the sterres fixe, and eke
       to knowe by night or by day the degree of any signe that
       assendeth on the Est Orisonte, which that is cleped com_munly
       the Assendent, or elles Oruscupum.

     [Ad cognoscendum quodlibet tempus diei per solis indi_cacionem, 
       et quodlibet tempus noctis per quasdam stellas
       in celo fixas; ac eciam ad inveniendum et cognoscendum
       signum super orizontem qui communiter vocatur as_cendens.]
  

       Tak the altitude of the sonne whan thee list, as I have said; and
     set the degree of the sonne, in cas that it be by-forn the middel of
     the day, among thyn almikanteras on the est side of thyn
     Astrolabie; and yif it be after the middel of the day, set the degree



|p190


   5 of thy sonne up-on the west side; tak this manere of setting for a
     general rewle, ones for evere. And whan thou hast set the degree
     of thy sonne up as many almikanteras of heyghte as was the
     altitude of the sonne taken by thy rewle, ley over thy label, up-on
     the degree of the sonne; and thanne wol the point of thy label
  10 sitten in the bordure, up-on the verrey tyd of the day. Ensample
     as thus: the yeer of oure lord 1391, the 12 day of March, I wold
     knowe the tyd of the day. I took the altitude of my sonne, and
     fond that it was 25 degrees and 30 of minutes of heyghte in the
     bordure on the bak-syde. Tho turnede I myn Astrolabie, and by-
  15 cause that it was by-forn midday, I turnede my riet, and sette the
     degree of the sonne, that is to seyn, the I degree of Aries, on the
     right syde of myn Astrolabie, up-on that 25 degrees and 30 of
     minutes of heyghte among myn almikanteras; tho leide I my label
     up-on the degree of my sonne, and fond the poynte of my label in
  20 the bordure, up-on a capital lettre that is cleped an X; tho rekened
     I alle the capitalles lettres fro the lyne of midnight un-to this for_seide 
     lettre X, and fond that it was 9 of the clokke of the day.
     Tho loked I down up-on the est orisonte, and fond there the 
     degree of Geminis assending; which that I tok for myn assendent.
  25 And in this wyse hadde I the experience for ever-mo in which
     maner I sholde knowe the tyd of the day, and eek myn assen_dent.
     Tho wolde I wite the same night folwing the hour of the
     night, and wroughte in this wyse. Among an heep of sterris fixe,
     it, lyked me for to take the altitude of the feire white sterre that is
  30 cleped Alhabor; and fond hir sitting on the west side of the lyne
     of midday, 18 degres of heighte taken by my rewle on the bak-syde
     Tho sette I the centre of this Alhabor up-on 18 degrees among
     myn almikanteras, up-on the west syde; by-cause that she was



|p191


     founden on the west syde.Tho leide I my label over the degree
  35 of the sonne that was descended under the weste orisonte, and
     rikened alle the lettres capitals fro the lyne of midday un-to the
     point of my label in the bordure; and fond that it was passed 8 of
     the clokke the space of 2 degrees. Tho loked I doun up-on myn
     est orisonte, and fond ther 23 degrees of Libra assending, whom I
  40 tok for myn assendent; and thus lerned I to knowe ones for ever
     in which manere I shuld come to the houre of the night and to
     myn assendent; as verreyly as may be taken by so smal an instru_ment.
     But natheles, in general, wolde I warne thee for evere, ne
     mak thee nevere bold to have take a iust ascendent by thyn
  45 Astrolabie, or elles to have set iustly a clokke, whan any celestial
     body by which that thow wenest governe thilke thinges ben ney
     the south lyne; for trust wel, whan that the sonne is ney the
     meridional lyne, the degree of the sonne renneth so longe consen_trik 
     up-on the almikanteras, that sothly thou shalt erre fro the iust
  50 assendent. The same conclusioun sey I by the centre of any
     sterre fix by night; and more-over, by experience, I wot wel that
     in oure orisonte, from 11 of the clokke un-to oon of the clokke,
     in taking of a iust assendent in a portatif Astrolabie, hit is to hard
     to knowe. I mene, from 11 of the clokke biforn the houre of
  55 noon til oon of the clok next folwing. And for the more declar_acion,
     lo here thy figure.

     4. Special declaracion of the assendent.

      [Specialis declaracio de ascendente.]

       The assendent sothly, as wel in alle nativitez as in questiouns
     and elecciouns of tymes, is a thing which that thise astrologiens
     gretly observen; wher-fore me semeth convenient, sin that I
     speke of the assendent, to make of it special declaracioun. The
   5 assendent sothly, to take it at the largeste, is thilke degree that



|p192


     assendeth at any of thise forseide tymes upon the est orisonte;
     and there-for, yif that any planet assende at that same tyme in
     thilke for-seide degree of his longitude, men seyn that thilke
     planete is in horoscopo. But sothly, the hous of the assendent,
  10 that is to seyn, the firste hous or the est angle, is a thing more
     brood and large. For after the statutz of astrologiens, what
     celestial body that is 5 degres above thilk degree that assendeth,
     or with-in that noumbre, that is to seyn, nere the degree that
     assendeth, yit rikne they thilke planet in the assendent. And
  15 what planete that is under thilke degree that assendith the space
     of 25 degrees, yit seyn they that thilke planete is lyk to him that
     is in the hous of the assendent, but sothly, yif he passe the
     bondes of thise forseide spaces, above or bynethe, they seyn
     that the planete is failling fro the assendent. Yit sein thise
  20 astrologiens, that the assrndent, and eke the lord of the assendent,
     may be shapen for to be fortunat or infortunat, as thus: a fortunat
     assendent clepen they whan that no wykkid planete, as Saturne
     or Mars, or elles the Tail of the Dragoun, is in the hous of the
     assendent, he that no wikked planete have non aspecte of enemite
  25 up-on the assendent; but they wol caste that they have a fortunat
     planete in hir assendent and yit 1n his felicitee, and than sey they
     that it is wel. Forther over, they seyn that the infortuning of an
     assendent is the contrarie of thise forseide thinges. The lord of
     the assendent, sey they, that he is fortunat, whan he is in good
  30 place fro the assendent as in angle, or in a succedent, where-as
     he is in his dignitee and conforted with frendly aspectes of planetes
     and wel resceived, and eek that he may seen the assendent, and
     that he be nat retrograd ne combust, ne ioigned with no sbrewe
     in the same signe, ne that he be nat in his descencioun, ne
  35 ioigned with no planete in his discencioun, ne have upon him
     non aspecte; infortunat, and than sey they that he is wel. Natheles,
     thise ben observauncez of iudicial matiere and rytes of payens,
     in which my spirit ne hath no feith, ne no knowing of hir horo_scopum;
     for they seyn that every signe is departed in 3 evene
  40 parties by 10 degrees, and thilke porcioun they clepe a Face.



|p193


     And al-thogh that a planete have a latitude fro the ecliptik, yit
     sey some folk, so that the planete aryse in that same signe with
     any degree of the forseide face in which his longitude is rekned,
     that yit is the planete in horoscopo, be it in nativite or in eleccioun,
  45 &c. And for the more declaracioun, lo here the figure.

     5. To knowe the verrey equacioun of the degree of the
     sonne, yif so be that it falle by-twixe thyn Almikanteras.

     [Ad cognoscendum veram equacionem de gradu solis, si
      contigerit fore in duas Almicanteras.]

       For as moche as the almikanteras in thyn Astrolabie been
     compouned by two and two, where-as some almikanteras in
     sondry Astrolabies ben compouned by on and on, or elles by two
     and two, it is necessarie to thy lerning to teche thee first to knowe
   5 and worke with thyn owne instrument. Wher-for, whan that the
     degree of thy sonne falleth by-twixe almikanteras, or elles yif
     thyn almikanteras ben graven with over gret a point of a compas,
     (for bothe thise thinges may causen errour as wel in knowing of
     the tyd of the day as of the verrey assendent), thou most werken
  10 in this wyse. Set the degree of thy sonne up-on the heyer
     almikanteras of bothe, and waite wel wher as thin almury touchet
     the bordure, and set ther a prikke of inke. Set doun agayn the
     degree of thy sonne up-on the nethere almikanteras of bothe, and
     set ther another prikke. Remewe thanne thyn almury in the
  15 bordure evene amiddes bothe prikkes, and this wol lede iustly the
     degree of thy sonne to sitte by-twixe bothe almikanteras in his
     right place. Ley thanne thy label over the degree of thy sonne;
     and find in the bordure the verrey tyde of the day or of the night.
     And as verreyly shaltow finde up-on thyn est orisonte thyn assen_dent.
  20 And for more declaracioun, lo here thy figure.

     6. To knowe the spring of the dawing and the ende of the
     evening, the which ben called the two crepusculis:

     [Ad cognoscendum ortum solis et eius occasum, que vocatur
      vulgariter crepusculum.]

       Set the nadir of thy sonne up-on 18 degrees of heighte among
     thyn almikanteras on the west syde, and ley thy label on the degree



|p194


     of thy sonne, and thanne shal tHe poynt of thy label schewe the
     spring of day. Also set the nadir of thy sonne up-on 18 degrees
     of heighte a-mong thyn almikanteras on the est side, and ley over
   5 thy label up-on the degree of the sonne, and with the point of
     thy label find in the bordure, the ende of the evening, that is,
     verrey night. The nadir of the sonne is thilke degree that is
     opposit to the degree of the sonne, in the seventhe signe, as thus:
  10 every degree of Aries by ordre is nadir to every degree of Libra
     by ordre; and Taurus to Scorpion, Gemini to Sagittare, Cancer
     to Capricorne; Leo to Aquarie; Virgo.to Pisces; and yif any degree
     in thy zodiak be dirk, his nadir shal declare him. And for the
     more declaracioun, lo here thy figure.

     7 To.knowe the arch of the day, that some folk callen the
     day artificial, from the sonne arysing til hit go to reste.

     [Ad cognoscendum archum diei, quem vulgus vocat diem
      artificialem, in hoc, ab ortu solis usque ad occasum.]

       Set the degree of thy sonne up-on thyn.est orisonte, and ley
     thy label on the degree of the sonne, and at the poynt of thy
     label in the bordure set a prikke. Turn thanne thy riet aboute
     til the degree of the sonne sit up on the west orisonte, and ley
   5 thy label up-on the same degree of the sonne, and at the point of
     thy label set a-nother prikke. Rekne thanne the quantitee of
     tyme in the bordure by-twixe bothe prikkes, and tak ther thyn ark
     of the day. The remenant of the bordure under the orisonte is
     the ark of the night. Thus maistovw rekne bothe arches, or
  10 every porcion, of whether that thee lyketh. And by this manere
     of wyrking maistow see how longe that any sterre fix dwelleth a_bove 
     the erthe, fro tyme that he ryseth til he go to reste. But



|p195


     the day natural, that is to seyn 24 houres, is the revolucioun of
     the equinoxial with as moche partie of the zodiak as the sonne
  15 of his propre moevinge passeth in the mene whyle. And for the
     more declaracioun, lo here thy figure.

     8. To turn the houres in-equales in houres equales.

     [Ad convertendum horas inequales in horas equales.]

       Knowe the nombre of the degrees in the houres in-equales, and
     departe hem by 15, and tak ther thyn houres equales. And for
     the more declaracioun, lo here thy figure.

     9. To kowe the quantitee of the day vulgare, that is to
     seyen, from spring of the day un-to verrey night.

     [Ad cognoscendum quantitatem diei vulgaris, viz. ab ortu
      diei usque ad noctem.]

       Know the quantitee of thy crepusculis, as I have taught in the
     chapitre bi-forn, and adde hem to the arch of thy day artificial;
     and tak ther the space of alle the hole day vulgar, un-to, verrey
     night. The same manere maystow worke, to knowe the quantitee
   5 of the vulgar night. And for the more declaracioun, lo here the
     figure.

     10. To knowe the quantite of houres in-equales by day.

     [Ad cognoscendum horas inequales in die.]

       Understond wel, that thise houres in-equales ben cleped houres
     of planetes, and understond wel that som-tyme ben they lengere
     by day than by night, and som-tyme the conitrarie. But under_stond 
     wel, that evermo, generaly, the hour in-equal of the day
   5 with the houre in-equal of the night contenen 30 degrees of the



|p196


     bordure, whiche bordure is ever-mo answering to the degrees of
     the equinoxial; wher-for departe the arch of the day artificial in
     12, and tak ther the quantitee of the houre in-equal by day.
     And yif thow abate the quantitee of the houre in-equal by daye
  10 out of 30, than shal the remenant that leveth performe the houre
     inequal by night. And for the more declaracioun, lo here the
     figure.

     11. To knowe the quantite of houres equales.

     [Ad cognoscendum quantitatem horarum inequalium.]

       The quantitee of houres equales, that is to seyn, the houres of
     the clokke, ben departed by 15 degrees al-redy in the bordure
     of thyn Astrolabie, as wel by night as by day, generaly for evere.
     What nedeth more declaracioun? Wher-for, whan thee list to
   5 know how manye houres of the clokke ben passed, or any part of
     any of thise houres that ben passed, or elles how many houres or
     partie of houres ben to come, fro swich a tyme to swich a tyme,
     by day or by nighte, knowe the degree of thy sonne, and ley thy
     label on it; turne thy riet aboute ioyntly with thy label, and with
  10 the point of it rekne in the bordure fro the sonne aryse un-to
     the same place ther thou desirest, by day as by nighte. This
     conclusioun wol I declare in the laste chapitre of the 4 partie of
     this tretis so openly, that ther shal lakke no worde that nedeth to
     the declaracioun. And for the more declaracioun, lo here the
  15 figure.

     12. Special declaracioun of the houres of planetes.

     [Specialis declaracio de horis planetarum.]

       Understond wel, that evere-mo, fro the arysing of the sonne til
     it go to reste, the nadir of the sonne shal shewe the houre of the



|p197


     planete, and fro that tyme forward al the night til the sonne
     aryse; than shal the verrey degree of the sonne shewe the houre
   5 of the planete. Ensample as thus. The 13 day of March fil
     up-on a Saterday per aventure, and, at the arising of the sonne, I
     fond the secounde degree of Aries sitting up-on myn est orisonte,
     al-be-it that it was but lite; than fond I the 2 degree of Libra,
     nadir of my sonne, dessending on my west orisonte, up-on which
  10 west orisonte every day generally, at the sonne ariste, entreth
     the houre of any planete, after which planete the day bereth his
     name; and endeth in the nexte stryk of the plate under the
     forseide west orisonte, and evere, as the sonne climbeth uppere
     and uppere, so goth his nadir dounere and dounere, teching by
  15 swich strykes the houres of planetes by ordre as they sitten in
     the hevene. The first houre inequal of every Satterday is to
     Saturne; and the secounde, to Iupiter; the 3, to Mars, the 4
     to the Sonne; the 5, to Venus; the 6, to Mercurius; the 7, to
     the Mone; and thanne agayn, the 8 is to Saturne; the 9, to
  20 Iupiter; the 10, to Mars; the 11, to the Sonne; the 12, to
     Venus; and now is my sonne gon to reste as for that Setterday.
     Thanne sheweth the verrey degree of the sonne the houre of
     Mercurie entring under my west orisonte at eve; and next him
     succedeth the Mone; and so forth by ordre, planete after
  25 planete, in houre after houre, al the night longe til the sonne
     aryse. Now ryseth the sonne that Sonday by the morwe; and



|p198


     the nadir of the sonne, up-on the west orizonte, sheweth me the
     entring of the houre of the forseide sonne. And in this maner
     succedeth planete under planete, fro Saturne un-to the Mone,
  30 and fro the Mone up a-gayn to Saturne, houre after houre
     generaly. And thus knowe I this conclusioun. And for the
     more declaracioun, lo here the figure.

     13. To knowe the altitude of the sonne in middes of the
     day, that is cleped the altitude meridian.

     [Ad cognoscendum altitudinem solis in medio diei, que
      vocatur altitudo meridiana.]

       Set the degree of the sonne up-on the lyne meridional, and
     rikene how many degrees of almikanteras ben by-twixe thyn est
     orisonte and the degree of the sonne. And tak ther thyn altitude
     meridian; this is to seyne, the heyest of the sonne as for that day.
   5 So maystow knowe in the same lyne, the heyest cours that any
     sterre fix climbeth by night; this is to seyn, that whan any sterre
     fix is passed the lyne meridional, than by-ginneth it to descende,
     and so doth the sonne. And for the more declaracioun, lo here
     thy figure.

     14. To knowe the degree of the sonne by thy riet, for a
     maner curiositee, &c.

     [Ad cognoscendum gradum solis curiose.]

       Sek bysily with thy rewle the heyest of the sonne in midde of
     the day; turne thanne thyn Astrolabie, and with a prikke of ink
     marke the nombre of that same altitude in the lyne meridional.
     Turne thanne thy riet a-boute til thou fynde a degree of thy



|p199


   5 zodiak acording with the prikke, this is to seyn, sittinge on the
     prikke; and in sooth, thou shalt finde but two degrees in al the
     zodiak of that condicioun; and yit thilke two degrees ben in
     diverse signes; than maistow lightly by the sesoun of the yere
     knowe the signe in whiche that is the sonne. And for the
  10 more declaracioun, lo here thy figure.

     15. To know which day is lyk to which day as of
     lengthe, &c.

     [Ad cognoscendum quales dies in longitudine sunt similes.]

       Loke whiche degrees ben y-lyke fer fro the hevedes of Cancer
     and Capricorn, and lok, whan the sonne is in any of thilke
     degrees, than ben the dayes y-lyke of lengthe. This is to seyn,
     that as long is that day in that monthe, as was swich a day in
   5 swich a month; ther varieth but lite. Also, yif thou take two
     dayes naturaly in the yer y-lyke fer fro eyther pointe of the
     equinoxial in the opposit parties, than as long is the day artificial
     of that on day as is the night of that othere, and the contrarie.
     And for the more declaracioun, lo here thy figure.

     16. This chapitre is a maner declaracioun to conclusiouns
     that folwen.

     [Illud capitulum est quedam declaracio ad certas
      conclusiones sequentes.]

       Understond wel that thy zodiak is departid in two halfe cercles,
     as fro the heved of Capricorne un-to the heved of Cancer; and
     agaynward fro the heved of Cancer un-to the heved of Capricorne.



|p200


     The heved of Capricorne is the lowest point, wher-as the sonne
   5 goth in winter; and the heved of Cancer is the heyest point, in
     wiche the sonne goth in somer. And ther-for understond wel,
     that any two degrees that ben y-lyke fer fro any of thise two
     hevedes, truste wel that thilke two degrees ben of y-lyke de_clinacioun,
     be it southward or northward, and the dayes of hem
  10 ben y-lyke of lengthe, and the nightes also; and the shadwes
     y-lyke, and the altitudes.y-lyke at midday for evere. And for
     more declaracioun, lo here thy figure.

     17. To knowe the verrey degree of any maner sterre
     straunge or unstraunge after his longitude, though he be
     indeterminat in thyn Astrolabie; sothly to the trowthe,
     thus he shal be knowe.

     [Ad cognoscendum verum gradum alicuius stelle aliene
      secundum eius longitudinem, quamvis sit indeterminata
      in astrolabio; veraciter isto modo.

       Tak the altitude of this sterre whan he is on the est side of the
     lyne meridional, as ney as thou mayst gesse; and tak an as_sendent 
     a-non right by som maner sterre fix which that thou
     knowest; and for-get nat the altitude of the firste sterre, ne thyn
   5 assendent. And whan that this is don, espye diligently whan this
     same firste sterre passeth any-thing the south westward, and hath
     him a-non right in the same noumbre of altitude on the west side
     of this lyne meridional as he was caught on the est side; and tak
     a newe assendent a-non right by som maner sterre fixe which that



|p201


  10 thou knowest; and for-get nat this secounde assendent. And
     whan that this is don, rikne thanne how manye degrees ben by_twixe 
     the firste assendent and the seconde assendent, and rikne
     wel the middel degree by-twene bothe assendentes, and set thilke
     middel degree up-on thin est orisonte; and waite thanne what degree
  15 that sit up-on the lyne meridional, and tak ther the verrey degree
     of the ecliptik in which the sterre stondeth for the tyme. For in
     the ecliptik is the longitude of a celestial body rekened, evene fro
     the heved of Aries un-to the ende of Pisces. And his latitude is
     rikned after the quantite of his declinacion, north or south to-warde
  20 the Poles of this world; as thus. Yif it be of the sonne or of any
     fix sterre, rekene his latitude or his declinacioun fro the equinoxial
     cercle; and yif it be of a planete, rekne than the quantitee of his
     latitude fro the ecliptik lyne. Al-be-it so that fro the equinoxial
     may the declinacion or the latitude of any body celestial be rikned,
  25 after the site north or south, and after the quantitee of his declin_acion.
     And right so may the latitude or the declinacion of any
     body celestial, save only of the sonne, after his site north or south,
     and after the quantitee of his declinacioun, be rekned fro the



|p202


     ecliptik lyne; fro which lyne alle planetes som tyme declynen
  30 north or south, save only the for-seide sonne. And for the more_declaracioun,
     lo here thy figure.

     18. To knowe the degrees of the longitudes of fixe sterres
     after that they ben determinat in thin Astrolabie, yif so
     be that they ben trewly set.

     [Ad cognoscendum gradus longitudinis de stellis fixis que
      determinatur in astrolabio, sicut in suis locis recte
      locentur.]

       Set the centre of the sterre up-on the lyne meridionial, and tak
     keep of thy zodiak, and loke what degree of any signe that sit on
     the same lyne meridional at that same tyme, and tak the degree in
     which the sterre standeth, and with that same degree comth that
     same sterre un-to that same lyne fro the orisonte. And for more
     declaracioun, lo here thy figure.

     19. To knowe with which degree of the zodiak any sterre
     fixe in thyn Astrolabie aryseth up-on the est orisonte, al_thogh 
     his dweliing be in a-nother signe.

     [Ad cognoscendum cum quibus gradibus zodiaci que stella
      fixa in astrolabio ascendit super orizontem orientalem,
      quamvis eius statio sit in alio signo.]

       Set the centre of the sterre up-on the est orisonte, and loke
     what degree of any signe that sit up-on the same orisonte at that
   5 same tyme. And understond wel, that with that same degree
     aryseth that same sterre; and this merveyllous arysing with a



|p203


   5 strange degree in another signe is by-cause that the latitude of the
     sterre fix is either north or south fro the equinoxial. But sothly
     the latitudes of planetes ben comunly rekned fro the ecliptik,
     bi-cause that non of hem declineth but fewe degrees out fro the
     brede of the zodiak. And tak good keep of this chapitre of arysing
  10 of the celestial bodies; for truste wel, that neyther mone ne sterre
     as in oure embelif orisonte aryseth with that same degree of his
     longitude, save in o cas; and that is, whan they have no latitude
     fro the ecliptik lyne. But natheles, som tyme is everiche of thise
     planetes under the same sonne lyne. And for more declaracioun, lo
  15 here thy figure.

     20. To knowe the declinacioun of any degree in the zodiak
     fro the equinoxial cercle, &c.

     [Ad cognoscendum declinacionem alicuius gradus in
     zodiaco a circulo equinoctiali.]

       Set the degree of any signe up-on the lyne meridional, and rikne
     his altitude in almikanteras fro the est orizonte up to the same
     degree set in the forseide lyne, and set ther a prikke. Turne up
     thanne thy riet, and set the heved of Aries or Libra in the same
   5 meridional lyne, and set ther a-nother prikke. And whan that
     this is don, considere the altitudes of hem bothe; for sothly the
     difference of thilke altitudes is the declinacion of thilke degree
     fro the equinoxiaI. And yif so be that thilke degree be northward



|p204


     fro the equinoxial, than is his declinacion north; yif it be south_ward,
  10 than is it south. And for the more declaracioun, lo here
     thy figure.

     21. To knowe for what latitude in any regioun the
     almikanteras of any table ben compounded.

     [Ad cognoscendum pro qua latitudine in aliqua regione
      almicantre tabule mee sunt composite.]

       Rikne how manye degrees of almikanteras, in the meridional
     lyne, be fro the cercle equinoxial un-to the senith; or elles fro the
     pool artik un-to the north orisonte, and for so gret a latitude or
     for so smal a latitude is the table compouned. And for more
   5 declaracion, lo here thy figure.

     22. To knowe in special the latitude of oure countray, I
     mene after the latitude of Oxenford, and the heighte of
     oure pol.

     [Ad cognoscendum specialiter latitudinem nostri regionis,
      scilicet latitudinem Oxonie, et altitudinem poli nostri.]

       Understond wel, that as fer is the heved of Aries or Libra in the
     equinoxial from oure orisonte as is the senith from the pole artik;
     and as hey is the pol artik fro the orisonte, as the equinoxial is
     fer fro the senith. I prove it thus by the latitude of Oxenford.
   5 Understond wel, that the heyghte of oure pool artik fro oure north
     orisonte is 51 degrees and 50 minutes; than is the senith from
     oure pool artik 38 degrees and 10 minutes; than is the equinoxial



|p205


     from oure senith 51 degrees and 50 minutes; than is oure south
     orisonte from oure equinoxial 38 degrees and 10 minutes. Under_stond 
  10 wel this rekning. Also for-get nat that the senith is 90
     degrees of heyghte fro the orisonte, and oure equinoxial is 90
     degrees from oure pool artik. Also this shorte rewle is soth, that
     the latitude of any place in a regioun is the distance fro the senith
     unto the equinoxial. And for more declaracioun, lo here thy
  15 figure.

     23. To prove evidently the latitude of any place in a
     regioun, by the preve of the heyghte of the pol artik in
     that same place.

     [Ad probandum evidenter latitudinem alicuius loci in
      aliqua regione, per probacionem altitudinis de polo artico
      in eodem loco.]

       In some winters night, whan the firmament is clere and thikke_sterred,
     waite a tyme til that any sterre fix sit lyne-right per_pendiculer 
     over the pol artik, and clepe that sterre A. And
     wayte a-nother sterre that sit lyne-right under A, and under the
   5 pol, and clepe that sterre F. And understond wel, that F is nat
     considered but only to declare that A sit evene overe the pool.
     Tak thanne a-non right the altitude of A from the orisonte, and
     forget it nat. Lat A and F go farwel til agayns the dawening a
     gret whyle; and come thanne agayn, and abyd til that A is evene
  10 under the pol and under F; for sothly, than wol F sitte over the pool,
     and A wol sitte under the pool. Tak than eft-sones the altitude of
     A from the orisonte, and note as wel his secounde altitude as his
     firste altitude; and whan that this is don, rikne how manye degrees



|p206


     that the firste altitude of A excedeth his seconde altitude, and tak
  15 half thilke porcioun that is exceded, and adde it to his seconde
     altitude; and tak ther the elevacioun of thy pool, and eke the
     latitude of thy regioun. For thise two ben of a nombre; this is
     to seyn, as many degrees as thy pool is elevat, so michel is the
     latitude of the regioun. Ensample as thus: par aventure, the
  20 altitude of A in the evening is 56 degrees of heyghte. Than
     wol his seconde altitude or the dawing be 48; that is 8 lasse than
     56, that was his firste altitude at even. Take thanne the half of
     8, and adde it to 48, that was his seconde altitude, and than
     hastow 52. Now hastow the heyghte of thy pol, and the latitude
  25 of the regioun. But understond wel, that to prove this conclusioun
     and many a-nother fair conclusioun, thou most have a plomet
     hanging on a lyne heyer than thin heved on a perche; and thilke
     lyne mot hange evene perpendiculer by-twixe the pool and thyn
     eye; and thanne shaltow seen yif A sitte evene over the pool and
  30 over F at evene; and also yif F sitte evene over the pool and
     over A or day. And for more declaracion, lo here thy figure.

     24. Another conclusioun to prove the heyghte of the pool
     artik fro the orisonte.

     [Alia conclusio ad probandum altitudinem de polo artico ab
      arizonte.]

       Tak any sterre fixe that nevere dissendeth under the orisonte in
     thilke regioun, and considere his heyest altitude and his lowest
     altitude fro the orisonte; and make a nombre of bothe thise
     altitudes. Tak thanne and abate half that nombre, and tak ther
   5 the elevacioun of the pol artik in that same regioun. And for
     more declaracioun, lo here thy figure.



|p207


     25. A-nother conclusioun to prove the latitude 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
   5 Astrolabie. And thilke space is as moche as the pool artik is hey
     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
  10 the altitude of the sonne in the middel of the day, whan the sonne
     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
  15 suppose that the sonne is thilke day at noon 38 degrees and 
     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
  20 so be that thee semeth to long a taryinge, to abyde til that the
     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
  25 thanne fro the sonnes altitude at noon the nombre of his de_clinacion,
     and thanne hastow the heyghte of the hevedes of Aries
     and Libra. As thus: my sonne is, par aventure, in the firste



|p208


     degre of Leoun, 58 degrees and 10 minutes of heyghte at noon
     and his declinacion is almost 20 degrees northward fro the
  30 equinoxial; abate thanne thilke 20 degrees of declinacion out of
     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 south_ward 
  35 fro the equinoxial, adde thanne thilke declinacion to the
     altitude of the sonne at noon, and tak ther the hevedes of Aries
     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
  40 fro the equinoxial. Or elles, yif thee lest, take the heyest altitude
     fro the equinoxil of any sterre fix that thou knowest, and tak his
     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 con_clusiouns,
     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
   5 ascensioun, with which more part of the cercle equinoxial and
     lasse part of the zodiak ascendeth; and thilke signe assendeth
     embelif, with whiche lasse part of the equinoxial and more part of



|p209


     the zodiak assendeth. Ferther-over they seyn, that in thilke
     cuntrey where as the senith of hem that dwellen there is in the
  10 equinoxial lyne, and her orisonte passing by the poles of this
     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
  15 han this forseide poeple. And the almikanteras in her Astrolabies
     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
  20 every degree and minut in al the zodiak, as shal be shewed. And



|p210


     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
  25 the more declaracioun, lo here the figure

     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
   5 sitte up-on the meridional lyne; and eft-sones waite wher thyn
     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.
  10 And for the more declaracioun, lo here thy figure.

     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
      oliquo, in omni regione.]

       Set the heved of the signe which as thee list to knowe his



|p211


     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
   5 orisonte, and waite eft-sones wher as thyn almury toucheth the
     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
  10 ende of Virgo, ben cleped signes of the north fro the equinoxial;
     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
  15 the verrey est and the verrey south in oure orisonte. Also every
     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
  20 they arisen embelif on oure orisonte; and thise crokede signes
     ben obedient to the signes that ben of right assencioun. The
     signes of right assencioun ben fro the heved of Cancer to the
     ende of Sagittare; and thise signes arysen more upright, and they
     ben called eke sovereyn signes; and everich of hem aryseth in
  25 more space than in two houres. Of which signes, Gemini obeyeth
     to Cancer; and Taurus to Leo; Aries to Virgo; Pisces to Libra;
     Aquarius to Scorpioun; and Capricorne to Sagittare. And thus



|p212


     ever-mo two signes, that ben y-lyke fer fro the heved of-Capricorne,
     obeyen everich of hem til other. And for more declaracioun, lo
  30 here the figure.

     29. To knowe iustly the foure quarters of the world, as
     est, west, north, and sowth.

     [Ad cognoscendum evidenter quatuor partes mundi, scili_cet,
     orientem, austrum, aquilonem, et occidentem.]

       Take the altitude of thy sonne whan thee list, and note wel the
     quarter of the world in which the sonne is for the tyme by the
     azimutz. Turne thanne thyn Astrolabie, and set the degree of
     the sonne in the almikanteras of his altitude, on thilke side that
   5 the sonne stant, as is the manere in taking of houres; and ley thy
     label on the degree of the sonne, and rikene how many degrees of
     the bordure ben by-twixe the lyne meridional and the point of thy
     label; and note wel that noumbre. Turne thanne a gayn thyn
     Astrolabie, and set the point of thy gret rewle, ther thou takest
  10 thyne altitudes, up-on as many degrees in his bordure fro his
     meridional as was the point of thy label fro the lyne meridional on
     the wombe-syde. Tak thanne thyn Astrolabie with bothe handes
     sadly and slely, and lat the sonne shyne thorow bothe holes of thy
     rewle; and sleyly, in thilke shyninge, lat thyn Astrolabie couch
  15 adoun evene up-on a smothe grond, and thanne wol the verrey
     lyne meridional of thyn Astrolabie lye evene south, and the est
     lyne wole lye est, and the west lyne west, and north lyne north, so
     that thou werke softly and avisely in the couching; and thus
     hastow the 4 quarters of the firmament. And for the more
  20 declaracioun, lo here the figure.



|p213


     30. To knowe the altitude of planetes fro the wey of the
     sonne, whether so they be north or south fro the for_seide 
     wey.

     [Ad cognoscendum altitudinem planetarum a cursu solis,
      utrum sint in parte australi vel boreali a cursu supra
      dicto.]

       Lok whan that a planete is in the lyne meridional, yif that hir
     altitude be of the same heyghte that is the degree of the sonne for
     that day, and than is the planete in the verrey wey of the sonne,
     and hath no latitude. And yif the altitude of the planete be
   5 heyere than the degree of the sonne, than is the planete north fro
     the wey of the sonne swich a quantite of latitude as sheweth by
     thyn almikanteras. And yif the altitude of the planete be lasse
     than the degree of the sonne, thanne is the planete south fro the
     wey of the sonne swich a quantite of latitude as sheweth by thyn
  10 almikanteras. This is to seyn, fro the wey wher-as the sonne
     wente thilke day, but nat from the wey of the sonne in every place
     of the zodiak. And for the more declaracioun, lo here the figure.

     31. To knowe the senith of the arysing of the sonne, this
     is to seyn, the partie of the orisonte in which that the sonne aryseth.

     [Ad cognoscendum signum de ortu solis, scilicet, illam
      partem orientis in qua oritur sol.]

       Thou most first considere that the sonne aryseth nat al-wey
     verrey est, but some tyme by north the est, and som tyme by southe
     the est. Sothly, the sonne aryseth never-mo verrey est in oure



|p214


     orisonte, but he be in the heved of Aries or Libra. Now is thyn
   5 orisonte departed in 24 parties by thy azimutz, in significacion of
     24 partiez of the world; al-be-it so that shipmen rikne thilke
     partiez in 32. Thanne is ther no more but waite in which azimut
     that thy sonne entreth at his arysing; and take ther the senith of
     the arysing of the sonne. The manere of the devisioun of thyn
  10 Astrolabie is this; I mene, as in this cas. First is it devided in
     4 plages principalx with the lyne that goth from est to west, and
     than with a-nother lyne that goth fro south to north. Than is it
     devided in smale partiez of azimutz, as est, and est by southe;
     whereas is the firste azimut above the est lyne; and so forth, fro
  15 partie to partie, til that thou come agayn un-to the est lyne.
     Thus maistow understond also the senith of any sterre, in which
     partie he ryseth, &c. And for the more declaracion, lo here
     the figure.

     32. To knowe in which partie of the firmament is the
     coniunccioun.

     [Ad cognoscendum in qua parte firmamenti sunt
      coniuncciones solis et lune.]

       Considere the tyme of the coniunccion by thy kalender, as thus;
     lok how many houres thilke coniunccion is fro the midday of the
     day precedent, as sheweth by the canoun of thy kalender. Rikne
     thanne thilke nombre of houres in the bordure of thyn Astrolabie,



|p215


   5 as thou art wont to do in knowing of the houres of the day or of
     the night; and ley thy label over the degree of the sonne, and
     thanne wol the point of thy label sitte up-on the hour of the con_iunccion.
     Loke thanne in which azimut the degree of thy sonne
     sitteth, and in that partie of the firmament is the coniunccioun.
     And for the more declaracioun, lo here thy figure.

     33. To knowe the senith of the altitude of the sonne, &c.

     [Ad cognoscendum signa de altitudine solis.]

       This is no more to seyn but any tyme of the day tak the altitude
     of the sonne, and by the azimut in which he stondeth, maystou
     seen in which partie of the firmament he is. And in the same
     wyse maystou seen, by the night, of any sterre, whether the
   5 sterre sitte est or west or north, or any partie by-twene, after the
     name of the azimut in which is the sterre. And for the more
     declaracioun, lo here the figure.

     34. To knowe sothly the degree of the longitude of the
     mone, or of any planete that hath no latitude for the
     tyme fro the ecliptik lyne.

     [Ad cognoscendum veraciter gradum de longitudine lune,
      vel alicuius planete qui non habet longitudinem pro tem_pore 
     causante linea ecliptica.]

       Tak the altitude of the mone, and rikne thyn altitude up among



|p216


     thyne almikanteras on which syde that the mone stande; and set
     there a prikke. Tak thenne anon-right, up-on the mones syde,
     the altitude of any sterre fix which that thou knowest, and set his
   5 centre up-on his altitude among thyn almikanteras ther the sterre
     is founde. Waite thanne which degree of the zodiak toucheth the
     prikke of the altitude of the mone, and tak ther the degree in
     which the mone standeth. This conclusioun is verrey soth, yif
     the sterres in thyn Astrolabie stonden after the trowthe; of
  10 comune, tretis of Astrolabie ne make non excepcioun whether the
     mone have latitude, or non; ne on whether syde of the mone the
     altitude of the sterre fix be taken. And nota, that yif the mone
     shewe himself by light of day, than maystow wyrke this same
     conclusioun by the sonne, as wel as by the fix sterre. And for the
  15 more declaracioun, lo here thy figure.

     35. This is the workinge of the 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
   5 moeving of a planete, whether so he moeve forthward or bakward.



|p217


     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
  10 lyne, so that his seconde altitude be lasse than his firste altitude
     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,
  15 thanne is he retrograde, and yif he be on the west syde, than is he
     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. Remeve thanne the degree that
     assendeth, and set him on the ende of the 10 hour inequal; and
   5 thanne wol the byginning of the 3 hous sitte up-on the midnight
     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



|p218


     the degree that first assendeth, and set him on the ende of the 2
  10 houre inequal; and thanne wol the by-ginning of the 5 hous sitte
     up-on the lyne of midnight; set thanne the nadir of the assendent
     on the ende of the 4 houre, than woI 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
  15 2; and the by-ginning of the 9 hous is nadir of the 3; and the
     by-ginning of the 10 hous is the nadir of the 4; and the byginning
     of the 11r 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
   5 opposit up-on the lyne of midnight. Thanne ley thy label over
     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 alIe thilke degrees in 3 evene parties, and take
     the evene equacion of 3; for ley thy label over everich of 3 parties,
  10 and than maistow see by thy label in which degree of the zodiak is
     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



|p219


     assendent; and thanne the beginning of the 11 house; and
     thanne the 10, up-on the meridional lyne; as I first seide. The
  15 same wyse wirke thou fro the assendent doun to the lyne of
     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.
   5 And in centre of the compas stike an evene pin or a wyr upright; 
     the smallere the betere. Set thy pin by a plom-rewIe 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
  10 shadwe of the pin entreth any-thing with-in the cercle of thy plate
     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
  15 of inke. Take than a compas, and mesure evene the middel
     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



|p220


     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
  20 the compas, iustly over the lyne meridional, than hastow est and
     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, 
   5 whan that the sonne by moeving of the firmament cometh to his
     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
  10 that other toun, truste wel that thilke tounes han diverse meri_dians.
     Nota also, that the arch of the equinoxial, that is con_teyned 
     or bounded by-twixe the 2 meridians, is cleped the longi_tude 
     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
  15 fer fro the est; and the contrarie. And in this manere they
     chaunge nat her meridian, but sothly they chaungen her almi_kanteras;
     for the enhausing of the pool and the distance of the



|p221


     sonne. The longitude of a clymat is a lyne imagined fro est to
     west, y-lyke distant by-twene them alle. The latitude of a clymat
  20 is a lyne imagined from north to south the space of the erthe, 
     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
  25 by-twixe the senith and the equinoxial. Thanne sey they that 
     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 zodiac that any
     planete ascendith 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
   5 folwinge in special, maystow wirke for sothe in every signe of the 
     zodiak. The degree of the longitude, par aventure, of Venus or
     of another planete, was 6 of Capricorne, and the latitude of him



|p222 


     was northward 2 degrees fro the ecliptik lyne. I tok a subtiI
     compas, and cleped that oon poynt i of my compas A, and that 
  10 other poynt. F. Than tok I the point of A, and set it in the
     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
  15 seyn, in the 6 degree fro the heved of Capricorne; and thus have
     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
  20 I this forseide label, and leide it fix over the degree of my
     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
  25 over the zodiak, that is to seyn, north-ward fro the ecliptik. Than
     leide I doun my compas, and lokede wel in the wey upon the
     prikke of A and of F; tho turned I my met 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
  30 of the 6 degree, in the heved of Capricorne. And nota, that in the
     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
  35 it may.



|p223


     Also the degree, par aventure, of Iuppiter or of another planete, 
     was in the first degree of Pisces in longitude, and his latitude was i
     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
  40 point of F dounward in the same signe, by-cause that the latitude 
     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
  45 point of A on my label, evene over the ecliptik lyne, in the ende 
     evene of the degree of the longitude, and sette i 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
  50 orisonte; thanne saw I wel that the body of Iuppiter, in his 
     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
  55 hir cours houre by houre; for she ne dwelleth nat in a degree of 
     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 shalt do wel y-now].

     Explicit tractatus de Conclusionibus Astrolabii, compilatus
     per Gralfridum Chauciers ad filium suum Lodewicum, 
     scolarem tunc temporis Oxonie, ac sub tutela illius
     nobilissimi philosophi Magistri N. Strode, ete.



|p224


     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 rewIe ligge
     even in a poynt. Ensample as thus: I see him thorw at the
   5 poynt of 4; than mete I the space be-tween me and the tour, and I
     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
  10 heyghte of the tour, with adding of thyn owne persone to thyn
     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



|p225


   5 a-nother 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 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
  10 note, that at the ferste altitude of 1, thou settest a prikke, and 
     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,
  15 as thus: L 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 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
  20 werke fro 2 to 12; and yif it be 4, 4 tymes;  or 5, 5 tymes; et sic 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
   5 beholde what is the differense be-tween 1 and 2, and thou shalt 
     finde that it is 1. Than mete the space between 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
  10 7, 7 party of 12;  and note, at the altitude of thy conclusioun, 
     adde the stature of thyn heyghte to thyn eye:



|p226


     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 plane, de anno in annum, de die in diem.]

       In this maner shalt 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
   5 date, and be-hold whether thy date be more or lasse than the yere
     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
  10 what thou findest in directe of the same yere of oure lord whiche
     is passid, be hit 8, or 9, or 10, or what nombre that evere it be, til
     the time 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
  15 December, for the same yere whiche that thou hast purposed.
     And if hit so be that hit passe 20, consider wel that fro 1 to 
     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
  20 there-of, that is to sayen, signes, degrees, minutes, and secoundes, 
     and adde to-gedere un-to thy rote; and thus to make rotes; and



|p227


     note, that if hit so be that the yere of oure lord be lasse than the
     rote, which 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
  25 table in the same yere that be lasse, as I taught be-fore; 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, and after with-drawe hem from the
     rote, the yere of oure lord 1397; and the residue that leveth
  30 is thy mene mote fro the laste meridie of December, the whiche 
     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
  35 behold how many monethis, dayes, and houres ben passid from 
     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
  40 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 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 with_drawe 
   5 the yeres out of the yeres that ben passed that rote.



|p228


     Ensaumpul 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 withdrow I the laste nombere
     out of that, and than fond I the residue was 3 yere; I wiste
  10 that 3 yere was passed fro the rote,the whiche was writen in
     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 singnes, degrees, and minutes, that
     I fond directe under the same planete that I wroghte for, and
  15 wroot 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 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
  20 mene mote of any planete in March, Aprile, or May, other
     in any other tyme or moneth of the yere, loke how many
     monethes and dayes ben passed from the laste day of De_cembere,
     the yere of oure lord 1400; and so with monethes
     and dayes entere in-to thy table ther thou findest thy mene
  25 mote y-writen in monethes and dayes, and take alle the sigmes, 
     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
  30 for that same day. And note, if hit so be that thou woldest
     wete the mene mote in ony yere that is lasse than thy rote, with_drawe 
     the nombere of so inany 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
  35 33 mote. And take alle the signes, degrees, and minutes, and
     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



|p229


  40 with-drawe alle the nethere signes 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 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.
   5 Bringe furth than the labelle, and set the point therof in that
     same cost that the mone maketh flode, and set thou there the
     degree of the mone according 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 bringe and
  10 sette it iustly upon the degree of the sonne: And the point of 
     the label shal than declare to thee; at what houre of the day or of
     the night shal be flode. And there also maist thou wite by the
     same point of the label, whether it be, at that same tyme, flode or
     ebbe, or half flode, or quarter flode, or ebbe, or half or quarter
  15 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 aboute the tyme of the
     coniunccioun, bringe furthe the degree of the mone with the 
     labelle to that coste as it is before seyd. But than thou shalt
  20 understonde that thou may not bringe furthe the label fro the 20.



|p230


     degree of the mone 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 labelle unremeved knowve the houre of
     the flode or of the ebbe, as it is before seyd, &c. And evermore
  25 as thou findest the mone passe fro the sonme, so remewe thou the
     labelle than fro the degree of the mone, and bringe it to the
     degree of the sonne. And worke thou than as thou dide before, 
     &c. Or elles knowe thou what houre it is that thou art inne, by
     thyn instrument. Than bringe thou furth fro thennes the labelle
  30 and ley it upon the degree of the mone, and therby may thou wite
     also whan it was flode, or whan it wol be next, be it night or
     day; &c.

|r[The_following_sections_are_spurious;_they_are_numbered_so_as_to_shew_what_propositons_they_repeat.]

     41 a. Umbra Recta.

       Yif thy rewle falle upon the 8 poynt on right schadwe, than make
     thy figure of 8; than loke how moche space of feet is be-tween thee
     and the tour, and multiplye that be 12, and whan thou hast multiplyed
     it, than divyde it be the same nombre of 8, and kepe the residue; and
   5 adde therto up to thyn eye to the residue, and that shal be the verry
     heyght of the tour. And thus mayst thou werke on the same wyse, fro
     1 to 12.

     41 b. Umbra Recta.

       An-other maner of werking upon the same syde. Loke upon which
     poynt thy rewle faIleth whan thou seest the top of the tour thorow two
     litil holes; and mete than the space fro thy foot to the baas of the
     tour; and right as the nombre of thy poynt hath him-self to 12, right 
   5 so the mesure be-tween thee and the tour hath him-self to the heighte



|p231


     of the same tour. Ensample: I sette caas thy rewle falle upon 8; 
     than is 8 two-thrid partyes of 12; so the space is the two-thrid partyes
     of the tour.

     42a. Umbra Versa.

       To knowe the heyghth by thy poyntes of umbra versa. Yif thy
     rewle falle upon 3, whan thou seest the top of the tour, set a prikke
     there-as thy foot stont; and go ner til thou mayst see the same top
     at the poynt of 4, and sette ther another lyk prikke. Than mete how
   5 many foot ben be-tween the two prikkes, and adde the lengthe up to 
     thyn eye ther-to; and that shal be the heyght of the tour. And note, 
     that 3 is [the] fourthe party of 12, and 4 is the thridde party of 12.
     Now passeth 4 the nombre of 3 be the distaunce of 1; therfore the
     same space, with thyn heyght to thyn eye, is the heyght of the tour.
  10 And yif it so be that ther be 2 or 3 distaunce in the nombres, so shulde 
     the mesures be-tween the prikkes be twyes or thryes the heyghte of
     the tour.

     43a. Ad  cognoscendum altitudinem alicuius rei per umbram rectam.

       To knowe the heyghte of thinges, yif thou mayst nat come to the
     bas of a thing. Sette thy rewle upon what thou wilt, so that thou may
     see the top of the thing thorw the two holes, and make a marke ther
     thy foot standeth; and go neer or forther, til thou mayst see thorw
   5 another poynt, and marke ther a-nother marke. And loke than what 
     is the differense be-twen the two poyntes in the scale, and right as
     that difference hath him to 12, right so the space be-tween thee and
     the two markes hath him to the heyghte of the thing. Ensample: I
     set caas thou seest it thorw a poynt of 4; after, at the poynt of 3.
  10 Now passeth the nombre of 4 the nombre of 3 be the difference of 1; 



|p232


     and right as this difference 1 hath himself to 12, right so the mesure
     be-tween the two markes hath him to the heyghte of the thing, putting
     to the heyghte of thy-self to thyn eye; and thus mayst thou werke
     fro 1 to 12.

     42b. Per umbram versam.

       Furthermore, yif thou wilt knowe in umbra versa, by the craft of
     umbra recta, I suppose thou take the altitude at the poynt of 4, and
     makest a marke; and thou goost neer til thou hast it at the poynt of
     3, and than makest thou ther a-nother mark. Than muste thou
   5 devyde 144 by eche of the poyntes be-fornseyd, as thus: yif thou
     devyde 144 be 4, and the nombre that cometh ther-of schal be 36, and
     yif thou devyde 144 be 3, and the nombre that cometh ther-of schal be
     48, thanne loke what is the differenee between 36 and 48, and ther
     shalt thou fynde 12; and right as 12 hath him to 12, right so the space
  10 be-tween two prikkes hath him to the altitude of the thing.
