A Treatise on the Astrolabe

A Treatise on the Astrolabe is a medieval scientific essay on the astrolabe by Geoffrey Chaucer.

Summary
According to the introduction, the work was intended to have five parts: However, Chaucer only completed the first two parts and a small collection of "Supplementary Propositions".
 * 1) A description of the astrolabe
 * 2) A rudimentary course in using the instrument
 * 3) Various tables of longitudes, latitudes, declinations, etc.
 * 4) A theory of the motion of the celestial bodies, including a table  showing the motion of the moon
 * 5) An introduction to the broader field of  astrology/astronomy

The Treatise is considered the oldest work in English describing a complex scientific instrument.

=Text=

Part I
Here begynneth the descripcioun of thin Astralabie.

1. Thyn Astrolabie hath a ring to putten on the thombe of thi right hond in taking the height of thinges. And tak kep, for from henes forthward I wol clepen the heighte of any thing that is taken by the rewle "the altitude," withoute moo wordes.

2. This ryng renneth in a maner toret fast to the moder of thyn Astrelabie in so rowm a space that it distourbith not the instrument to hangen after his right centre.

3. The moder of thin Astrelabye is thikkest plate, perced with a large hool, that resceiveth in hir wombe the thynne plates compowned for diverse clymates, and thy reet shapen in manere of a nett or of a webbe of a loppe.

4. This moder is dividid on the bakhalf with a lyne that cometh descending fro the ring doun to the netherist bordure. The whiche lyne, fro the forseide ring unto the centre of the large hool amidde, is clepid the south lyne, or ellis the lyne meridional. And the remenaunt of this lyne doun to the bordure is clepid the north lyne, or ellis the lyne of midnyght.

5. Overthwart this forseide longe lyne ther crossith him another lyne of the same lengthe from eest to west. Of the whiche lyne, from a litel cros (+) in the bordure unto the centre of the large hool, is clepid the est lyne, or ellis the lyne orientale. And the remenaunt of this lyne, fro the forseide centre unto the bordure, is clepid the west lyne, or ellis the lyne occidentale. Now hast thou here the foure quarters of thin Astrolabie divided after the foure principales plages or quarters of the firmament.

6. Tlle est syde of thyn Astrolabie is clepid the right syde, and the west syde is clepid the left syde. Forget not thys, litel Lowys. Put the ryng of thyn Astrolabie upon the thombe of thi right hond, and than wol his right side be toward thi lift side, and his left side wol be toward thy right side. Tak this rewle generall, as wel on the bak as on the wombe syde. Upon the ende of this est lyne, as I first seide, is marked a litel cros (+), where as evere moo generaly is considerid the entring of the first degre in which the sonne arisith.

7. Fro this litel cros (+) up to the ende of the lyne meridionall, under the ryng, shalt thou fynden the bordure divided with 90 degrees; and by that same proporcioun is every quarter of thin Astrolabie divided. Over the whiche degrees there ben noumbres of augrym that dividen thilke same degres fro 5 to 5, as shewith by longe strikes bitwene. Of whiche longe strikes the space bitwene contenith a myle wey, and every degre of the bordure conteneth 4 minutes, this is seien, mynutes of an houre.

8. Under the compas of thilke degrees ben writen the names of the Twelve Signes: as Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricornus, Aquarius, Pisces. And the nombre of the degrees of thoo signes be writen in augrym above, and with longe divisiouns fro 5 to 5, dyvidid fro the tyme that the signe entrith unto the last ende. But understond wel that these degres of signes ben everich of hem considred of 60 mynutes, and every mynute of 60 secundes, and so furth into smale fraccions infinite, as saith Alkabucius. And therfore knowe wel that a degre of the bordure contenith 4 minutes, and a degre of a signe conteneth 60 minutes, and have this in mynde.

9. Next this folewith the cercle of the daies, that ben figured in manere of degres, that contenen in nombre 365, dividid also with longe strikes fro 5 to 5, and the nombre in augrym writen under that cercle.

10. Next the cercle of the daies folewith the cercle of the names of the monthes, that is to say, Januarius, Februarius, Marcius, Aprilis, Maius, Junius, Julius, Augustus, September, October, November, December. The names of these monthes were clepid thus, somme for her propirtees and somme by statutes of lordes Arabiens, somme by othre lordes of Rome. Eke of these monthes, as liked to Julius Cesar and to Cesar Augustus, somme were compouned of diverse nombres of daies, as Julie and August. Than hath Januarie 31 daies, Februarie 28, March 31, Aprill 30, May 31, Junius 30, Julius 31, Augustus 31, September 30, October 31, November 30, December 31. Natheles, all though that Julius Cesar toke 2 daies out of Feverer and putte hem in his month of Juyll, and Augustus Cesar clepid the month of August after his name and ordeined it of 31 daies, yit truste wel that the sonne dwellith therfore nevere the more ne lasse in oon signe than in another.

11. Than folewen the names of the holy daies in the Kalender, and next hem the lettres of the A B C on whiche thei fallen.

12. Next the forseide cercle of the A B C, under the cross lyne, is marked the skale in manere of 2 squyres, or ellis in manere of laddres, that serveth by his 12 pointes and his dyvisiouns of ful many a subtil conclusioun. Of this forseide skale fro the cross lyne unto the verrey angle is clepid Umbra Versa, and the nethir partie is clepid Umbra Recta, or ellis Umbra Extensa.

13. Than hast thou a brod reule, that hath on either ende a square plate perced with certein holes, somme more and somme lasse, to resceyve the stremes of the sonne by day, and eke by mediacioun of thin eye to knowe the altitude of sterres by night.

14. Than is there a large pyn in manere of an extre, that goth thorugh the hole that halt the tables of the clymates and the riet in the wombe of the moder; thorugh which pyn ther goth a litel wegge, which that is clepid the hors, that streynith all these parties to-hepe. Thys forseide grete pyn in manere of an extre is ymagyned to be the Pool Artik in thyn Astralabie.

15. The wombe syde of thyn Astrelabie is also divided with a longe croys in 4 quarters from est to west, fro southe to northe, fro right syde to left side, as is the bakside.

16. The bordure of which wombe side is divided fro the point of the est lyne unto the point of the south lyne under the ring, in 90 degrees; and by that same proporcioun is every quarter divided, as is the bakside. That amountith 360 degrees. And understondwel that degres of this bordure ben aunswering and consentrike to the degrees of the equinoxiall, that is dividid in the same nombre as every lo othir cercle is in the highe hevene. This same bordure is divided also with 23 lettres capitals and a small crosse (+) above the south lyne, that shewith the 24 houres equals of the clokke. And, as I have seid, 5 of these degres maken a myle wey, and 3 milewei maken an houre. And every degre ot thys bordure contenith 4 minutes, and every minute 60 secundes. Now have I told the twyes.

17. The plate under the riet is discrived with 3 principal cercles, of whiche the leest is clepid the cercle of Cancre by cause that the heved of Cancre turnith evermo consentrik upon the same cercle. In this heved of Cancer is the grettist declinacioun northward of the sonne, and therfore is he clepid solsticium of somer; which declinacioun, after Ptholome, is 23 degrees and 50 minutes as wel in Cancer as in lo Capricorn. This signe of Cancer is clepid the tropik of somer, of tropos, that is to seien " ageynward. " For than beginneth the sonne to passen from us-ward.

The myddel cercle in wydnesse, of these 3, is clepid the cercle equinoxiall, upon which turnith evermo the hevedes of Aries and Libra. And understond wel that evermo thys cercle equinoxiall turnith justly from verrey est to verrey west as I have shewed the in the speer solide. This same cercle is clepid also Equator, that is the weyer of the day- for whan the sonne is in the hevedes of Aries and Libra, than ben the dayes and the nightes ylike of lengthe in all the world. And therfore ben these 2 signes called the equinoxiis. And all that moeveth withinne the hevedes of these Aries and Libra, his moevyng is clepid north- ward; and all that moevith withoute these hevedes, his moevyng is clepid southward, as fro the equinoxiall. Tak kep of these latitudes north and south, and forget it nat. By this cercle equinoxiall ben considred the 24 houres of the clokke; for evermo the arisyng of 15 degrees of the equinoxiall makith an houre equal of the clokke. This equinoxiall is clepid the gurdel of the first moeving, or ellis of the first moevable. And note that the first moevyng is clepid moevyng of the first moevable of the 8 speer, which moeving is from est into west, and eft ageyn into est. Also it is clepid girdel of the first.moeving for it departith the first moevable, that is to seyn the spere. in two llke partyes evene distantz fro the poles of this world.

The widest of these 3 principale cercles is clepid the cercle of Capricorne, by cause that the heved of Capricorne turneth evermo consentrik upon the same cercle. In the heved of this forseid Capricorne is the grettist declinacioun southward of the sonne, and therfore it is clepid the solsticium of wynter. This signe of Capricorne is also clepid the tropic of wynter, for than begynneth the sonne to come ageyn to us- ward.

18. Upon this forseide plate ben compassed certeyn cercles that highten almycanteras, of whiche somme of hem semen parfit cercles and somme semen inparfit. The centre that stondith amyddes the narwest cercle is clepid the cenyth. And the netherist cercle, or the first cercle, is clepid the orizonte, that is to seyn, the cercle that divideth the two emysperies, that is, the partie of the lo hevene above the erthe and the partie bynethe. These almykanteras ben compowned by 2 and 2, all be it so that on diverse Astrelabies somme almykanteras ben divided by oon, and somme by two, and somme by thre, after the quantite of the Astrelabie. This forseide cenyth is ymagined to ben the verrey point over the crowne of thin heved. And also this cenyth is the verray pool of the ori- zonte in every regioun.

19. From this cenyth, as it semeth, there comen a maner croked strikes like to the clawes of a loppe, or elles like the werk of a wommans calle, in kervyng overthwart the almykanteras And these same strikes or divisiouns ben clepid azimutz, and thei dividen the orisounte of thin Astrelabie in 24 divisiouns. And these azymutz serven to knowe the costes of the firmament, and to othre conclusions, as for to knowe the cenyth of the sonne and of every sterre.

20. Next these azymutz, under the cercle of Cancer, ben there 12 divisouns embelif, muche like to the shap of the azemutz, that shewen the spaces of the hollres of planetes.

21. The riet of thin Astrelabie with thy zodiak, shapen in manere of a net or of a lopwebbe after the olde descripcioun, which thou maist turnen up and doun as thiself liketh, contenith certein nombre of sterres fixes, with her longitudes and latitudes determinat, yf so be that the maker have not errid. The names of the sterres ben writen in the margyn of the riet there as thei sitte, of whiche sterres lo the smale point is clepid the centre. And understond also that alle the sterres sitting within the zodiak of thin Astrelabie ben clepid sterres of the north, for thei arise by northe the est lyne. And all the remenaunt fixed oute of the zodiak ben clepid sterres of the south. But I seie not that thei arisen alle by southe the est lyne; witnesse on Aldeberan and Algomeyse. Generaly understond this rewle, that thilke sterres that ben clepid sterres of the north arisen rather than the degre of her longitude, and alle the sterres of the south arisen after the degre of her longitude - this is to seyn, sterres fixed in thyn Astrelabie. The mesure of the longitude of sterres is taken in the lyne ecliptik of hevene, under which lyne, whan that the sonne and the mone be lyne-right, or ellis in the superficie of this lyne, than is the eclipse of the sonne or of the mone, as I shal declare, and eke the cause why. But sothly the ecliptik lyne of thy zodiak is the utterist bordure of thy zodiak there the degrees be marked.

Thy zodiak of thin Astrelabie is shapen as a compas which that contenith a large brede as after the quantite of thyn Astrelabie, in ensample that the zodiak in hevene is ymagyned to ben a superfice contenyng a latitude of 12 degrees, whereas alle the remenaunt of cercles in the hevene ben ymagyned verrey Iynes withoute eny latitude. Amiddes this celestial zodiak is ymagined a lyne which that is clepid the ecliptik lyne, under which lyne is evermo the wey of the sonne. Thus ben there 6 degres of the zodiak on that oo syde of the lyne and 6 degrees on that othir. This zodiak is dividid in 12 principale divisiouns that departen the 12 signes, and, for the streitnesse of thin Astrolabie, than is every smal divisoun in a signe departed by two degrees and two! I mene degrees contenyng 60 mynutes. And this forseide hevenysshe zodiak is clepid the cercle of the signes, or the cercle of the bestes, for " zodia " in langage of Grek sowneth " bestes " in Latyn tunge. And in the zodiak ben the 12 signes that han names of bestes, or ellis for whan the sonne entrith into eny of tho signes he takith the propirte of suche bestes, or ellis that for the sterres that ben ther fixed ben disposid in signes of bestes or shape like bestes, or elles whan the planetes ben under thilke signes thei causen us by her influence operaciouns and effectes like to the operaciouns of bestes.

And understond also that whan an hot planete cometh into an hot signe, than encrescith his hete; and yf a planete be cold, than amenusith his coldnesse by cause of the hoote sygne. And by thys conclusioun maist thou take ensample in alle the signes, be thei moist or drie, or moeble or fixe, reknyng the qualite of the planete as I first seide. And everich of these 12 signes hath respect to a certeyn parcel of the body of a man, and hath it in governaunce; as Aries hath thin heved, and Taurus thy nekke and thy throte, Gemini thin armholes and thin armes, and so furth, as shall be shewid more pleyn in the 5 partie of this tretis.

This zodiak, which that is part of the speer, over-kervith the equinoxial, and-he over-kervith him ageyn in evene parties; and that oo half declineth so southward; and that othir northward, as pleinly declarith the Tretys of the Speer.

Than hast thou a label that is shapen like a reule, save that it is streit and hath no plates on either ende with holes. But with the smale point of the forseide label shalt thou calcule thin equaciouns in the bordure of thin Astralabie, as by thin almury.

Thin almury is clepid the denticle of Capricorne, or ellis the calculer. This same almury sitt fix in the heved of Capricorne, and it serveth of many a necessarie conclusioun in equacions of thinges as shal be shewid.

Here endith the descripcioun of the Astrelabie and here begynne the conclusions of the Astrelabie.

Part II
1. To fynde the degre in which the sonne is day by day, after his cours aboute. Rekne and knowe which is the day of thy month, and ley thy rewle up that same day, and than wol the verrey poynt of thy rewle sitten in the bordure upon the degre of thy sonne.

Ensample as thus: -The yeer of oure Lord 1391, the 12 day of March at midday, I wolde knowe the degre of the sonne. I soughte in the bakhalf of myn Astrelabie and fond the cercle of the daies, lo the whiche I knowe by the names of the monthes writen under the same cercle. Tho leyde I my reule over this forseide day, and fond the point of my reule in the bordure upon the firste degre of Aries, a litel within the degre. And thus knowe I this conclusioun.

Anothir day I wolde knowen the degre of my sonne, and this was at midday in the 13 day of December. I fond the day of the month in manere as I seide; tho leide I my rewle upon this forseide 13 day, and fond the point of my rewle in the bordure upon the firste degre of Capricorne a lite within the degre. And than had I of this conclusioun the ful experience.

2. To knowe the altitude of the sonne or of othre celestial bodies.

Put the ryng of thyn Astrelabie upon thy right thombe, and turne thi lift syde ageyn the light of the sonne; and remewe thy rewle up and doun til that the stremes of the sonne shine thorugh bothe holes of thi rewle. Loke than how many degrees thy rule is areised fro the litel crois upon thin est lyne, and tak there the altitude of thi sonne. And in this same wise maist thow knowe by night the alti- tude of the mone or of brighte sterres.

This chapitre is so generall evere in oon that there nedith no more declaracioun; but forget it not.

3. To knowe every tyme of the day by light of the sonne; and every tyme of the nyght by the sterres fixe; and eke to knowe by nyght or by day the degre of eny signe that ascendith on the est orisonte, which that is clepid comounly the ascendent, or ellis horoscopum.

Tak the altitude of the sonne whan the list, as I have seid, and set the degre of the sonne, in caas that it be beforn the myddel of the day, among thyn almykanteras on the est syde of thin Astrelabie; and if it be after the myddel of the day, set the degre of thy sonne upon the west syde. Take this manere of settyng for a general rule, ones for evere. And whan thou hast set the degre of thy sonne upon as lo many almykanteras of height as was the altitude of the sonne taken by thy rule, ley over thi label upon the degre of the sonne; and than wol the point of thi labell sitte in the bordure upon the verrey tyde of the day.

Ensample as thus: -The yeer of oure lord 1391, the 12 day of March, I wolde knowe the tyde of the day. I tok the altitude of my sonne, and fond that it was 25 degrees and 30 of minutes of height in the bordure on the bak side. Tho turned I myn Astrelabye, and by cause that it was beforn mydday, I turned my riet and sette the degre of the sonne, that is to seyn the first degre of Aries, on the right side of myn Astrelabye upon 25 degrees and 30 mynutes of height among myn almykanteras. Tho leide I my label upon the degre of my sonne, and fond the point of my label in the bordure upon a capital lettre that is clepid an X. Tho rekned I alle the capitale lettres fro the lyne of mydnight unto this forseide lettre X, and fond that it was 9 of the clokke of the day. Tho loked I doun upon the est orizonte, and fond there the 20 degre of Geminis ascendyng, which that I tok for myn ascendent. And in this wise had I the experience for evermo in which manere I shulde knowe the tyde of the day and eke myn ascendent.

Tho wolde I wite the same nyght folewyng the houre of the nyght, and wroughte in this wise: - Among an heep of sterres fixe it liked me for to take the altitude of the faire white sterre that is clepid Alhabor, and fond hir sittyng on the west side of the lyne of midday, 12 degrees of heighte taken by my rewle on the bak side. Tho sette I the centre of this Alhabor upon 12 degrees among myn almykanteras upon the west side, by cause that she w as founde on the west side. Tho leyde I my label over the degre of the sonne, that was discendid under the west orisounte, and rekned all the lettres capitals fro the lyne of midday unto the point of my Iabel in the bordure, and fond that it was passed 9 of the c lokke the space of 10 degrees. Tho lokid I doun upon myn est orisounte, and fond there 10 degrees of Scorpius ascendyng, whom I tok for myn ascendent. And thus lerned I to knowe onys for evere in which manere I shuld come to the houre of the nyght, and to myn ascendent, as verrely as may be taken by so smal an instrument.

But natheles this rule in generall wol I warne the for evere: - Ne make the nevere bold to have take a just ascendent by thin Astrelabie, or elles to have set justly a clokke, whan eny celestial body by which that thou wenyst governe thilke thinges be nigh the south Iyne. For trust wel, whan the sonne is nygh the meridional lyne, the degre of thc sonne renneth so longe consentrik upon the almykanteras that sothly thou shalt erre fro the just ascendent. The same conclusion sey I by the centre of eny sterre fix by nyght. And more over, by experience I wot wel that in our orisounte, from xi of the clokke unto oon of the clokke, in taking of a just ascendent in a portatif Astrelabie it is to hard to knowe - I mene from xi of the clokke before the houre of noon til oon of the clokke next folewyng.

4. A special declaracioun of the ascendent.

The ascendent sothly, as wel in alle nativites as in questions and eleccions of tymes, is a thing which that these astrologiens gretly observen. Wherfore me semeth convenyent, syth that I speke of the ascendent, to make of it speciall declaracioun.

The ascendent sothly, to take it at the largest, is thilke degre that ascendith at eny of these forseide tymes upon the est orisounte. And therfore, yf that eny planete ascende at thatt same tyme in thilke forseide degre, than hath he no latitude fro the ecliptik lyne, but he is than in the degre of the ecliptik which that is the degre of his longitude. Men sayn that thilke planete is in horoscopo.

But sothly the hous of the ascendent, that is to seyn, the first hous or the est angle, is a thing more brod and large. For, after the statutes of astrologiens, what celestial body that is 5 degrees above thilke degre that ascendith, or withinne that nombre, that is to seyn neer the degree that ascendith, yit rekne they thilke planete in the ascendent. And what planete that is under thilke degre that ascendith the space of 25 degres, yit seyn thei that thilke planete is "like to him that is the hous of the ascendent." But sothly, if he passe the boundes of these forseide spaces, above or bynethe, thei seyn that the planete is "fallyng fro the ascendent." Yit saien these astrologiens that the ascendent and eke the lord of the ascendent may be shapen for to be fortunat or infortunat, as thus: - A "fortunat ascendent " clepen they whan that no wicked planete, as Saturne or Mars or elles the Tayl of the Dragoun, is in the hous of the ascendent, ne that no wicked planete have noon aspect of enemyte upon the ascendent. But thei wol caste that thei have a fortunat planete in hir ascendent, and yit in his felicite; and than sey thei that it is wel. Further over thei seyn that the infortunyng of an ascendent is the contrarie of these forseide thinges. The lord of the ascendent, sey thei that he is fortunat whan he is in god place fro the ascendent, as in an angle, or in a succident where as he is in hys dignite and comfortid with frendly aspectes of planetes and wel resceyved; and eke that he may seen the ascendent; an that he be not retrograd, ne combust, ne joyned with no shrewe in the same signe; ne that he be not in his discencioun, ne joyned with no planete in his descencioun, ne have upon him noon aspect infortunat; and than sey thei that he is well.

Natheles these ben observaunces of judicial matere and rytes of payens, in whiche my spirit hath no feith, ne knowing of her horoscopum. For they seyn that every signe is departid in thre evene parties by 10 degrees, and thilke porcioun they clepe a face. And although that a planete have a latitude fro the ecliptik, yit sey somme folk, so that the planete arise in that same signe with eny degre of the forseide face in which his longitude is rekned, that yit is the planete in horoscopo, be it in nativyte or in eleccion, etc.

5. To knowe the verrey equacioun of the degre of the sonne yf so be that it falle bitwene two almykanteras.

For as muche as the almykanteras in thin Astrelabie ben compowned by two and two, where as somme almykanteras in sondry astrelabies be compowned by 1 and 1, or elles by 3 and 3, it is necessarie to thy lernyng to teche the first to knowe and worke with thin owne instrument. Wherfore whan that the degre of thi sonne fallith bytwixe 2 almykanteras, or ellis yf thin almykanteras ben graven with over-gret a poynt of a compas (for bothe these thinges may causen errour as wel in knowing of the tide of the day, as of the verrey ascendent), thou must worken in this wise: -

Set the degre of thy sonne upon the hyer almykanteras of bothe, and wayte wel where as thin almury touchith the bordure and set there a prikke of ynke. Sett doun agayn the degre of the sunne upon the nether almykanteras of bothe, and sett there another pricke. Remeve than thin almury in the bordure evene amiddes bothe prickes, and this wol lede justly the degre of thi sonne to sitte atwixe bothe almykanteras in his right place. Ley than thy label over the degre of thi sonne, and fynd in the bordure the verrey tyde of the day, or of the night. Andasverrailyshaltthoufynde upon thin est orisonte thin ascendent.

6. To knowe the spryng of the dawenyng and the ende of the evenyng, the whiche ben called the two crepuscules.

Set the nadir of thy sonne upon 18 degrees of height among thyn almykanteras on the west syde; and ley thy label on the degre of thy sonne, and than shal the point of thy label shewen the spryng of the day. Also set the nader of thy sonne upon 18 degrees of height among thin almykanteras on the est side, and ley over thy lahel upon the degre of the sonne, and with the point of thy label fynd in the bordure lo the ende of the evenyng, that is verrey nyght.

The nader of the sonne is thilke degre that is opposyt to the degre of the sonne, in the 7 signe, as thus: - every degre of Aries by ordir is nadir to every degre of Libra by ordre, and Taurus to Scorpioun, Gemini to Sagittarie, Cancer to Capricorne, Leo to Aquarie, Virgo to Pisces. And if eny degre in thy zodiak be derk, his adir shal declare hym.

7. To knowe the arch of the day, that sorne folk callen the day artificiall, fro sonne arisyng tyl it go to reste.

Set the degre of thi sonne upon thin est DriSonte and ley thy label on the degre of the sonne, and at the point of thy label in the bordure set a pricke. Turne than thy riet aboute tyl the degre of thy sonne sitte upon the west orisonte, and ley thy label upon the same degre of the sonne, and at the poynt of thy label set there another pricke. Rekne than the quantite of tyme in the bordure bitwixe bothe prickes, and tak there thyn arch of the day. The remenaunt of the bordure under the orisonte is the arch of the nyght. Thus maist thou rekne bothe arches, or every porcioun, of whether that the liketh. And by this manere of worching maist thou se how longe that eny sterre fix dwelleth above the erthe, fro tyme that he riseth til he go to reste. But the day naturall that is to seyn 24 houres, is the revolu- cioun of the equinoxial with as muche partie of the zodiak as the sonne of his propre moeving passith in the mene while.

8. To turne the houres inequales in houres equales.

Know the nombre of the degrees in the houres inequales, and depart hem by 15, and tak there thin houres equales.

9. To knowe the quantite of the day vulgar, that is to seyn fro spryng of the day unto verrey nyght.

Know the quantite of thy crepuscles, as I have taught in the 2 chapitre bifore, and adde hem to the arch of thy day artificial, and tak there the space of all the hool day vulgar unto verrey night. The same manere maist thou worche to knowe the quantite of the vulgar nyght.

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

Understond wel that these houres inequales ben clepid houres of planetes. And understond wel that som tyme ben thei lenger by day than by night, and som tyme the contrarie. But understond wel that evermo generaly the houre inequal of the day with the houre inequal of the night contenen 30 degrees of the bordure, which bordure is evermo answeryng to the degrees of the equinoxial. Wherfore departe the arch of the day artificial in 12, and tak there the quantite of the houre inequale by day. And if thou abate the quantite of the houre inequale by day out of 30, than shal the remenaunt that levith parforme the houre inequale by night.

11. To knowe the quantite of houres equales.

The quantite of houres equales, that is to seyn the houres of the clokke, ben departid by 15 degrees alredy in the bordure of thin Astrelaby, as wel by night as by day, generaly for evere. What nedith more declaracioun?

Wherfore whan the list to knowe how many houres of the clokke ben passed, or eny part of eny of these houres that ben passed, or ellis how many houres lo or parties of houres ben to come fro such a tyme to such a tyme by day or by night, know the degre of thy sonne, and ley thy label on it. Turne thy ryet aboute joyntly with thy label, and with the poynt of it rekne in the bordure fro the sonne ariste unto that same place there thou desirist, by day as by nyght. This conclusioun wol I declare in the last chapitre of the 4 partie of this tretys so openly that ther shal lakke no word that nedith to the declaracioun.

12. Special declaracioun of the houres of planetes.

Understond wel that evermo, fro the arisyng of the sonne til it go to reste, the nadir of the sonne shal shewe the houre of the planete; and fro that tyme forward al the night til the sonne arise, than shal the verrey degre of the sonne shewe the houre of the planete.

Ensample as thus: -The xiij day of March fyl upon a Saturday, peraventure, and atte risyng of the sonne I lo fond the secunde degre of Aries sittyng upon myn est orisonte, all be it that it was but litel. Than fond I the 2 degre of Libra, nadir of my sonne, discending on my west orisonte, upon which west orisonte every day generaly, atte sonne arist, entrith the houre of every planete, after which planete the day berith his name, and endith in the next strike of the plate under the forseide west orisonte. And evere as the sonne clymbith upper and upper, so goth his nadir downer and downer, teching by suche strikes the houres of planetes by ordir as they sitten in the hevene. The firste houre inequal of every Saturday is to Saturne, and the seconde to Jupiter, the thirde to Mars, the fourthe to the sonne, the fifte to Venus, the sixte to Mercurius, the seventhe to the mone. And then ageyn the 8 houre is to Saturne, the 9 is to Jupiter, the 10 to Mars, the 11 to the sonne, the 12 to Venus. And now is my sonne gon to reste as for that Saturday. Than shewith the verrey degre of the sonne the houre of Mercurie entring under my west orisonte at eve; and next hilr succedith the mone, and so furth by ordir planete after planete in houre after houre, all the nyght longe til the sonne arise. Now risith the sonne that Sonday by the morwe, and the nadir of the sonne upon the west orisonte shewith me the entring of the houre of the forseide sonne. And in this manere succedith planete under planete fro Saturne unto the mone, and fro the mone up ageyn to Saturne, houre after houre generaly. And thus have I this conclusyoun.

13. To knowe the altitude of the sonne in myddes of the day that is clepid the altitude meridian.

Set the degre of the sonne upon the lyne meridional, and rekne how many degrees of almykanteras ben bitwyxe thin est orisonte and the degre of thy sonne; and tak there thin altitude meridian, this to seyn, the highest of the sonne as for that day. So maist thou knowe in the same lyne the heighest cours that eny sterre fix clymbeth by night. This is to seyn that whan eny sterre fix is passid the lyne merid- ional, than begynneth it to descende; and so doth the sonne.

14. To knowe the degre of the sonne by thy ryet, for a maner curiosite.

Sek besily with thy rule the highest of the sonne in mydde of the day. Turne than thin Astrelabie, and with a pricke of ynke marke the nombre of that same altitude in the lyne meridional; turne than thy ryet aboute tyl thou fynde a degre of thy zodiak according with the pricke, this is to seyn, sitting on the pricke. And in soth thou shalt finde but 2 degrees in all the zodiak of that condicioun; and yit lo thilke 2 degrees ben in diverse signes. Than maist thou lightly, by the sesoun of the yere, knowe the signe in which that is the sonne.

15. To knowe which day is lik to which day as of lengthe.

Loke whiche degrees ben ylike fer fro the hevedes of Cancer and Capricorne, and loke when the sonne is in eny of thilke degrees; than ben the dayes ylike of lengthe. This is to seyn that as longe is that day in that month, as was such a day in such a month- there varieth but litel.

Also, yf thou take 2 dayes naturales in the yere ylike fer fro either point of the equinoxiall in the opposyt parties, than as longe is the day artificiall of that oon day as is the night of that othir, and the contrarie.

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

Understond wel that thy zodiak is departed in two halve circles, as fro the heved of Capricorne unto the heved of Cancer, and ageynward fro the heved of Cancer unto the heved of Capricorne. The heved of Capricorne is the lowest point where as the sonne goth in wynter, and the heved of Cancer is the heighist point in which the sonne goth in somer. And therfore understond wel that eny two degrees lo that ben ylike fer fro eny of these two hevedes, truste wel that thilke two degrees hen of ilike declinacioun, be it southward or northward, and the daies of hem ben ilike of lengthe and the nyghtes also, and the shadewes ilyke, and the altitudes ylike atte midday for evere.

17. To knowe the verrey degre of eny maner sterre, straunge or unstraunge, after his longitude; though he be indetermynat in thin Astralabye, sothly to the trouthe thus he shal be knowe.

Tak the altitude of this sterre whan he is on the est syde of the lyne meridionall, as neigh as thou mayst gesse; and tak an ascendent anon right by som manere sterre fix which that thou knowist; and forget not the altitude of the firste sterre ne thyn ascendent. And whan that this is don, aspye diligently whan this same firste sterre passith eny thyng the south westward; and cacche him anon right in the same nombre of altitude on the west syde of this lyne meridional, as he was kaught on the est syde; and tak a newe ascendent anon-ryght by som manere sterre fix which that thou knowist, and forget not this secunde ascendent. And whan that this is don, rekne than how many degrees ben bitwixe the first ascendent and the secunde ascendent; and rekne wel the myddel degre bitwene bothe ascendentes, and set thilke myddel degre upon thyn est orizonte; and wayte than what degre that sitte upon the Iyne meridional, and tak there the verrey degre of the ecliptik in which the sterre stondith for the tyme. For in the ecliptik is the longitude of a celestiall body rekned, evene fro the heved of Aries unto the ende of Pisces; and his latitude is rekned after the quantite of his declynacioun north or south toward the polys of this world.

As thus: -Yif it be of the sonne or of eny fix sterre, rekne hys latitude or his declinacioun fro the equinoxiall cercle; and if it be of a planete, rekne than the quantite of his latitude fro the ecliptik lyne, all be it so that fro the equinoxiall may the declinacioun or the latitude of eny body celestiall be rekned after the site north or south and after the quantite of his declinacioun. And right so may the latitude or the declinacioun of eny body celestiall, save oonly of the sonne, after hys site north or south and after the quantite of his declinacioun. be rekned fro the ecliptik lyne; fro which lyne alle planetes som tyme declinen north or south save oonly the forseide sonne.

18. To knowe the degrees of longitudes of fixe sterres after that they be determynat in thin Astrelabye, yf so be that thei be trewly sette.

Set the centre of the sterre upon the lyne meridionall, and tak kep of thy zodiak, and loke what degre of eny signe that sitte upon the same lyne meridionall at that same tyme, and tak there the degre in which the sterre stondith; and with that same degre cometh that same sterre unto that same lyne fro the orisonte.

19. To knowe with which degre of the zodiak eny sterre fix in thin Astrelabie arisith upon the est orisonte, all though his dwellyng be in another signe.

Set the centre of the sterre upon the est orisonte, and loke what degre of eny signe that sitt upon the same orisonte at that same tyme. And understond wel that with that same degre arisith that same sterre.

And thys merveylous arisyng with a straunge degre in another signe is by cause that the latitude of the sterre fix is either north or south fro the equi- noxiall. But sothly the latitudes of planetes be comounly rekened fro the ecliptyk, by cause that noon of hem declyneth but fewe degrees out fro the brede of the zodiak. And tak god kep of this chapitre of arisyng of celestialle bodies; for truste wel that neyther mone ne sterre, as in our embelif orisonte, arisith with that same degre of his longitude save in oo cas, and that is whan they have no latitude fro the ecliptyk lyne. But natheles som tyme is everich of these planetes under the same lyne.

20. To knowe the declinacioun of eny degre in the zodiak fro the equinoxiall cercle.

Set the degre of eny signe upon the lyne meridionall, and rekne hys altitude in the almykanteras fro the est orisonte up to the same degre set in the forseide lyne, and set there a prikke; turne up than thy riet, and set the heved of Aries or Libra in the same meridionall lyne, and set there a nother prikke. And whan that this is don, considre the altitudes of hem bothe; for sothly the difference of thilke alti- tudes is the declinacioun of thilke degre fro the equinoxiall. And yf it so be that thilke degre be northward fro the equinoxiall, than is his declinacyoun north; yif it be southward, than is it south.

21. To knowe for what latitude in eny regioun the almykanteras of eny table ben com powned .

Rekene how many degrees of almykanteras in the meridionall lyne ben fro the cercle equinoxiall unto the cenyth, or elles from the pool artyk unto the north orisonte; and for so gret a latitude, or for so smal a latitude, is the table compowned.

22. To know in speciall the latitude of oure countre, I mene after the latitude of Oxenford, and the height of oure pool.

Understond wel that as fer is the heved of Aries or Libra in the equinoxiall fro oure orisonte as is the cenyth fro the pool artik; and as high is the pool artik fro the orisonte as the equinoxiall is fer fro the cenyth. I prove it thus by the latitude of Oxenford: understond wel that the height of oure pool artik fro oure north orisonte is 51 degrees and 50 mynutes; than is the cenyth fro oure pool artik 38 degrees and 10 mynutes; than is the equinoxial from oure cenyth 51 degrees and 50 mynutes; than is oure south orisonte from oure equinoxiall 38 degres and 10 mynutes. Understond wel this rekenyng. Also forget not that the cenyth is 90 degrees of height from oure orisonte, and oure equinoxiall is 90 degres from oure pool artik. Also this shorte rule is soth, that the latitude of eny place in a regioun is the distaunce fro the cenyth unto the equinoxiall.

23. To prove evidently the latitude of eny place in a regioun by the preve of the height of the pool artik in that same place.

In som wynters nyght whan the firmament is cler and thikke sterred, wayte a tyme til that eny sterre fix sitte lyne-right perpendiculer over the pool artik, and clepe that sterre A; and wayte another sterre that sitte lyne right under A, and under the pool, and clepe that sterre F. And understond wel that F is not considrid but oonly to declare that A sitte evene over the pool. Tak than anoon-right the altitude of A from the orisonte, and forget it not; let A and F goo fare wel tyl ageynst the dawenyng a gret while, and com than ageyn, and abid til that A is evene under the pool, and under F, for sothly than wol F sitte over the pool, and A wol sitte under the pool. Tak than eftsonys the altitude of A from the orisonte, and note as wel his secunde altitude as hys first altitude. And whan that this is doon, rekene how many degrees that the first altitude of A excedith his secunde altitude, and tak half thilke porcioun that is excedid and adde it to his secunde altitude, and tak there the elevacioun of thy pool, and eke the latitude of thyregioun; for these two ben of oo nombre, this is to seyn, as many degres as thy pool is elevat, so muche is the latitude of the regioun.

Ensample as thus: - peraventure the altitude of A in the evenyng is 56 degrees of height; than wol his secunde altitude or the dawenyng be 48 degres that is 8 degrees lasse than 56, that was his first altitude att even. Tak than the half of 8 and adde it to 48 that was his secunde altitude, and than hast thou 52. Now hast thou the height of thy pool and the latitude of the regioun. But understond wel that to prove this con- clusioun and many another faire conclusioun, tholu must have a plomet hangyng on a lyne, heygher than thin heved, on a perche; and thilke lyne must hange evene perpendiculer bytwixe the pool and thin eye; and than shalt thou seen yf A sitte evene over the pool, and over F atte evene; and also yf F sitte evene over the pool and over A or day.

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

Tak eny sterre fix that never discendith under the orisonte in thilke regioun, and considre his heighist altitude and his lowist altitude fro the orisonte, and make a nombre of bothe these altitudes; tak than and abate half that nombre, and tak there the elevacioun of the pool artik in that same regioun.

25. Another conclusioun to prove the latitude of the regioun.

Understond wel that the latitude of eny place in a regioun is verrely the space bytwexe the cenyth of hem that dwellen there and the equinoxiall cercle north or south, takyng the mesure in the meridional Iyne, as shewith in the almykanteras of thin Astrelabye. And thilke space is as much as the pool artike is high in that same place fro the orisonte. And than is the depressioun of the pool antartik, that is to seyn, than is the pool antartik, bynethe the orisonte the same quantite of space neither more ne lasse.

Than if thou desire to knowe this latitude of the regioun, tak the altitude of the sonne in the myddel of the day, whan the sonne is in the hevedes of Aries or of Libra; for than moeveth the sonne in the lyne equinoxiall; and abate the nombre of that same sonnes altitude out of 90 degrees, and than is the remenaunt of the nombre that leveth the latitude of that regioun. As thus: - I suppose that the sonne is thilke day at noon 38 degrees of height; abate than 38 oute of 90; so leveth there 52; than is 52 degrees the latitude. I say not this but for ensample; for wel I wot the latitude of Oxenford is certeyn minutes lasse, as thow might preve.

Now yf so be that the semeth to longe a tarieng to abide til that the sonne be in the hevedes of Aries or of Libra, than wayte whan the sonne is in eny othir degre of the zodiak, and considre the degre of his declinacioun fro the equinoxiall lyne; and if it so be that the sonnes declinacioun be northward fro the equinoxiall, abate than fro the sonnes altitude at non the nombre of his declinacioun, and than hast thou the height of the hevedes of Aries and Libra. As thus: -My sonne is peraventure in the first degre of Leoun, 58 degrees and 10 minutes of height at non, and his declinacioun is almost 20 degrees northward fro the equinoxiall; abate than thilke 20 degrees of declinacioun out of the altitude at non; than leveth there 38 degrees and odde minutes. Lo there the heved of Aries or Libra and thin equinoxiall in that regioun. Also if so be that the sonnes declinacioun be southward fro the equinoxiall, adde than thilke declinacioun to the altitude of the sonne at noon, and tak there the hevedes of Aries and Libra and thin equinoxial; abate than the height of the equinoxial out of 90 degrees; than leveth there the distance of the pool of that regioun fro the equinoxiall. Or elles, if the list, tak the highest altitude fro the equinoxial of eny sterre fix that thou knowist, and tak the netherest elongacioun (lengthing) fro the same equinoxial lyne, and work in the manere forseid.

26. Declaracioun of the ascensioun of signes.

The excellence of the spere solide, amonges othir noble conclusiouns, shewith manyfest the diverse ascenciouns of signes in diverse places, as wel in the right cercle as in the embelif cercle. These auctours writen that thilke signe is cleped of right ascensioun with which more part of the cercle equinoxiall and lasse part of the zodiak ascendith- and thilke signe ascendith embelif with which lasse part of the equinoxiall and more part of the zodiak ascendith. Ferther-over they seyn that in thilke cuntrey where as the senith of hem that dwellen there is in the equinoxial lyne, and her orisonte passyng by the two poles of this world, thilke folk han this right cercle and the right orisonte; and evermore the arch of the day and the arch of the night is there ilike longe- and the sonne twies every yer passing thorugh the cenith of hir heed, and two someres and two wynters in a yer han these forseide peple. And the almycanteras in her Astrelabyes ben streight as a lyne, so as it shewith in the figure.

The utilite to knowe the ascensions of signes in the right cercle is this: - Truste wel that by mediacioun of thilke ascensions these astrologiens, by her tables and her instrumentes, knowen verreily the ascensioun of every degre and minute in all the zodiak in the embelif cercle, as shal be shewed. And nota that this forseide right orisonte, that is clepid Orison Rectum, dividith the equinoxial into right angles; and the embelif orisonte where as the pool is enhaunced upon the orisonte, overkervith the equinoxiall in embilif angles, as shewith in the figure.

27. This is the conclusioun to knowe the ascensions of signes in the right cercle, that is circulus directus.

Set the heved of what signe the lyst to knowe his ascendyng in the right cercle upon the lyne meridionall, and wayte where thyn almury touchith the bordure, and set there a prikke; turne than thy riet westward til that the ende of the forseide signe sitte upon the meridional lyne and eftsonys wayte where thin almury touchith the bordure, and set there another pricke. Rekene than the nombre of degres in the bordure bitwixe bothe prikkes, and tak the ascensioun of the signe in the right cercle. And thus maist thou werke with every porcioun of thy zodiak.

28. To knowe the ascensions of signes in the embelif cercle in every regioun, I mene, in circulo obliquo.

Set the heved of the signe which as the list to knowe his ascensioun upon the est orisonte, and wayte where thin almury touchith the bordure, and there set a prikke. Turne than thy riet upward til that the ende of the same signe sitte upon the est orisonte, and wayte eftsonys where as thin almury touchith the bordure, and set there a nother prikke. Rekene than the nombre of degrees in the bordure bitwyxe bothe prikkes and tak there the ascensioun of the signe in the embelif cercle. And understond wel that alle the signes in thy zodiak, fro the heved of Aries unto the ende of Virgo, ben clepid signes of the north fro the equinoxiall. And these signes arisen bitwyxe the verrey est and the verrey north in oure orisonte generaly for evere. And alle the ignes fro the heved of Libra unto the ende of Pisces ben clepid signes of the south fro the equinoxial; and these signes arisen evermore bitwexe the verrey est and the verrey south in oure orisonte. Also every signe bitwixe the heved of Capricorne unto the ende of Geminis arisith on oure orisonte in lasse than 2 houres equales. And these same signes fro the heved of Capricorne unto the ende of Geminis ben cleped tortuose signes, or croked signes, for thei arise embelyf on oure orisonte. And these croked signes ben obedient to the signes that ben of right ascensioun. The signes of right ascencioun ben fro the heved of Cancer unto the ende of Sagittarie; and these signes arisen more upright, and thei ben called eke sovereyn signes and everich of hem arisith in more space than in 2 houres. Of whiche signes Gemini obeieth to Cancer, and 'raurus to Leo, Aries to Virgo, Pisces to Libra, Aquarius to Scorpioun, and Capricorne to Sagittarie. And thus evermore 2 signes that ben ilike fer fro the heved of Capricorne obeyen everich of hem til othir.

29. To knowe justly the 4 quarters of the world, as Est, West, North, and South.

Tak the altitude of thy sonne whan the list, and note wel the quarter of the world in which the sonne is for the tyme by the azymutz. Turne than thin Astrelabie, &nd set the degre of the sonne in the almykanteras of his altitude on thilke syde that the sonne stant, as is the manere in takyng of houres, and ley thy label on the degre of the sonne; and rekene how many degrees of the bordure ben bitwixe the Iyne meridional and the point of thy label, and note wel that nombre. Turne than ageyn thin Astrelabie, and set the point of thy gret rule there thou takist thin altitudes upon as many degrees in his bordure fro his meridional as was the point of thy label fro the lyne meridional on the wombe side. Take than thin Astrelabie with bothe hondes sadly and slighly, and lat the sonne shyne thorugh bothe holes of thy rule, and slighly in thilke shynyng lat thin Astrelabie kouche adoun evene upon a smothe ground, and than wol the verrey lyne meridional of thin Astrelabie lye evene south, and the est Iyne wol Iye est, and the west Iyne west, and the north lyne north, so that thou worke softly and avysely in the kouching. And thus hast thou the 4 quarters of the firmament.

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

Loke whan that a planete is in the lyne meridional, yf that hir altitude be of the same height that is the degre of the sonne for that day, and than is the planete in the verrey wey of the sonne and hath no latitude. And if the altitude of the planete be heigher than the degre of the sonne, than is the planete north fro the wey of the sonne such a quantite of latitude as shewith by thin almykanteras. And if the altitude of the planete be lasse than the degre of the sonne, than is the planete south fro the wey of the sonne such a quantite of latitude as shewith by thin almykanteras. This is to seyn, fro th(wey where as the sonne went thilke day but not fro the wey of the sonne in every place of the zodiak.

31. To knowe the cenyth of the arising of the sonne, this is to seyn, the partie of the orisonte in which that the sonne arisith.

Thou must first considere that the sonne arisith not alwey verrey est, but somtyme by northe the est and somtyme by south the est. Sothly the sonne arisith nevere moo verrey est in oure orisonte, but he be in the heved of Aries or Libra. Now is thin orisonte departed in 24 parties by thin azimutes in significacioun of 24 parties of the world; al be it so that shipmen rekene thilke parties in 32. Than is there no more but wayte iIl which azimut that thy sonne entrith at his arisyng, and take there the cenith of the arisyng of the sonne.

The manere of the divisioun of thin Astrelabie is this, I mene as in this cas: - First it is divided in 4 plages principalis with the lyne that goth from est to west; and than with another lyne that goth fro south to north; than is it divided in smale parties of azymutz, as est, and est by south, where as is the first azymut above the est lyne; and so furth fro partie to partie til that thou come ageyn unto the est lyne. Thus maist thou understonde also the cenyth of eny sterre, in which partie he riseth.

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

Considere the tyme of the conjunccyoun by the kalender, as thus: - Loke hou many houres thilke conjunccioun is fro the midday of the day precedent, as shewith by the canon of thy kalender. Rekene than thilke nombre of houres in the bordure of thin Astrelabie, as thou art wont to do in knowyng of the houres of the day or of the nyght, and ley thy label over the degre of the sonne, and than wol the point of thy label sitte upon the houre of the conjunccioun. Loke than in which azymut the degre of thy sonne sittith, and in that partie of the firmament is the conjunccioun.

33. To knowe the cenyth of the altitude of the sonne.

This is no more to seyn but eny tyme of the day tak the altitude of the sonne, and by the azymut in which he stondith maist thou seen in which partie of the firmament he is. And in the same wise maist thou seen by night, of eny sterre, whether the sterre sitte est or west, or north or south, or eny partie bitwene, after the name of the azimut in which the sterre stondith.

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

Tak the altitude of the mone, and rekne thy altitude up among thyn almykanteras on which syde that the mone stondith, and set there a prikke. Tak than anon-right upon the mones syde the altitude of eny sterre fix which that thou knowist, and set his centre upon his altitude among thyn almykanteras there the sterre is founde. Wayte than which degre of the zodiak touchith the prykke of the altitude of the mone, and tak there the degre in which the mone stondith. This conclusioun is verrey soth, yf the sterres in thin Astrelabie stonden after the trouthe. Comoun tretes of the Astrelabie ne maken non excepcioun whether the mone have latitude or noon, ne on wheyther syde of the mone the altitude of the sterre fixe be taken.

And nota that yf the mone shewe a himself by light of day, than maist thou worche this same conclusioun by the sonne, as wel as by the fixe sterre.

35. This is the worchynge of the conclusioun to knowe yf that eny planete be direct or retrograd.

Tak the altitude of any sterre that is clepid a planete, and note it wel; and tak eke anon the altitude of any sterre fix that thou knowist, and note it wel also. Com than ageyn the thridde or the fourthe nyght next folewing, for than shalt thou perceyve wel the moeving of a planete, whether so he moeve forward or bakward. Awayte wel than whan that thy sterre fixe is in the same altitude that she was whan thou toke hir firste altitude. And tak than eft-sones the altitude of the forseide planete and note it wel; for truste wel yf so be that the planete be on the right syde of the meridional lyne, so that his secunde altitude be lasse than hys first altitude was, than is the planete direct; and yf he be on the west syde in that condicioun, than is he retrograd. And yf so be that this planete be upon the est side whan his altitude is ytaken, so that his secunde altitude be more than his first altitude, than is he retrograd. And if he be on the west syde, than is he direct. But the contrarie of these parties is of the cours of the mone; for certis the mone moeveth the contrarie from othre planetes as in hir epicicle, but in noon othir manere.

36. The conclusioun of equaciouns of houses after the Astrelabie.

Set the begynnyng of the degre that ascendith upon the ende of the 8 houre inequal; than wol the begynnyng of the 2 hous sitte upon the lyne of mydnight. Remeve than the degre that ascendith, and set him on the ende of the 10 houre inequal, and than wol the begynnyng of the 3 hous sitte up on the mydnight lyne. Bring up ageyn the same degre that ascended first, and set him upon the est orisonte, and than wol the begynnyng of the 4 hous sitte upon the lyne of mydnight. Tak than the nader of the degre that first ascendid, and set him in the ende of the 2 houre inequal; and than wol the begynnyng of the 5 hous sitte upon the Iyne of mydnight. Set than the nader of the ascendent in the ende of the 4 houre inequal, and than wol the begynnyng of the 6 hous sitte on the mydnight lyne. The begynnyng of the 7 hous is nader of the ascendent, and the begynnyng of the 8 hous is nader of the 2 hous, and the begynnyng of the 9 hous is nader of the 3, and the begynnyng of the 10 hous is nader of the 4, and the begynnyng of the 11 hous is nader of the 5, and the begynnyng of the 12 hous is nader of the 6.

37. Another maner of equaciouns of houses by the Astrelabie.

Tak thin ascendent, and than hast thou thy 4 angles; for wel thou wost that the opposit of thin ascendent, that is to seyn, the begynnyng of the 7 hous, sitt upon the west orisonte, and the begynnyng of the hous sitt upon the lyne meridional, and his opposyt upon the lyne of mydnight. Than ley thy label over the degre that ascendith, and rekne fro the point of thy label alle the degrees in the bordure tyl thou come to the meridional lyne; and departe alle thilke degrees in 3 evene parties, and take there the evene equacions of 3 houses; for ley thy label over everich of these 3 parties, and than maist thou se by thy label, lith in the zodiak, the begynnyng of everich of these same houses fro the ascendent; that is to seyn the begynnyng of the 12 hous next above thin ascendent, the begynnyng of the 11 hous, and than the 10 upon the meridional lyne, as I first seide. The same wise worch thou fro the ascendent doun to the lyne of mydnyght, and thus hast thou othre 3 houses; that is to seyn, the begynnyng of the 2, and the 3, and the 4 hous. Than is the nader of these 3 houses the begynnyng of the 3 houses that folewen.

38. To fynde the lyne meridional to dwelle fix in eny certeyn place.

Tak a round plate of metal; for werpyng, the brodder the better; and make there upon a just compas a lite within the bordure. And ley this rounde plate upon an evene ground, or on an evene ston, or on an evene stok fix in the ground; and ley it evene by a level. And in the centre of the compas styke an evene pyn, or a wyr, upright, the smaller the better; set thy pyn by a plom-rule evene upright, and let this pyn be no lenger than a quarter of the dyametre of thy compas, fro the centre amiddes. And wayte bisely aboute 10 or 11 of the clokke, whan the sonne shineth, whan the shadewe of the pyn entrith enythyng within the cercle of thy compas an heer-mele- and marke there a pricke with inke. Abid than stille waityng on the sonne til after 1 of the clokke, til that the shadwe of the wyr, or of the pyn, passe enything out of the cercle of the compas, be it nevere so lyte, and set there another pricke of ynke. Tak than a compas, and mesure evene the myddel bitwixe bothe prickes, and set there a prikke. Tak me than a rule and draw a strike evene a-lyne, fro the pyn unto the middel prikke- and tak there thi lyne mer heved. And it is cleped the lyne meridional, for in what place that eny man ys at any tyme of the yer, whan that the sonne, by mevynge of the firmament, cometh to his verrey meridian place, than is it verrey mydday, that we clepen oure non, as to thilke man. And therefore is it clepid the Iyne of mydday. And nota that evermore of eny 2 cytes or 2 townes, of which that oo town approchith more toward the est than doth that othir town, truste wel that thilke townes han diverse meridians. Nota also that the arch of the equinoxial that is contened or bownded bitwixe the 2 meridians is clepid the longitude of the toun. And yf so be that two townes have ilike meridian or oon meridian, than is the distaunce of hem both ilike fer fro the est, and the contrarie; and in this manere thei change not her meridian. But sothly thei chaungen her almykanteras, for the enhaunsyng of the pool and the distance of the sonne.

The longitude of a climat is a lyne ymagined fro est to west ilike distant fro the equinoxiall. And the latitude of a climat may be cleped the space of the erthe fro the begynnyng of the first clymat unto the verrey ende of the same clymat evene direct ageyns the pool artyke. Thus sayn somme auctours; and somme of hem sayn that yf men clepe the latitude of a cuntrey the arch meridian that is contened or intercept bitwix the cenyth and the equinoxial, than say they that the distance fro the equinoxial unto the ende of a climat evene ageynst the pool artik is the latitude of a clymat forsoothe.

40. To knowe with which degre of the zodiak that eny planete ascendith on the orisonte, whether so that his latitude be north or south.

Know by thin almenak the degre of the ecliptik of eny signe in which that the planete is rekned for to be, and that is clepid the degre of his longitude. And know also the degre of his latitude fro the ecliptik north or south. And by these ensamples folewynge in speciall maist thou worche forsothe in every signe of the zodiak: -

The degree of the longitude per-aventure of Venus or of another planete was 6 of Capricorne, and the latitude of hir was northward 2 degrees fro the ecliptik lyne. Than tok I a subtil compas and clepid that oo point of my compas. and that other point F. Than tok I the point of A and sette it in the ecliptik ]yne in my zodiak in the degre of the longitu(lc of Venus, that is to seyn, in the 6 degre of Capricorne; and than sette I the point of F upward in the same signe by cause that latitude was north upon the latitude of Venus, that is to seyn, in the 6 degre fro the heved of Capricorne; and thus have I 2 degrees bitwixe my two prickes. Than leide I down softly my compas, and sette the degre of the longitude upon the orisonte; tho tok I and waxed my label in manere of a peire tables to receyve distinctly the prickes of my compas. Tho tok I thys forseide label, and leyde it fix over the degre of my longitude; tho tok I up my compas and sette the point of A in the wax on my label, as evene as I koude gesse, over the ecliptik lyne in the ende of the longitude, and sette the point of F endelong in my label upon the space of the latitude, inward and over the zodiak, that is to seyn northward fro the ecliptik. Than leide I doun my compas, and loked wel in the wey upon the prickes of A and of F; tho turned I my ryet til that the pricke of F satt upon the orisonte; than saw I wel that the body of Venus in hir latitude of 2 degrees septemtrionals ascendid, in the ende of the 6 degre, in the heved of Capricorne.

And nota that in this manere maist thou worche with any latitude septem- trional in alle signes. But sothly the latitude meridional of a planete in Capricorne ne may not be take by cause of the litel space bitwixe the ecliptyk and the bordure of the Astrelabie; but sothely in all othre signes it may.

2 pars hujus conclusio.

Also the degre peraventure of Jupiter, or of another planete, was in the first degre of Piscis in longitude, and his latitude was 2 degrees meridional; tho tok I the point of A and sette it in the first degre of Piscis on the ecliptik; and than sette I the point of F dounward in the same signe by cause that the latitude was south 2 degres, that is to seyn, fro the heved of Piscis; and thus have 2 degres bitwexe bothe 66 prikkes. Than sette I the degre of the longitude upon the orisonte; tho tok I my label, and leide it fix upon the degre of the longitude; tho sette I the point of A on my label evene over the ecliptik lyne in the ende of the degre of the longitude, and sette the point of F endlong in my label the space of 2 degres of the latitude outward fro the zodiak (this is to seyn southward fro the ecliptik toward the bor- dure), and turned my riet til that the pricke of F saat upon the orisonte. Than say I wel that the body of Jupiter in his latitude of 2 degres meridional ascendid with 8 degres of Piscis in horoscopo. And in this manere maist thou worche with any latitude meridional, as I first seide, save in Capricorne. And yf thou wilt pleye this craft with the arisyng of the mone, loke thou rekne wel hir cours houre off by houre, for she ne dwellith not in a degre of hir longitude but litel while, as thow wel knowist. But natheles yf thou rekne hir verrey moevyng by thy tables houre after houre, [thou shalt do wel ynow]. 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 tour, in this maner thou shalt werke. Tak the altitude of the tour by bothe holes, so that thy rewle ligge even in a poynt. Ensample as thus: I see him thorw at the poynt of 4; than mete I the space between me and the tour, and I finde it 20 feet; than beholde 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 between thee and the tour the thridde part of the altitude of the tour; than thryes 20 feet is the heyghte of the tour, with adding of thyn owne persone to thyn 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 between thee and the tour; with adding of thyn owne heyghte.

42. Umbra Versa.

Another maner of werkinge, by umbra 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 fot; than go I neer to the tour, and I see him thorw at the poynt of 2, and there I sette another 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 thoushaltfinde that as 12 above 6 is the numbre of 6, right so is the space between thy two prikkes the space of 6 tymes thyn altitude. And note, that at the ferste altitude of 1, thou settest a prikke; and afterward, whan thou seest him at 2, ther thou settest another prikke; than thou findest between two prikkys 60 feet; than thou shalt finde that 10 is the 6-party of 60. And then is 10 feet the altitude of the tour. For other poyntis, yif it fille in umbra versa, as thus: I sette caas it fill upon 2, and at the secunde upon 3; than schalt thou finde that 2 is 6 partyes of 12; and 3 is 4 partyes of 12; than passeth 6 4, by nombre of 2; so is the space between two prikkes twyes the heyghte of the tour. And yif the differens were thryes, than shulde it be three tymes; and thus mayst thou werke fro 2 to 12; and yif it be 4, 4 tymes; or 5, 5 tymes; et sic de ceteris.

43. Umbra Recta.

Another maner of wyrking, by umbra recta. Yif it so be that thou mayst nat come to the baas of the tour, in this maner thou schalt werke. Set thy rewle upon 1 till thou see the altitude, and set at thy foot a prikke. Than set thy rewle upon 2, and behold what is the differense between 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 7, 7 party of 12; and note, at the altitude of thy onclusioun, adde the stature of thyn heyghte to thyn eye.

44. ''Another maner conclusion, to knowe the mene mote and the argumentis of any planete. To know the mene mote and the argumentis of every planete fro yere to yere, from day to day, from houre to houre, and from smale fraccionis infinite.''

In this maner shalt thou worche; consider thy rote first, the whiche is made the beginning of the tables fro the yer of oure Lord 1397, and enter hit into thy slate for the laste meridie of December- and than consider the yer of oure Lord, what is the date, and behold whether thy date be more or lasse than the yer 1397. And yf hit so be that hit be more, loke how many yeres hit passeth, and with so many enter into thy tables in the first Iyne theras is writen anni collecti et expansi. And loke where the same planet is writen in the hed of thy table, and than loke what thou findest in direct of the same yer of oure Lord which is passid, be hit 8, or 9, or 10, or what nombre that evere it be, til the tyme that thou come to 20, or 40, or 60. And that thou findest in direct wryt in thy slate under thy rote, and adde hit togeder, and that is thy mene mote, for the laste meridian of the December, for the same yer which that thou hast purposed. And if hit so be that hit passe 20, consider wel that fro 1 to 20 ben anni expansi, and fro 20 to 3000 ben anni collecti; and if thy nomber passe 20, than tak that thou findest in direct of 20, and if hit be more, as 6 or 18, than tak that thou findest in direct thereof, that is to sayen, signes, degrees, minutes, and secoundes, and adde togedere unto thy rote; and thus to make rotes. And note that if hit so be that the yer of oure Lord be lasse than the rote, which is the yer of oure Lord 1397, than shalt thou wryte in the same wyse furst thy rote in thy slate, and after enter into thy table in the same yer that be lasse, as I taught before; and than consider how many signes, degrees, minutes, and secoundes thyn entringe conteyneth. And so be that thebe 2 entrees, than adde hem togeder, anafter withdraw hem from the rote, the yer of oure Lord 1397; and the residue that leveth is thy mene mote for 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 December in the maner as I have taught, and afterward behold how many monethes, dayes, and houres ben passid from the meridie of December, and with that enter with the laste moneth that is ful passed, and take that thou findest in direct of him, and wryt hit in thy slate; and enter with as mony dayes as be more, and wryt that thou findest in direct of the 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 tak thy rote, the whiche is for the yer of oure Lord 1397; and if so be that thy yer be passid the date, wryt that date, and than wryt the nomber of the yeres. Than withdraw the yeres out of the yeres that ben passed that rote. Ensampul as thus: the yer of oure Lord 1400, I wolde witen, precise, my rote; than wroot I furst 1400. And under that nomber I wrot a 1397; than withdrow I the laste nomber out of that, and than fond I the residue was 3 yer; I wiste that 3 yer was passed fro the rote, the whiche was writen in my tables. Than afterward soghte I in my tables the annis collectis et expansis, and among myn expanse yeres fond I 3 yeer. Than tok I alle the signes, degrees, and minutes, that I fond direct under the same planete that I wroghte for, and 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 yer of oure Lord 1397; and kepte the residue; and than had I the mene mote for the laste day of December. And if thou woldest wete the mene mote of any planete in March April, or May, other in any other tyme or moneth of the yer, loke how many monethes and dayes ben passed from the laste day of December, the yer of oure Lord 1400; and so with monethes and dayes enter into thy table ther thou findest thy mene mote ywriten in monethes and dayes, and tak alle the signes, degrees, minutes, and secoundes that thou findest ywrite in direct of thy monethes, and adde to signes, degrees, minutes, and secoundes that thou findest with thy rote the yer of oure Lord 1400, and the residue that leveth is the mene mote for that same day. And note, if hit so be that thou woldest wete the mene mote in any yer that is lasse than thy rote, withdraw the nomber of so many yeres as hit is lasse than the yer of oure Lord a 1397, and kep the residue; and so many yeres, monethes, and dayes enter into thy tabels of thy mene mote. And tak alle the signes, degrees, and minutes, and secoundes, that thou findest in direct of alle the yeres, monethes, and dayes, and wryt hem in thy slate; and above thilke nomber wryt the signes, degrees, minutes and secoundes, the whiche thou findest with thy rote the yer of oure Lord a 1397; and withdraw alle the nethere signes and degrees fro the signes and de- grees, 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 flod or ebbe.

First wite thou certeinly, how that haven stondeth, that thou list to werke for; that is to say in which place of the firmament the mone being, maketh full see. Than awayte thou redily in what degree of the zodiak that the mone at that tyme is inne. Bring furth than the label, and set the point therof in that same cost that the mone maketh flod, 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 tlle label fro the mone, and bring and set it justly 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 flod. And there also maist thou wite by the same point of the label, whether it be, at that same tyme, flod or ebbe, or half flod, or quarter flod, or ebbe, or half or quarter 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 conjunccioun, bring furth the degree of the mone with the label to that coste as it is before seyd. But than thou shalt under- stonde that thou may not bringe furth the label fro the 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 label unremeved knowe the houre of the flod or of the ebbe, as it is before seyd, &c. And evermore as thou findest the mone passe fro the sonne, so remeve thou the label than fro the degree of the mone, and bring it to the degree of the sonne. And work thou than as thou dide before, &c. Or elles know thou what houre it is that thou art inne, by thyn instrument. Than bring thou furth fro thennes the label and ley it upon the degree of the mone, and therby may thou wite also whan it was flod, or whan it wol be next, be it night or day;