A Treatise on the Astrolabe
Modern English translated by and copyright James E Morrison. PDF with editors's comments. Used with permission. Middle English text from W.W. Skeat. Web version with editorial comments, PDF of the book. Text is in the public domain.
Little Lewis, my son, I see some evidence that you have the ability to learn science, number and proportions, and I recognize your special desire to learn about the astrolabe. So, as the philosopher said, “he serves his friend who grants his friend’s wishes”, I propose to teach you some facts about the instrument with this treatise. There are several reasons for this treatise. First, no one in this region has complete knowledge of the noble astrolabe. Another reason is that there are errors in the astrolabe treatises that I have seen and some of them present material too difficult for a ten year old to understand. Litell Lowis my sone, I have perceived wel by certeyne evidences thyn abilite to lerne sciences touchinge noumbres and proporciouns; and as wel considere I thy bisy preyere in special to lerne the Tretis of the Astrolabe. Than, for as mechel as a philosofre seith, "he wrappeth him in his frend, that condescendeth to the rightful preyers of his frend", ther-for have I geven thee a suffisaunt Astrolabe 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 apertening to the same instrument. I seye a certein of conclusions, 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 Astrolabe, ben un-knowe perfitly to any mortal man this regioun, as I suppose. A-nother cause is this; that sothly, in any tretis of the Astrolabe 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 treatise is divided into five parts and is written clearly and in plain English, because your Latin is still not good enough, my little son. But the facts are the same in English as Greek was to the Greeks, Arabic to the Arabs, Hebrew to the Jews and Latin to the Romans, who learned them first from other diverse languages and rewrote them in Latin. And, as God wills, all of these facts have been completely learned and taught in all these languages, but by different methods, much as all roads lead to Rome. Now I ask every person who reads or hears this little treatise to excuse my crude editing and my excessive use of words for two reasons. First, it is hard for a child to learn from complex sentences. Second, it seems better to me to write a good sentence twice for a child so he will not forget the first. This tretis, divided in fyve partis, wole I shewe thee under ful lighte rewles and naked wordes in English; for Latin ne canstow yit but smal, my lyte sone. But natheles, suffyse to thee thise trewn conclusiouns in English, as wel as suffyseth to thise noble clerkes Grekes thise same conclusions in Greek, and to Arabiens in Arabi, and to Iewes in Ebrew, and to the Latin folk in Latin; whiche Latin folk han hem forst out of othre diverse languages, and writen in hir owne tonge, that is to sein, in Latin. And god wot, that in alle thise languages, 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 way to Rome. Now wol I prey meekly 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 a child twyes a good sentence, than he for-gete in ones.
And Lewis, I get my satisfaction if my English treatise presents as many and the same facts as any Latin treatise on the astrolabe. And praise God and save the king, who is lord of this language, and all who obey him, each in his own way, more or less. But consider well that have not claimed to create this work from own work or energy. I am but a lewd compiler of the labor of old astronomers (astrologers) and have translated it into English only for your use. With this statement I slay envy. 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 Astrolabe, con me the more thank; and 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 of olde Astologiens, and have hit translated in myn English only for thy doctrine; and with this swerd shal I sleen envye.
First part - The first part of this treatise presents the parts of your astrolabe so you can become familiar with your own instrument. I.  The firste partie of this tretis shal reherse the figures and the membres of thyn Astrolabe, bi-cause that thou shalt han the grettre knowing of thyn owne instrument.
Second part - The second part teaches practical uses of previous facts, as much as possible for such a small portable instrument, for every astronomer (astrologer) knows that the smallest fractions shown in special tables that are calculated for a specific reason are not visible on such a small instrument. II.  The second partie shal teche thee werken the verrey practik of the forseide conclusiouns, as ferforth and as narweas 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 calculed for a cause.
Third part - The third part contains various tables of longitudes and latitudes of fixed stars for the astrolabe, a table of declinations of the Sun, tables of longitudes of cities and towns, tables for setting a clock and to find the meridian altitude and other notable conclusions from the calendars of the reverend clerks, Brother J. Somes1 and Brother N. Lenne.2  III. The thridde partie shal contienen diverse tables of longitudes and latitudes of sterres fixe for the Astrolabie, and tables of declinaciouns of the sonne, and tables of longitudes of citeez and of townes; and as wel for the governance of a 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.
Fourth part - The fourth part contains a theory to explain the movements of the celestial bodies and their causes. In particular, the fourth part contains a table of the moon’s motion for every hour of every day and in every sign from your almanac. A rule adequate to teach the manner of the working of the moon based on this table follows which allows you to know the degree of the zodiac that the moon rises in for any latitude and the rising of any planet based on its latitude from the ecliptic. IV. The ferthe partie shal ben a theorik to declare the moevinge of the celestial bodies with the causes. The whiche 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 comclusioun, as to knowe in oure orizonte with which degree of the zodiac that mone ariseth in any latitude; and the arising of any planete after his latitude fro the ecliptik lyne.
Fifth part – The fifth part shall be an introduction, following the style of our scholars, in which you can learn most of the general theory of astrology. You will find tables of equations of the houses for the latitude of Oxford and tables of dignities of the planets and other relevant things, if God and his Mother the Virgin wills, more than I am asked. V.  The fifte partie shal ben an introductorie after the statutz of oure doctours, in which thou maist lerne a gret part of the 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-safe and his modur the mayde, mo than I be-hete, &c.

PART I
The description of your astrolabe begins here. Here biginneth the Description of the Astrolabie.
1. Your astrolabe has a ring in which you put the thumb of your right hand when measuring the height of things. And take care, for this point forward I will call the height of anything that is taken as “the altitude” without more words. 1. 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 goes through a kind of eyelet connected to the body of your astrolabe with enough room so the instrument center always hangs straight down. 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 body of your astrolabe, the thickest plate, is hollowed out with a cavity that receives the thin plates created for various latitudes, and your rete shaped like a net or spider’s web. 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, lo here the figure.
4. 3The back of the body of your astrolabe is divided by a line that descends from the ring to the bottom border. This line is called the south line or meridional line from the ring to the hole in the center. The rest of the line down to the border is called the north line or else the line of midnight. Here is a figure that shows the idea: 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, for the for-seide ring un-to the centre of the large hole amidde, is cleped the south lyne, or elles the lyne meridional. 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.
5. Another line of the same length crosses the meridional line at a right angle from east to west. The part of this line from a little cross (+) on the edge to the hole in the center is called the east line or the oriental line. The rest of this line, from the center to the edge, is called the west line or the occidental line. You now have the four quarters of your astrolabe divided like the four principal zones of the compass or the quarters of the Earth. The figure shows the idea. 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; and the remenant of this lyne from the forseide + un-to the bordure, is cleped the West lyne, or the lyne Occidentale. Now hastow here the foure quarters of thin Astrolabie, devyed after the foure principals plages or quarters of the firmament. And for the more declaracioun, lo here thy figure.
6. The east side of your astrolabe is called the right side and the west side is called the left side. Don’t forget this, little Lewis. Put the astrolabe ring on the thumb of your right hand and then its right side will be toward your left side and its left side will be toward your right side. Take this as a general rule that applies to the back as well as the hollow side. As I have said, there is a small cross (+) at the end of this line, which is always regarded as the first degree where the Sun rises.4  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 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 figure.
7. The border is divided into 90 degrees from the little cross (+) to the end of the meridional line under the ring. Each quadrant of the astrolabe is also divided the same way. Numbers are engraved over the degrees to divide the scale in 5 degree sections as shown by the long strokes between the numbers. Each long stroke divides the scale into a mile-way.5  and every degree represents 4 minutes of time. The figure shows the scale. 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, that devyden thilke same degrees fro fyve to fyve, as sheweth by longe strykes by-twene. Of whiche longe strykes the space betwene 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. The names of the twelve signs (of the zodiac) are written below the circle of degrees: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricornus, Aquarius, Pisces. The number of degrees for each sign is shown in arabic numerals above6 and the sign is divided in 5 degree intervals from the beginning to the end of the sign. But understand that these divisions of the signs are considered to be 60 minutes,7 and each minute 60 seconds, and so forth into infinitely small fractions as shown by Alkabucius.8  Note carefully that a degree of the border represents 4 minutes and a degree of a sign contains 60 minutes.9  8. Under the compas of thilke degrees ben writen the names of the Twelve Signes, as Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarus, Capricornus, Aquarius, Pisces; and the nombres of the degrees of tho signes ben writen in augrim 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 degree of signes be everich of hem considered of 60 minutes, and every minute of 60 seconds, and so forth in-to smale fraccions infinit, as seith Alkabucius. And 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 declaraciouns, lo here thy figure.
9. Next is the circle of the days divided in the same way as the degree scale but containing 365 divisions, divided by long strokes into 5s with the number in arabic numerals written under the circle. 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 declaraciouns, lo here thy figure.
10. Next comes the circle of the names of the months, that is: Januarius, Februarius, Marcius, Aprilis, Maius, Junius, Julius, Augustus, September, October, November, December. Some of the month names come from their properties, some by Arabian lords and others by lords of Rome. The lengths of the months were defined of various numbers of days, such as July and August, at the pleasure of Julius Caesar and Caesar Augustus. Then January had 31 days, February 28, March 31, April 30, May 31, June 30, July 31, August 31, September 30, October 31, November 30 and December 31. Nevertheless, although Julius Caesar took 2 days from February and put them in his month of July and Augustus Caesar named August after himself and made it 31 days, the Sun is still in each sign for the same amount of time.10  10. Next the Cercle 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 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 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 Fevere 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, yit truste wel, that the sonne dwelleth ther-for nevere the more ne lesse is oon signe than in another.
11. Then follow the names of the holy days in the calendar and next to them the letters A, B, C.. on which day they follow.11  11. Than folwen the names of the Halidayes in the Kalendar, and next hem the lettres of the Abc, on which they fallen. And for the more declaracioun, lo here thy figure.
12. Next to the A, B, C circle described above and under the East-West line is marked a scale for many uses in the form of two squares, or in the style of ladders, that has 12 points and their divisions. This scale is called the Umbra Versa from the line to the right angle and the bottom part is called the Umbra Recta or Umbra Extensa as shown in the figure.12

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 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. You also have a broad rule that has a square plate at each end that is drilled with a hole (one large and one smaller) to receive the rays of the Sun during the day and to determine the altitude of stars with your eye at night.13  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 nighte. And for the more declaracioun, lo here thy figure.
14. There is also a large pin, like an axle, that goes through the hole. It holds the tables of the climates and the rete in the mater. A little wedge called the horse holds all the parts together. This pin is imagined to be the North Pole of your astrolabe. 14. Thanne is ther a large Pyn, in maner of an extree, that 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 thise parties to-hepe; this forseide grete Pyn, in maner of an extree, is imagined to be the Pol Artik in thyn Astrolabe. And for the more declaracioun, lo here the figure.
15. The cavity side or your astrolabe is also divided into four quarters from east to and north to south by a large cross, just like the back. 15. The wombe-side of thyn Astrolabe 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. Each border of each quadrant of the cavity side is divided into 90 degrees, just like the back. The total is 360 degrees. Note carefully that the border divisions are concentric to the equator and is divided in the same way as every other circle in the sky. The border is also divided by 23 capital letters and a small cross (+) showing the 24 hours of time in a day. And, as noted earlier, five of these degrees make a mile-way14 and three mile-ways make an hour. Every division of the border contains four minute, and every minute 60 seconds. Now I have said this twice. 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 degrees; and by that same proporcioun is ever quarter devyded as is the bak-syde, that amonteth 360 degrees. And understond wel, that degrees of this bordure ben answering and consentrik to the degrees of the Equinonxial, 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 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 60 secoundes; now have I told thee twye. And for the more declaracioun, lo here the figure.
17. The plate under the rete is engraved with three principal circles, of which the smallest is called the circle of Cancer because Cancer’s head15 always follows this circle. The beginning of Cancer is the greatest north declination of the Sun and, therefore, it is called the summer solstice. Ptolemy gives this declination as 23 degrees and 50 minutes as well in Cancer as in Capricorn.16 The sign of Cancer is called the summer tropic, from tropos, that is “turning”, because the Sun then begins to move away from it. 17. The plate under thy rict is descryved with 3 principal 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 declinacioun 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 fro us-ward. And for the more declaracioun, lo here the figure.
The middle circle in diameter of the three is called the equinoctial, on which the start of Aries and Libra always fall. Note carefully that the equinoctial circle always goes from due east to due west, as I have shown you on the solid sphere.17 This circle is also called the Equator, that is the measurer of the day, because when the Sun is at the start of Aries and Libra, the days are same length everyplace in the world. Therefore, these two signs are called the equinoxes. The movement of everything inside these points (on the astrolabe) is north of the equator and everything outside the equator (on the astrolabe) is south of the equator. Do not forget the north and south latitudes. The 24 hours of the day are defined by the equinoctial circle because each 15 degrees of the equinoctial is equal to one hour of time. The equinoctial is called the “girdle of the first mover” or primum mobile. And note that first mover means moving the first of the eight moveable spheres from east to west and back to the east. It is called the girdle of the first mover because it divides the first mover, that is the (celestial) sphere into two equal parts the same distance from the poles.

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 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 hevedes of thise Aries and Libra, his moeving is cleped northward; and alle that moeveth with-oute thise hevedes, his moeving 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 evermo 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 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 largest of the three circles is called the circle of Capricorn because the beginning of Capricorn always falls on this circle. The beginning of the sign of Capricorn is greatest southern declination of the Sun, and there is called the winter solstice. The sign of Capricorn is also called the winter tropic, because then the Sun then begins to come to us again. Here is the picture. The wydest of thise three principal cercles is cleped the 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 thanne byginneth the sonne to come agayn to us-ward. And for the more declaracioun, lo here thy figure.
18. Circles of altitude called almucantars are drawn on the plate mentioned earlier. Some are complete circles and some are partial circles. The center of the smallest circle is called the zenith. The bottom most circle represents the horizon, that is, the circle that divides the two hemispheres; the part of the heaven above the Earth and the part below. The almucantars are drawn for each two degrees, but some astrolabes have them for each degree, some for each two degrees and others for three degrees, depending on the size of the astrolabe. The zenith is imagined to the exact point above the top of your head. The zenith is the exact pole of the horizon for every place. 18. Upon the forseide plate ben compassed certein cercles that highten Almicanteras, of which som of hem semen perfit cercles, and somme semen imperfit. The centre that standith a-middes the narwest cercle is cleped the Senith; and the 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, and some by two, and somme by three, after the quantite of the Astrolabe. This forseide senith is imagened to ben the verrey point over the crowne of thyn heved; and also this senith is the verray pool of the orisonte in every regioun. And for the more declaracioun, lo here thy figure.
19. A type of curved lines, like the legs of a spider or a woman’s hairnet, come from the zenith and cross the almucantars at right angles. These curves or divisions are called azimuths and the divide the horizon of your astrolabe into 24 parts. The azimuths show directions and other results, such as finding the hour angle of the Sun and every star.18 The figure shows the azimuth curves. 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 divisouns ben cleped Azimuthz. And they devyden the orisonte of thyn Astrolabe 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 to the azimuths, under the Tropic of Cancer, are 12 oblique divisions, shaped similar to the azimuths, that show the planetary hours. 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 rete of your astrolabe with the zodiac, shaped like a net or spider’s web according to the traditional description, which you can rotate to any desired position, contains several fixed stars according to their latitudes and longitudes (if the instrument is correctly made). The names of the stars are shown in the margin of the rete near their locations and the tip of the pointer shows the position. Note that all the stars inside the zodiac are the northern stars because they rise to the north of east. And all of the stars outside the zodiac are called southern stars. But I see that they do not all rise south of east; Aldebaran and Algol, for example. The general rule is that those stars called northern stars rise earlier than the degree of their longitude and the southern stars rise later than the degree of their longitude, that is, for the stars on your astrolabe. The longitude of the stars is measured from the ecliptic, on which line, when the Sun and moon are aligned or else on the surface of this line, then there is an eclipse of the Sun or the moon, which I will explain later. But truthfully, the ecliptic of your zodiac is the extreme border of the zodiac where the degrees are marked.19  21. The Riet of thyn Astrolabe 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 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 Astrolabe ben cleped `sterres of the north', for they arysen by 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 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 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 Astrolabe. 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, 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.
The zodiac of your astrolabe is shaped like a wide circle for the proportions of your astrolabe, to show that the zodiac in the sky is seen as a surface with a width of 12 degrees, whereas all the other circles in the sky are thought of as having no width. Imagine a line in the middle of the zodiac that is called the ecliptic line, on which the Sun always travels. Thus, there are six degrees of the zodiac are on one side of the ecliptic line and six degrees are on the other side. The zodiac is divided into 12 principal sections that represent the 12 signs, and as made on your astrolabe, every small division of a sign represents two degrees (I mean degrees containing 60 minutes). This heavenly zodiac is called the ‘circle of the signs’ or the ‘circle of the beasts’, because the Greek “zodia” means “beast” in Latin. And the twelve signs of the zodiac have the names of animals, or else the Sun takes on the characteristics of such animals when it enters into any of the signs, or else the fixed stars are arranged in animal shapes, or else when the planets are under these signs their actions influence effects like the behavior of animals. Thy Zodiak of thyn Astrolabie is shapen as a compas which that conteneth a large brede, as after the quantite of thyn Astrolabe; 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 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 streitness of thin Astrolabie, than is 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 the Greek sowneth "bestes" in Latin tonge; and in the zodiak ben the twelve sgines that han 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 signes, they causen us by hir influence operaciouns and effectes lyk to the operaciouns of bestes. 
And also understand that, when a hot planet comes into a hot sign, its heat increases. And, if a planets is cold, then its coldness is reduced by a hot sign. And by this conclusion you can take examples in all the signs, be they moist or dry or mobile or fixed, determining the characteristics of the planet as I first said. And each of the 12 signs has characteristics of a certain part of a man’s body and governs it; Aries for your head, Taurus your neck and throat, Gemini your arm pits and arms, and so forth, as will be shown in more detail in part 5 of this treatise. 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; rekening 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 partie of this tretis. 
The zodiac, which is that part of the 8th sphere, intersects the equinoctial and intersects it again in equal parts, with one half of southern declination and the other northern, as is clearly stated in the Treatise on the Sphere. 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. You have a ‘label’20 shaped like the alidade except that it is straight and does not have sights on the ends. But, with the small point of the label, you shall calculate your equations on the border of the astrolabe, as by your almuri.21 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 Astrolabe, as by thyn almury. And for the declaracioun, lo here thy figure.
23. The almuri is called the tooth of Capricorn or the calculator. It is fixed in the head of Capricorn and is used for many necessary elements of equations of things, as will be shown. 23. Thyn Almury is cleped the Denticle of Capricorne, or elles the Calculer. This same Almury sit fix in the hed of Capricorne, and it serveth of many a necessarie conclusioun in equaciouns of thinges, as shal be shewed; and for the more declaracioun, lo here thy figure.
This ends the description of the Astrolabe and now begins the uses of the astrolabe. Here endeth the descripcion of the Astrolabie.

Part II
The uses of the astrolabe begin here. Here Biginnen the Conclusions of the Astrolabie
1. To find the Sun’s longitude for each day in its orbit. 1.
To fynde the degree in which the sonne is day by day, after hir cours a-boute.
Determine the day of the month and set the rule22 on that day. The tip of the rule points to the Sun’s longitude on the scale on the border. Rekene and knowe which is the day of thy monthe; and ley thy rewle up that same day; and thanne wol the verrey point of thy rewle sitten in the bordure, up-on the degree of thy sonne. 
For example, to find the Sun’s longitude at noon, March 12, 1391, I find the scale of days on the back of my astrolabe, which I recognize by the names of the months written under the circle. I set the rule over this day and find that the tip of the rule lies on the first degree of Aries and a little. Thus, I have solved the problem. Ensample as thus: the yeer of oure Lord 1391, the 12 day of 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 whiche 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 firste degree of Aries, a litel with-in the degree; and thus knowe I this conclusioun. 
I would also like to know the Sun’s longitude at noon on December 13. I find the day of the month as before and set the rule on this date and find the point of the rule is on the first degree of Capricorn and a little. Now I have good practice for this problem. Another day, I wolde knowe the degree of my sonne, and this was at midday in the 13 day of December; I fond the day of the month in maner as I seide; tho leide I my rewle up-on this forseide 13 day, and fond the point of my rewle 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 find the altitude of the Sun or other celestial bodies. 2. To knowe the altitude of the sonne or of othre celestial bodies.
Put the astrolabe’s ring on your right thumb and turn your left side towards the Sun. Move the rule up and down until the sunlight goes through both holes of the rule’s sights. Note how many degrees the rule has moved from the little cross on the east line and take this as the altitude of the Sun. In the same way you can find the altitude of the moon or bright stars. 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 thy rule is areised fro the litel crois up-on thyn est lyne, 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 function is so simple that it needs no further explanation, but remember it well. This chapitre is so general ever in oon, that ther nedith no more declaracioun; but forget it nat. And for the more declaracioun, lo here the figure.
3.
To find the time of day from sunlight and the time at from the fixed stars and also to find the ecliptic degree rising on the eastern horizon, commonly called the ascendant or ‘horoscopium’. 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 communly the Assendent, or elles Oruscupum.
Take the altitude of the Sun when you can, as I have said, and set the altitude of the Sun on almucantars on the east side of the astrolabe if it is morning and one the west if it is afternoon. This is always the rule for setting the Sun’s altitude on the astrolabe. Once you have set the altitude of the Sun on the almucantar corresponding to the Sun’s altitude measured with the alidade, position the label over the Sun’s longitude and the tip of the label will point to the time of day on the border. 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 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 lo 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 sitten in the bordure, up-on the verrey tyd of the day. 
An example is: Find the time on March 12, 1391.23 I took the altitude of the Sun and found it to be 25 degrees and 30 minutes by using the scale on the back side. Then I turned the astrolabe over and, because it was before midday, I set the first point of Aries at the almucantar for 25 degrees, 30 minutes on the east side of my astrolabe. Then I set the label on the Sun’s position and found the tip of the label was on the capital ‘X’ on the border. Then I counted the capital letters from midnight to the X and found it to 9 o’clock in the morning. Then I looked at the eastern horizon and found that Gemini 20° ascending, which is the ascendant. Using this method I can always find the time of day and the ascendant.24 Ensample as thus: the yeer of oure lord 1391, the 12 day of March, I wolde 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-cause that it was by-forn midday, I turnede my riet, and sette the degree of the sonne, that is to seyn, the 1 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 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 forseide 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 20 degree of Geminis assending; which that I tok for myn assendent. 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 assendent. 
I want to find the time at night for the same day and proceed as follows: Among the group of fixed stars, it seemed best to measure the altitude of the star named Alhabor,25 using the alidade on the back, found its altitude to be 12 degrees in the west. Then I set the pointer for Alhabor on the 12° almucantar on the west side because the star was in the west. Then I set the label on the longitude of the Sun, which was below the western horizon, and counted the capital letters from noon to the tip of the label and found that was 10° past nine o’clock.26 Then I looked at the eastern horizon and found Scorpio 10° rising. Thus I learned once and for all how to find the time at night and the ascendant as accurately as it can be found on such a small instrument.27 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 cleped Alhabor; (E36) and fond hir sitting on the west side of the lyne of midday, 18 degrees 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 founden on the west syde. Tho leide I my label over the degree of the sonne that was descended under the weste orisonte, and rekened 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 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 instrument. 
But, despite the generality of this method, I must warn you – never use a celestial body that is near the meridian to determine an ascendant or set a clock. Because, when the Sun is near the meridian its altitude stays on the same almucantar for so long that you will get the wrong ascendant.28 The same rule applies to the fixed stars at night. In my experience, for our latitude you should never take a reading from 11 to 1.29 But natheles, in general, wolde I warne thee for evere, ne mak thee nevere bold to have take a iust ascendent by thyn Astrolabie, or elles to have set iustly a clokke, whan any celestial body by which that thou 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 consentrik up-on the almikanteras, that sothly thou shalt erre fro the iust assendent. The same conclusion 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 noon til oon of the clok next folwing. And for the more declaracion, lo here thy figure.
4.
A special note about the ascendant. 4. A special declaracioun of the assendent.
The ascendant is an item of great interest to astrologers for all births and selecting (auspicious) times. Therefore, this seems to be a convenient place to make special note of it. 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 ascendant, in the largest sense, is the degree (of the zodiac) that rises on the eastern horizon at a specific time. Therefore, if any planet rises at the same time as does that degree (of the zodiac), then the planet has no latitude from the ecliptic, and its position on the ecliptic is equal to its longitude. People then say that this planet is in ‘horoscopo’.30,31 
The assendent sothly, to take it at the largeste, is thilke degree that 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
The house of the ascendant, that is, the first house or east angle, is larger. For, according to astrological rules, a celestial body that is five degrees or less above the (zodiac) degree that is rising, that is, near the ascendant, they say the planet is in the ascendant.32 And a planet that is within 25 degrees below the ascending angle is also said to be in the house of the ascendant. But if a planet is outside these bounds it is said to be “falling from the ascendant”. Yet, the astrologers say that the ascendant and also the lord of the ascendant may be fortunate or unfortunate. A “fortunate ascendant” is declared when no wicked planet such as Saturn or Mars or the Tail of the Dragon33 is in the house of the ascendant, nor any wicked planets have any aspect or enmity on the ascendant. But they will predict that they have a fortunate planet in the ascendant and all is joyful and well. An unfortunate ascendant is the opposite. They say that the lord of the ascendant is lucky when it is in a good position from the ascendant, as in an angle or in succident (?) where he has his dignity and is comforted by friendly aspects of planets well received and also that he may see the ascendant and not be retrograde nor quenched nor joined with an evil presence in the same sign, nor that he is not in his descent (?) nor joined with another planet in its descent nor have any unfortunate aspect, then they say that he is well.34  But sothly, the hous of the assendent, 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 degrees 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 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 astrologiens, that the assendent, 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, ne that no wikked planete have non aspecte of enemite up-on the assendent. But they wol caste that they have a fortunat planete in hir assendent and yit in 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 place fro the assendent as in an angle; or in a succedent where-as he is in his dignitee and comforted with frendly aspectes of planetes and wel resceived, and eke that he may seen the assendent, and that he be nat retrograd ne combust,  ne ioigned with no shrewe in the same signe; ne that he be nat in his descencioun, ne ioigned with no planete in his discencioun, ne have up-on him non aspecte infortunat; and than sey they that he is well. 
In any case, these are observances of judicial matters and the rites of pagans in which I have no faith nor knowledge of their observations.35 Because they say that every sign is divided into the three equal parts of 10 degrees, and they call each section a face. And yet some people say that although a planet has a latitude from the ecliptic, if the planet rises in the face in which its longitude is found, then the planet is in horoscopo, be it birth or decision, etc. Natheles, thise ben observauncez of iudicial matiere and rytes of payens, in whiche my spirit ne hath no feith, ne no knowing of her horoscopum; for they seyn that every signe is departed in 3 evene parties by 10 degrees, and thilke porcioun they clepe a Face.  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, &c. And for the more declaracioun, lo here the figure.
5.
To find the position of the Sun if it falls between two almucantars.36  5. To knowe the verrey equacioun of the degree of the sonne, yif so be that it falle by-twixe thyn Almikanteras.
In as much as the almucantars on your astrolabe are for each two degrees, whereas some astrolabes have almucantars for each degree or each three degrees, it is necessary for your training to learn how to work your own instrument. If the altitude of the Sun falls between two almucantars, or if the almucantar lines are engraved with tool that is too wide (because these factors may also cause an error in finding the time of day or the true ascendant) you work it this way: For as muche 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 and worke with thyn owne instrument. Wher-fore, whan that the degree of thy sonne falleth by-twixe two 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 in this wyse. 
Set the altitude of the Sun on the almucantar just greater than the altitude and note where the almuri is on the degree scale on the border. Mark this point with dot of ink. Set the Sun on the lower of the two almucantars and make another dot. Now set the almuri halfway between the to dots and this will set the correct position of the Sun between the almucantars. Now set the label over the Sun and find the true time of day or night. You can find the ascendant on the eastern horizon in the same way. Set the degree of thy sonne up-on the heyer almikanteras of bothe, and waite wel where as thin almury toucheth the bordure, and set ther a prikke of inke. Set doun agayn the degree of the sonne up-on the nethere almikanteras of bothe, and set ther another prikke. Remewe thanne thyn almury in the 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 assendent. And for more declaracioun, lo here thy figure.
6.
To find daybreak and the end of evening twilight, which are called the two crepuscules.37 6. To knowe the spring of the dawing and the ende of the evening, the which ben called the two crepusculis:
Set the Sun’s nadir38 on the 18° almucantar in the west and set the label on Sun’s position. The point of the label shows the time of daybreak. Similarly, set the Sun’s nadir on the 18° almucantar in the east and set the label on the Sun’s position. The tip of the label shows the end of evening twilight, that is, the beginning of true night. 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 of thy sonne, and than 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 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 Sun is the point opposite the position of the Sun on the ecliptic in the seven signs as follows: each degree in Aries in order is the nadir to each degree in Libra in order, and Taurus to Scorpio, Gemini to Capricorn, Leo to Aquarius, Virgo to Pisces.39 And if any degree in your zodiac is dark, its nadir will demonstrate it. The nadir of the sonne is thilke degree that is opposit to the degree of the sonne, in the seventhe signe, as thus: 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 find the length of the day, which some people call the artificial day, from sunrise to sunset. 7. To knowe the arch of the day, that some folk callen the day artificial, from the sonne arysing til hit go to reste.
Set the degree of the Sun on the eastern horizon and set the label on the Sun’s position. Mark the position of the tip of the label. Turn the rete until the Sun’s position is on the western horizon and mark the point of the tip of the label. Calculate the length of time between to two marks which is the length of the day. That part of the border below the horizon is the length of the night. In this way you can calculate both lengths, or any portion, as you choose. And, using this technique, you can find the length of time that any fixed star is above the horizon, from the time it rises until it sets. But the complete day of 24 hours is the revolution of the equinoctial with as much of the zodiac as the Sun in its proper motion in the same time.40  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 thy sonne sit up-on the west orisonte, and ley 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 bordere by-twixe bothe prikkes, and tak there thyn ark of the day. The remenant of the bordure under the orisonte is the ark of the night. Thus maistow rekne bothe arches, or 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 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 of his propre moevinge passith in the mene whyle. And for the more declaracioun, lo here thy figure.
8.
To convert unequal hours to equal hours 8. To turne the houres in-equales in houres equales.
Find the number of degrees in the unequal hours and divide by 15, giving the equal hour.41 Know 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 find the length of the vulgar day, that is, from the beginning of morning twilight to the end of evening twilight. 9. To knowe the quantitee of the day vulgare, that is to seyen, from spring of the day un-to verrey night.
Find the time of the twilights as shown in item 2, above, and add them to the length of the artificial day, taking the length of the complete day until complete night. You can find the length of vulgar night in the same way. 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 of the vulgar night. And for the more declaracioun, lo here the figure.
10.
To find the unequal hour during the day.42 10. To knowe the quantite of houres in-equales by day.
The unequal hours are called planetary hours. Some of the time they are longer during the day than at night, and sometimes the opposite. But, in general, the sum of length of the unequal hours of the day and the length of the unequal hours of the night is 30° of the border, which corresponds to equinoctial degrees. Therefore, divide the arc of the day into 12 equal parts to find the length43 of an unequal hour during the day. If you subtract the length of the unequal hour during the day from 30, the difference is the length of the unequal hour of the night. 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 contrarie. But understond wel, that evermo, generaly the hour in-equal of the day with the houre in-equal of the night contenen 30 degrees of the bordure, which bordure is ever-mo answering to the degrees of the equinoxial; wher-fore 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 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 find the size of the equal hours. 11. To knowe the quantite of houres equales.
The number of the equal hours, that is, the hours of the clock, are divided in 15 degree sections on the border of your astrolabe, for both night and day. Nothing more needs to be said. 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? 
When you want to know how many clock hours have passed, or what part of any of these hours have passed, or how many hours or parts of hours are to come by day or night, find the position of the Sun and set the label on it. Turn your rete and label together and, using the its tip, calculate the time interval from sunrise to the time of interest, for the day or night. I will cover this result with such completeness in the last chapter of part IV of this treatises that no more explanation is needed. Wher-for, whan thee list to 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 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 figure.
12.
Special explanation of the planetary hours. 12. Special declaracioun of the houres of planetes.
Understand well that, from sunrise to sunset, the nadir of the Sun shows the planetary hour, and from sunset to sunrise the Sun itself shows the planetary hour.44 
Understond wel, that ever-mo, fro the arysing 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 degree of the sonne shewe the houre of the planete. 
45For example: Say the 13th day of March is a Saturday46 and I find a little less than Aries 2° on the east horizon at sunrise. I then find Libra 2°, the Sun’s nadir, descending on the western horizon. The planetary hours begin at sunrise and the planet for the day gives its name to the first hour which is begins at the western horizon and ends at the first unequal hour arc below the western horizon47 And, as the Sun rises higher, the nadir descends, reaching each planetary hour division in their order in the sky. The first unequal hour of every Saturday belongs to Saturn and second belongs to Jupiter, the third to Mars, the fourth to the Sun, the fifth to Venus, the sixth to Mercury and the seventh to the moon. And then again the eighth hour is Saturn’s, the 9th Jupiter’s, the 10th Mar’s, the 11th the Sun’s and the 12th Venus’. Now the Sun rises on Sunday morning and the Sun’s nadir on the western horizon shows the beginning of the Sun’s hour.48 And the successive planets from Saturn to the moon and from the moon again to Saturn, hour after hour, generally. Thus, this conclusion if complete. Ensample as thus. The 13 day of March fil up-on a Saturday, 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 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 climbith uppere and uppere, so goth his nadir dounere and dounere, teching by 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 seconde, 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 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 planete, in houre after houre, all the night longe til the sonne aryse. Now ryseth the sonne that Sonday by the morwe; and the nadir of the sonne, up-on the west orisonte, 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, and fro the Mone up a-gayn to Saturne, houre after houre generaly. And thus have I this conclusioun. And for the more declaracioun, lo here the figure.
13.
To find the Sun’s noon altitude which is called the meridian altitude 13. To knowe the altitude of the sonne in middes of the day, that is cleped the altitude meridian.
Set the degree of the Sun on the meridian line and note how the degree of the almucantar. This is the meridian altitude, that is the Sun’s maximum altitude for that day. You can find the maximum altitude attained by any fixed star using the same line. This is to say that any fixed star begins to descend when it has passed the meridian, just like the Sun. 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. 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 find the degree of the Sun using the rete for any date.49 14. To knowe the degree of the sonne by thy riet, for a maner curiositee, &c.
Carefully measure the maximum altitude of the Sun at noon with rule. Turn your astrolabe over and mark that altitude on the meridian line with a dot of ink. Turn the rete until you find the degree of the zodiac that that matches mark. In this way you can find the position in the zodiac within two degrees. If these two degrees are in different signs you will have to find the correct sign from the date. 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 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 more declaracioun, lo here thy figure.
15.
To find which days have the same length. 15. To know which day is lyk to which day as of lengthe &c.
Find which degrees are the same distance from the heads of Cancer and Capricorn and note when the Sun is in any of these locations. The lengths of these days are the same. That is to say, the length of that day in that month will not be much different.50  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 swich a monthe; ther varieth but lite. 
Also, if you take two natural days in the year of equal distance from either point of the equator, but in opposite directions, then length of the artificial day for one will be the length of the night for the other, and vice versa. 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 chapter explains the following conclusions. 16. This chapitre is a maner declaracioun to conclusiouns that folwen.
Note that the zodiac is divided into to two half circles; from the beginning of Capricorn to the beginning of Cancer and again, from the beginning of Cancer to the beginning of Capricorn. The beginning of Capricorn is the lowest point of the Sun in winter and the beginning of Cancer is the highest point of the Sun in summer. Note, therefore, that any two position in the zodiac that are the same distance from these two points have the same declination, whether it is north or south. And the lengths of the days and nights, the shadows and midday altitudes will always be he same. 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. The heved of Capricorne is the lowest point, wher-as the sonne goth in winter; and the heved of Cancer is the heyest point, in whiche the sonne goth in somer. And ther-for understond wel, that eny two degrees that ben y-lyke fer fro any of thise two hevedes, truste wel that thilke two degrees ben of y-lyke declinacioun, be it southward or northward; and the dayes of hem 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 find the coordinates of any star, known or unknown, from its mediation, even if the star is not included on your astrolabe.51
17. To knowe the verrey degree of any maner sterre, straunge or unstraunge, after his longitude; though he be indetermynat in thin Astralabie, sothly to the trouthe thus he shal be knowe.
Measure the altitude of the star as closely as possible when it is on the east side of the meridian and make a note of it. Also, quickly find the ascendant for some star that is on your rete that is close to the same azimuth and note the value.52 Take another reading of the ascendant of the known star when the unknown star is at the same altitude in the west as it was when you made your first measurement in the east and note the ascendant.53 Find the ascendant halfway between the two measured values and set the that degree on the eastern horizon.54 Note the degree of the ecliptic that is on the meridian. This is the mediation of the unknown star. Its north or south declination is measured toward the celestial pole. 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 assendent a-non right by som maner sterre fix which that thou knowest; and for-get nat the altitude of the firste sterre, ne thyn assendent. And whan that this is don, espye diligently whan this same firste sterre passeth any-thing the south westward, and 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 manere sterre fixe which that thou knowest; and for-get nat this secounde assendent. 
Furthermore, measure the declination of the Sun or fixed star from the equator. Measure the latitude of planets from the ecliptic. Note that the latitude of any celestial body except the Sun can be determined from its position north or south of the ecliptic, from which line all planets vary north or south except the Sun. And whan that this is don, rikne thanne how manye degrees ben by-twixe the first 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 degre 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 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, after the site north or south, and after the quantitee of his declinacion. 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 declinacion, be rekned fro the ecliptik lyne; fro which lyne alle planetes som tyme declynen north or south, save only the for-seide sonne. And for the more declaracioun, lo here thy figure.
18. To find the mediation of stars included on your astrolabe, if they are correctly placed. 18. To knowe the degrees of longitudes of fixe sterres after that they ben determinat in thin Astrolabie, yif so be that they ben trewly set.
Set the point for the star on the meridian and note the degree of the zodiac that is on the meridian line. This star will be on the same ecliptic degree from the horizon to the meridian.55  Set the centre of the sterre up-on the lyne meridional, 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 find the ecliptic degree that rises on the eastern horizon at the same time as a fixed star, even if the star is in a different sign.56
19. To knowe with which degree of the zodiak any sterre fixe in thyn Astrolabie arysith up-on the est orisonte, althogh his dwelling be in a-nother signe.
Set the point for the star on the eastern horizon and note the zodiac degree that is also on the same horizon at the some time. This zodiac degree rises at the same time as the star.
This marvelous rising with a strange degree in another sign is because the latitude of the fixed star is either north or south of the equator. But the latitudes of planets are normally measured from the ecliptic because none of them vary more than a few degrees within the width of the zodiac. Note the contents of this chapter on the rising of celestial bodies, because neither the moon nor stars rise with the same degree as its longitude on our oblique horizon unless they have no latitude from the ecliptic line. But, nonetheless, each of these planets is eventually on this line.
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 same tyme. And understond wel that with that same degree aryseth that same sterre; and this merveyllous arysing with a 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 be 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 of 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 ecliptyk lyne. But natheles, som tyme is everiche of thise planetes under the same lyne. And for more declaracioun, lo here thy figure.
20. To find the declination of any degree in the zodiac from the equator. 20. To knowe the declinacioun of any degree in the zodiak fro the equinoxial cercle, &c.
Set the degree of any sign on the meridian and note the altitude on the almucantars. Then rotate the rete until the beginning of Aries or Libra is on the meridian and note the altitude.57 The difference in the altitudes taken is the declination of this degree (of the zodiac) from the equator. If the zodiac degree is north of the equator then the declination is north and it is south of the equator, the declination is south. Set the degree of any signe up-on the lyne meridional, and rikne his altitude in the almikanteras fro the est orizonte up to the same degree set in the forseide lyne, and set there a prikke. Turne up thanne thy riet, and set the heved of Aries or Libra in the same 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 equinoxial. And yif so be that thilke degree be northward fro the equinoxial, than is his declinacion north; yif it be southward, than is it south. And for more declaracioun, lo here thy figure.
21. To find the latitude for which the almucantars on the astrolabe plate are designed. 21. To knowe for what latitude in any regioun the almikanteras of any table ben compouned.
Note the number of degrees on the almucantars on the meridian from the equator to the zenith or from the north celestial pole to the northern horizon. This is the latitude for the plate. Rikene 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 declaracioun, lo here thy figure.
22. To find the latitude of our region, I mean the latitude of Oxford and the altitude of our pole 22. To know in special the latitude of oure countray, I mene after the latitude of Oxenford, and the heighte of oure pol.
Note that the distance of the beginning of Aries or Libra58 from our horizon is the same as the zenith from the north pole and the altitude of the north pole from the horizon is the same as the equator from the zenith.59 I shall prove this for the latitude of Oxford. Note that the altitude of the north pole in Oxford is 51 degrees and 50 minutes and the distance of our zenith from the north pole is 39 degrees, 10 minutes. The distance from the equator to our zenith is 51 degrees 50 minutes and our southern horizon is 38 degrees 10 minutes from the equator. Note these calculations carefully. Also, do not forget that the zenith is 90 degrees in altitude from our horizon and the equator is 90 degrees from the north pole. There is this short rule: the latitude of an place is the distance from the zenith to the equator. Understond wel, that as fer is the heved of Aries or Libra in the equinoxial fro 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. 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 from oure senith 51 degrees and 50 minutes; than is oure south orisonte from oure equinoxial 38 degrees and 10 minutes. Understond wel this rekning. Also forget nat that the senith is 90 degrees of heyghte fro the orisonte, and oure equinoxial is 90 degres 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 figure.
23. To use the previous article to find the latitude of any place by measuring the altitude of the north pole 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.
On a winter’s night when the sky is clear and filled with stars, wait until a fixed star is directly above the north pole and name that star A. Find another star that is directly under A and below the pole and call that star F. Note that F is considered only to establish that A is directly above the pole. Measure the altitude of A quickly and not the value. Let A and F rotate until near daybreak, go out again and wait until A is directly under the pole and under F (F will be directly above the pole and A will be directly beneath it). Measure the altitude of A and note it. When this is done, calculate how many degrees the first altitude is greater than the second, take half of the result and add it to second altitude. This is the altitude of the pole and equal to the latitude of your place because the polar altitude equals the latitude of a place. In som winters night, whan the firmament is clere and thikke-sterred, waite a tyme til that any sterre fix sit lyne-right perpendiculer over the pol artik, and clepe that sterre A. And wayte a-nother sterre that sit lyne-right under A, and under the 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 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 that the first altitude of A excedeth his seconde altitude, and tak half thilke porcioun that is exceded, and adde it to his seconde altitude; and tak there the elevacion of thy pool, and eke the latitude of thy regioun. For thise two ben of a nombre; this is to seyn, as many degres as thy pool is elevat, so michel is the latitude of the regioun.
For example: Say the altitude of A in the evening is 56° and the second altitude taken near dawn is 48°, which is 8° less than 56°. Take half of the 8 and add it to 48 giving 52°. You now have the altitude of the pole and the latitude of the region. But you should understand to conduct this measurement correctly you must have a plumb line that hangs from a point higher than your head and this line must hang vertically between the pole and your eye. This will allow you to see when A is directly over the pole and F and when F is directly over the pole and A.60  Ensample as thus: par aventure, the 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 of the regioun. But understond wel, that to prove this conclusioun and many a-nother fair conclusioun, thou must 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 over F at evene; and also yif F sitte evene over the pool and over A or day. And for more declaracioun, lo here thy figure.
24. Another method of finding the altitude of the pole. 24. Another conclusioun to prove the heyghte of the pool artik fro the orisonte.
Take any star that never sets in the region of interest and determine its maximum and minimum altitude from the horizon. Then take the altitude that is halfway between as the altitude of the pole in that place.61  Tak any sterre fix 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 the elevacioun of the pol artik in that same regioun. And for more declaracioun, lo here thy figure.
25. Another method of finding the latitude of a place 25. A-nother conclusioun to prove the latitude of the regioun, &c.
The latitude of any place is the distance between the local zenith and the equator, north or south, taking the measurement on the meridian line of your astrolabe.62 This distance is equal to the altitude of the pole at the same place. And is also the same as the depression of the antarctic pole, that is to say, the antarctic pole below the horizon is the same distance, neither more nor less. Understond wel that the latitude of any place in a regioun is verreyly the space by-twixe the senith of hem that dwellen there and the equinoxial cerkle, north or southe, taking the mesure in the meridional lyne, as sheweth in the almikanteras of thyn Astrolabie. And thilke space is as moche as the pool artik is hey in that 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. 
If you want to find the latitude of this place, take the altitude of the Sun at noon when the Sun is at the beginning of Aries or Libra63 because the Sun is on the equator at this time.64 Subtract the Sun’s altitude from 90 degrees. The difference is the latitude of the place. Suppose the Sun’s altitude on that day was 38°. 90° - 38° = 52°. So, the latitude is 52°. This is only an example. The actual latitude of Oxford is a few minutes less, as you might demonstrate.65  Thanne, yif thow desire to knowe this latitude of the regioun, tak the altitude of the sonne in the middel of the day, whan the sonne 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 that regioun. As thus: I suppose that the sonne is thilke day at noon 38 degrees and 10 minutes of heyghte. Abate thanne thise degrees and minutes out of 90; so leveth there 51 degrees and 50 minutes, the latitude. I say nat this but for ensample; for wel I wot the latitude of Oxenforde is certein minutes lasse, as I mighte prove. 
Now, if it seems to long to wait for an equinox, then wait until the Sun is any other degree in the zodiac and measure its angle from the equator. If the Sun is in the north, subtract the Sun’s declination from its noon altitude, which gives the altitude of the equator. Say the Sun is in the first degree of Leo, its noon altitude is 58° 10′ and its declination is almost 20° north. Subtract the 20° of declination from the noon altitude leaving 38° and odd minutes. This is the altitude of the equator in this area. Also, if the Sun’s declination is to the south, add the declination to the Sun’s noon altitude, giving the altitude of the equator. Subtract the equator’s altitude from 90° to get the altitude of the pole of that place from the equator.66 Or else, as a last resort, take the highest altitude from the equator of any fixed star that you know and take the lowest elongation (in distance) from the equator and work in the manner above. Now yif 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 thanne fro the sonnes altitude at noon the nombre of his declinacion, and thanne hastow the heyghte of the hevedes of Aries and Libra. As thus: my sonne is, par aventure, in the firste degre of Leoun, 58 degrees and 10 minutes of heyghte at noon and his declinacion is almost 20 degrees northward fro the equinoxial; abate thanne thilke 20 degrees of declinacion out of the altitude at noon, than leveth thee 38 degrees and odde minutes; lo ther the heved of Aries or Libra, and thyn equinoxial in that regioun. Also yif so be that the sonnes declinacioun be southward fro the equinoxial, adde thanne thilke declinacion to the altitude of the sonne at noon; and tak there 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 fro the equinoxial. Or elles, yif thee lest, take the heyest altitude fro the equinoxial of any sterre fix that thou knowest, and tak his nethere elongacioun lengthing fro the same equinoxial lyne, and wirke in the maner forseid. And for more declaracioun, lo here thy figure.
26. Declaration on the ascension of signs. 26. Declaracioun of the assensioun of signes, &c.
The excellence of the solid sphere67 shows the rising of the signs in various places clearly, as well as the right circle68 and the oblique circle.69 These authors70 have written that a sign if called ‘of right ascension’ if more degrees of the equator rise than the degrees of the zodiac when the sign rises. A sign is called ‘oblique’ if fewer equatorial degrees than zodiac degrees rise when the sign rises. Furthermore, they say that people have this right horizon and right circle in a region where the zenith is the equator and the poles are on the horizon71 and length of the day and night is always the same and twice a year the Sun passes directly overhead and they have two summers and two winters in a year. And the almucantars are straight lines, as shown in the figure72 The excellence of the spere solide, amonges other noble conclusiouns, sheweth manifeste the diverse assenciouns of signes in diverse places, as wel in the righte cercle as in the embelif cercle. Thise auctours wryten that thilke signe is cleped of right ascensioun, with which more part of the cercle equinoxial and lasse part of the zodiak ascendeth; and thilke signe assendeth embelif, with which lasse part of the equinoxial and more part of the zodiak assendeth. Ferther-over they seyn, that in thilke cuntrey where as the senith of hem that dwellen there is in the equinoxial lyne, and her orisonte passing by the poles of this worlde, thilke folk han this right cercle and the right orisonte; and evere-mo the arch of the day and the arch of the night is ther y-like long, and the sonne twyes every yeer passinge thorow the senith of her heved; and two someres and two winteres in a yeer han this forseide poeple.  And the almikanteras in her Astrolabies ben streighte as a lyne, so as sheweth in this figure.  
The value of knowing the ascensions of the signs in the right circle is this: the measurement of these ascensions with their tables and instruments allows the astrologers to determine the altitude of every degree and minute in the entire zodiac in the oblique circle, as shall be shown. And note that the right horizon, called Orison Rectum, divides the equator into right angles and the oblique horizon, where the pole is above the horizon, intersects the equator at oblique angles, as is shown in the figure. The utilite to knowe the assenciouns in the righte cercle is this: truste wel that by mediacioun of thilke assenciouns thise astrologiens, by hir tables and hir instrumentz, knowen verreyly the assencioun of every degree and minut in al the zodiak, as shal be shewed.  And nota, that this forseid righte orisonte, that is cleped orison rectum, divydeth the equinoxial in-to right angles; and the embelif orisonte, wher-as the pol is enhaused up-on the orisonte, overkerveth the equinoxial in embelif angles, as sheweth in the figure.  And for the more declaracioun, lo here the figure. 
27. The conclusion to determining the rising time of signs in the right circle, that is circulus directus 27. This is the conclusioun to knowe the assenciouns of signes in the right cercle, that is, circulus directus, &c.
Set the start of sign for which you want to find the rising time on the meridian and note where the almuri falls on the border and mark that point. Turn the rete westward until the end of the sign is on the meridian and make another mark at the position of the almuri on the border. Calculate the number of degrees between the marks. This is the ascension of the sign in the right circle.73 You can do this with every part of the zodiac. Set the heved of what signe thee liste to knowe his assending in the right cercle up-on the lyne meridional; and waite wher thyn almury toucheth the bordure, and set ther a prikke. Turne thanne thy riet westward til that the ende of the forseide signe sitte up-on the meridional lyne; and eft-sones waite wher thyn almury toucheth the bordure, and set ther another prikke. Rikne thanne the nombre of degrees in the bordure by-twixe bothe prikkes, and tak the assencioun of the signe in the right cercle. And thus maystow wyrke with every porcioun of thy zodiak, &c. And for the more declaracioun, lo here thy figure.
28. To find the rising time of signs in the oblique circle in every region, I mean, in circulo oblique 28. To knowe the assencions of signes in the embelif cercle in every regioun, I mene, in circulo obliquo.
Set the beginning of the sign for which you want to find the ascension on the eastern horizon and note the position of the almuri on the border. Turn the rete upward until the end of the same sign is on the eastern horizon and note the position of the almuri on the border. Calculate the number of degrees on the border between the two positions. This is the rising time of the sign on the oblique horizon.74 Note that the signs from beginning of Aries to the end of Virgo are known as the northern signs. These signs are always rise north of east. And all the signs from the beginning of Libra to the end of Pisces are known as southern signs because they always rise south of the equator. Also, the signs between the beginning of Capricorn to the end of Gemini rise in less than two equal hours on our horizon. These signs, from the beginning of Capricorn to the end of Gemini, are known as ‘tortured signs’ or ‘crooked signs’ because they rise at an oblique angle on our horizon. The signs of right ascension are those from the beginning of Cancer to the end of Sagittarius and these signs rise more upright, so they are called ‘sovereign signs’ and they all take more than two hours to rise. Thus, two signs that are of equal distance from the beginning of Capricorn have the same characteristics. Set the heved of the signe which as thee list to knowe his ascensioun up-on the est orisonte, and waite wher thyn almury toucheth the bordure, and set ther a prikke. Turne thanne thy riet upward til that the ende of the same signe sitte up-on the est orisonte, and waite eft-sones wher as thyn almury toucheth the 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 the signes in thy zodiak, fro the heved of Aries unto the 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 the signes fro the heved of Libra un-to the ende of Pisces ben cleped signes of the south fro the equinoxial; and thise signes arysen ever-mo by-twixe the verrey est and the verrey south in oure orisonte. Also every signe by-twixe the heved of Capricorne un-to the ende of Geminis arysith on oure orisonte in lasse than two houres equales; and thise same signes, fro the heved of Capricorne un-to the ende of Geminis ben cleped `tortuos signes' or `croked signes', for they arisen embelif on oure orisonte; and thise crokede signes ben obedient to the signes that ben of right assencioun. The signes of right assencion 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 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 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 here the figure.
29. The find the four cardinal directions; East, West, North and South. 29. To knowe iustly the foure quarters of the world, as est, west, north, and south.
Measure the altitude of the Sun a the selected time and note its azimuth.75 Turn the astrolabe over and set the degree of the Sun on the almucantar for the Sun’s altitude on the side where the Sun is, as when finding the time, set the rule on the Sun’s position and note the number of degrees from the meridian to the point of the rule. Turn the astrolabe over and set the alidade to the number of degrees that the rule was from the meridian on the front of the instrument. Now, set the astrolabe carefully and gently on a smooth, flat place and let the Sun shine through the sights on the alidade. The meridian line now points south and the east will point east and the west line will point west. You now have the cardinal compass points if you work carefully and easily when setting the astrolabe down.76  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 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 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 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 the 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 declaracioun, lo here the figure.
30.
To find the latitude of the planets 30. To knowe the altitude of planetes fro the wey of the sonne, whether so they be north or south fro the forseide wey.
77Measure the altitude of a planet when it on the meridian. If the altitude is the same as the degree of the Sun for that day then the planet is on the ecliptic and has no altitude. If the planet’s altitude is greater than the Sun’s, the planet is north of the ecliptic by the amount shown by the almucantars. If the planet’s altitude is less than the Sun’s then the planet is south of the ecliptic by the amount shown by the almucantars. This to be seen from the position of the Sun for this day only, and not for every place in the zodiac.78 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 heyere than the degree of the sonne, than is the planete north fro the wey of the sonne swich a quantite of latitude as shewith 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 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 find the azimuth of the rising Sun, that is the point on the horizon where the Sun rises. 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.
The Sun does not always rise in due east, but sometimes rises north of east and sometimes south of east. The only time the Sun rises due east is when the Sun is at the beginning of Aries or Libra. The horizon of your astrolabe is divided into 24 parts by the azimuth arcs, showing the 24 compass directions, although sailors use 32 directions. All you have to do is note the azimuth arc where the Sun rises and take that as the azimuth of sunrise. Thou most first considere that the sonne arysith not 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 orisonte, but he be in the heved of Aries or Libra. Now is thyn orisonte departed in 24 parties by thyn 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. 
Your astrolabe is divided as follows: First, it is divided into the four cardinal quarters by the line from east to west and the line from north to south.79 Then it is divided into smaller parts by azimuths as east, east by south (the first azimuth above the east line) an so forth from section to section until you come back to the east line. In this way you can fine the azimuth of rising of any star and section where it rises.80  The manere of the devisioun of thyn Astrolabie is this; I mene, as in this cas. First it is 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 parties of azimutz, as est, and est by southe, whereas is the firste azimut above the est lyne; and so forth, fro 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 declaracioun, lo here the figure.
32. To find the direction of conjunction [of the Sun and Moon] 32. To knowe in which partie of the firmament is the coniunccioun.
Find the time of the conjunction from a calendar thus: note the number of hours of the conjunction from noon of the preceding day as shown by the canon of your calendar. Calculate the number of hours on the border of your astrolabe, as in finding the time of day or night, and set the rule over the Sun’s position. The point of the rule will be on the time of the conjunction. Note the Sun’s azimuth. This is the direction of the conjunction. Considere the tyme of the coniunccioun 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, 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 coniunccion. Loke thanne in which azimut the degree of thy sonne sittith, and in that partie of the firmament is the coniunccion. And for the more declaracioun, lo here thy figure.
33. To find the azimuth from the Sun’s altitude 33. To knowe the senith of the altitude of the sonne, &c.
There is nothing more to do than measure the altitude of the Sun at any time and note the azimuth of the Sun’s position. This can also be done at night for any star, whether is in the east, west, north or south, or any place in between, from the azimuth of the star’s position. 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 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 find the longitude of the moon or any planets that has no latitude at the time 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.
Measure the altitude of the moon and mark its location on the almucantars on the appropriate side of the meridian. Then quickly measure the altitude of a known fixed star on the same side of the meridian and set its pointer on the appropriate almucantar. Note the degree of the zodiac that touches the moon’s position. This is the moon’s longitude. This procedure works well if the stars on your astrolabe are accurately made. Other astrolabe treatises do not make an exception for whether the moon has a latitude or not and on which side of the meridian the altitude of the fixed star should be taken.
Note also that you can perform this same procedure when the moon is visible during the day using the Sun.
Tak the altitude of the mone, and rikne thyn altitude up among thyn 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 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 comune, tretis of the 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 worche this same conclusioun by the sonne, as wel as by the fix sterre. And for the more declaracioun, lo here thy figure.
35. The procedure to find if a planet’s motion is direct or retrograde. 35. This is the workinge of the conclusioun, to knowe yif that any planete be directe or retrograde.
Measure the altitude of any planet and note the value. Then quickly take the altitude of any fixed star on your astrolabe and note this value also. Wait three or four nights in order for the forward or backward movement of the planet to be visible. Then wait until the fixed star is at the same altitude that was measured before and measure the altitude of the same planet and note the value. If the planet is on the right of the astrolabe81 and the second altitude is less than the first altitude, then the planet’s movement is direct. And if the planet is on the east side and the second altitude is greater than the first altitude, then its motion is retrograde. If it is on the west, then the motion is direct. But the opposite applies to the path of the moon because the motion of the moon is different in its epicycle from the other planets, but not in other ways.82 Tak the altitude of any sterre that is cleped a planete, and note it wel. And tak eek anon the altitude of any sterre fix that thou knowest, and note it wel also. Come thanne agayn the thridde or the ferthe night next folwing; for thanne shaltow aperceyve wel the moeving of a planete, whether so he moeve forthward or bakward. Awaite wel thanne whan that thy sterre fix is in the same altitude that she was whan thou toke hir firste altitude; and tak than eftsones the altitude of the forseide planete, and note it wel.  For trust wel, yif so be that the planete be on the right syde of the meridional lyne, so that his seconde altitude be lasse than his first altitude was, thanne is the planete direct. 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 first altitude, 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. Determining the houses using the astrolabe 36. The conclusiouns of equaciosns of houses, after the Astrolabie, &c.
Set the beginning of the ascending degree on the end of the 8th unequal hour. The beginning of the second house will be on the midnight line. Move the ascending degree and set it on the end of the 10th unequal hour and the beginning of the 3rd house will be on the midnight line. Set the ascending degree on the eastern horizon and the beginning of the 4th house will be on the midnight line. The beginning of the 7th house is the nadir of the ascendant and the beginning of the 8th house is the nadir of the 2nd house and the beginning of the 9th is the nadir of the 3rd and the beginning of the 10th house is the nadir of the 4th and the beginning of the 11th house is the nadir of the 5th and the beginning of the 12th house is the nadir of the 6th.83 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 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 the degree that first assendeth, and set him on the ende of the 2 houre inequal; and thanne wol the by-ginning of the 5 hous sitte up-on the lyne of midnight; set thanne the nadir of the assendent on the ende of the 4 houre, than wol the byginning of the 6 house sitte on the midnight lyne. The byginning of the 7 hous is nadir of the assendent, and the byginning of the 8 hous is nadir of the 2; and the by-ginning of the 9 hous is nadir of the 3; and the by-ginning of the 10 hous is nadir of the 4; and the byginning of the 11 hous is nadir of the 5; and the byginning of the 12 hous is nadir of the 6. And for the more declaracion, lo here the figure.
37. Another method of determining the houses using the astrolabe 37. A-nother manere of equaciouns of houses by the Astrolabie.
Take the ascendant, which gives you four angles because the opposite of the ascendant, the beginning of the 7th house, is on the western horizon and the beginning of the 10th house sits on the meridian and its opposite84 is on the midnight line. Then set the rule on the degree that is ascending and calculate the number of degrees from the point of the rule to the meridian. Divide this angle into three equal parts, which defines three houses. Set the rule on each of the house divisions and you can see the beginning of each house in the zodiac. The beginning of the houses from the ascendant, that is, the start of the 12th house just above the ascendant, the beginning of the 11th house and then the 10th on the meridian line, as I have said. Continue in the same way below the ascendant and you have the other three houses, that is to say, the beginning of the 2nd, 3rd and 4th. The nadir of these three houses are the beginning of the three houses that follow. 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 orisonte; and the byginning of the 10 hous sit up-on the lyne meridional; and his opposit up-on the lyne of midnight. Thanne ley thy label over the degree that assendeth, and rekne fro the point of thy label alle the degrees in the bordure, til thou come to the meridional lyne; and departe alle thilke degrees in 3 evene parties, and take the the evene equacion of 3; for ley thy label over everich of 3 parties, and than maistow see by thy label in which degree of the zodiak is the by-ginning of everich of thise same houses fro the assendent: that is to seyn, the beginning of the 12 house next above thyn assendent; and thanne the beginning of the 11 house; and thanne the 10, up-on the meridional lyne; as I first seide. The same wyse wirke thou fro the assendent doun to the lyne of 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 find the meridian line for any location. 38. To finde the lyne merydional to dwelle fix in any certein place.
Take a round metal plate, the thicker the better to avoid warping, and draw a full circle a little inside the edge. Set the round plate on even ground, a flat stone or post in the ground and make it true using a level. Insert a compass stake, even pin or wire, the thinner the better, with a length no longer than one-quarter of the diameter of the circle, in the center of the plate and make it vertical using plumb rule. Wait until about 10 or 11 by the clock on a sunny day. Mark the point where the shadow of the pin just touches the circle. Then wait until after 1 o’clock when the shadow of the pin just touches the circle and mark that point. Take a compass and find the point exactly halfway between the marks. Take a rule and draw a line from the pin through the middle mark. This line is the meridian for that place.85 Tak a rond plate of metal; for warping, the brodere the bettre; and make there up-on a iust compas, a lite with-in the bordure; and ley this ronde plate up-on an evene grond, or on an evene ston, or on an evene stok fix in the gronde; and ley it even by a level. And in centre of the compas stike an evene pin or a wyr upright; the smallere the betere. Set thy pin by a plom-rewle evene upright; and let this pin be no lengere than a quarter of the diametre of thy compas, fro the centre. And waite bisily, aboute 10 or 11 of the clokke and whan the sonne shyneth, whan the shadwe of the pin entreth any-thing with-in the cercle of thy plate an heer-mele, and mark ther a prikke with inke. Abyde thanne stille waiting on the sonne after 1 of the clokke, til that the schadwe of the wyr or of the pin passe ony-thing out of the cercle of the compas, be it never so lyte; and set ther a-nother prikke of inke. Take than a compas, and mesure evene the middel by-twixe bothe prikkes, and set ther a prikke. Take thanne a rewle, and draw a stryke, evene a-lyne fro the pin un-to the middel prikke; and tak ther thy lyne meridional for evere-mo, as in that same place. And yif thow drawe a cros-lyne over thwart the compas, iustly over the lyne meridional, than the nadir of the south lyne is the north lyne. And for more declaracioun, lo here thy figure.
39. Description of the meridian line and the longitudes and latitudes of cities and towns relative to one another 39. Descripcion of the meridional lyne, of longitudes, and latitudes of citees and townes from on to a-nother of clymatz.
It is called the meridian because, regardless of the time of year, whenever the Sun comes to this place it is midday, or what we call noon. Therefore, it is called the midday line. Also note that any two towns, one of which is more easterly than the other, have different meridians. 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, what that the sonne by moeving of the firmament cometh to his verrey meridian place, than is hit verray midday, that we clepen oure noon, as to thilke man; and therfore is it cleped the lyne of midday. And nota, for evermo, of 2 citees or of 2 tounes, of whiche that o toun aprocheth more toward the est than doth that other toun, truste wel that thilke tounes han diverse meridians. 
Note also that arc of the equinoctial that is contained in or bounded between the two meridians is called the longitude of the town. And if it be that two towns have the same meridian, then they are the same distance to the east, and vice versa. But they have different almucantars for the elevation of the pole and the distance of the Sun. Nota also, that the arch of the equinoxial, that is conteyned or bounded by-twixe the 2 meridians, is cleped the longitude of the toun. And yif so be that two tounes have y-lyke meridian, or oon meridian, than is the distance of hem bothe y-lyke fer fro the est, and the contrarie. And in this manere they chaunge nat her meridian, but sothly they chaungen her almikanteras; for the enhausing of the pool and the distance of the sonne. 
The longitude of a climate is an imaginary line from east to west, always the same distance from the equator. And the latitude of a climate may be defined as the distance on the Earth from the beginning of the first climate to the end of that climate, up to the north pole.86 Some authors say that if the latitude of a country is measured, the meridian arc that is contained in or intercepted between the zenith and equator, then the distance from the equator to the end of a climate in the direction of the north pole is the true latitude of a climate. 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 is a lyne imagined from north to south the space of the erthe, fro the byginning of the first clymat unto the verrey ende of the same climat, evene directe agayns the pole artik. Thus seyn some auctours; and somme of hem sayn that yif men clepen the latitude, they mene the arch meridian that is contiened or intercept 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 find the degree of the zodiac where any planet rises on the horizon, regardless of whether its latitude is north or south 40. To knowe with which degree of the zodiak that any planete assendith on the orisonte, whether so that his latitude be north or south.
Look up the degree of the ecliptic for any sign where a planet is calculated to be in your almanac and this is planet’s longitude. Also look up the planet’s north or south latitude. You will be able to work in any sign of the zodiac by the following examples.
For example, the longitude of Venus or another planet was Capricorn 6° and the latitude was 2° north. Then I took a pair of dividers and called one point A and the other point F. I set point A on the longitude of Venus, Capricorn 6°, and I set point F upward 2° in the same sign because the latitude was north, so I have two degrees between the points.87 I then laid by compass down gently and set the degree of the longitude on the horizon. I applied a coat of wax to the rule, such as one waxes a pair of tables, so the marks of my dividers will be distinct. Then a set the rule over the degree of longitude and used the dividers to mark point A on the rule and, as closely as possible, marked the point F inside the ecliptic so it is to the north. Then a laid down the compass and examined marks A and F. I turned the rete and rule together until mark F is on the horizon and saw Venus with northern latitude of 2° at Capricorn 6°.88 
Know by thyn almenak the degree of the ecliptik of any signe in which that the planete is rekned for to be, and that is cleped the degree of his longitude; and knowe also the degree of his latitude fro the ecliptik, north or south. And by thise samples folwinge in special, maystow wirke for sothe in every signe of the zodiak. The degree of the longitude, par aventure, of Venus or of another planete, was 6 of Capricorne, and the latitude of him was northward 2 degrees fro the ecliptik lyne. I tok a subtil compas, and cleped that oon poynt of my compas A, and that other poynt F. Than tok I the point of A and set it in the 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 latitude was north, up-on the latitude of Venus, that is to seyn, in the 6 degree fro the heved of Capricorne; and thus have I 2 degrees by-twixe my two prikkes. Than leide I down softly my compas, and sette the degree of the longitude up-on the orisonte; tho tok I and wexede my label in manere of a peyre tables to resceyve distinctly the prikkes of my compas. Tho tok I this forseide label, and leide it fix over the degree of my longitude; tho tok I up my compas, and sette the point of A in the wex on my label, as evene as I coude gesse over the ecliptik lyne, in the ende of the longitude; and sette the point of F endlang in my label up-on the space of the latitude, inwarde and over the zodiak, that is to seyn, north-ward fro the ecliptik. 
You can use this technique with any northern latitude in all of the signs. But you will not be able to work with southern planetary latitudes in Capricorn because of the small space between the ecliptic and the border of the astrolabe, but you will be able to in of the other signs. Than leide I doun my compas, and lokede wel in the wey upon the prikke of A and of F; tho turned I my riet til that the prikke of F sat up-on the orisonte; than saw I wel that the body of Venus, in hir latitude of 2 degrees septentrionalis, assended, in the ende of the 6 degree, in the heved of Capricorne. And nota, that in the same maner maistow wirke with any latitude septentrional in alle signes; but sothly the latitude meridional of a planete in Capricorne may not be take, by-cause of the litel space by-twixe the ecliptik and the bordure of the Astrolabie; but sothly in alle other signes it may.
Also, assume the longitude of Jupiter, or some other planet was the first degree of Pisces and its latitude was 2° south. I set the point A on the first degree of Pisces on the ecliptic and set the point F downward in the same sign because the latitude was 2° south of the beginning of Pisces. Thus, I have two degrees between the two points. Then I set the degree of longitude on the horizon, set the rule over the ecliptic on the longitude degree and set point F on the rule 2° of latitude outward from the zodiac (that is, south of the ecliptic toward the border) and turned the rete [and rule together] point F is on the horizon. I then see that Jupiter, with a latitude of 2° south rises with Pisces 8° in horoscopo. You can use this method to work with any southern latitude, except in Capricorn, as I said earlier. If you use this technique with the rising of the moon, you must calculate its path hour by hour because it stays in a degree of longitude for only a short time, as well you know. But nonetheless, if you calculate its movement hourly from the tables  Also the degree, per aventure, of Iuppiter or of a-nother planete, was in the first degree of Pisces in longitude, and his latitude was 3 degrees meridional; tho tok I the point of A, and sette it in the firste degree of Pisces on the ecliptik, and anne sette I the point of F dounward in the same signe, by-cause that the latitude was south 3 degres, that is to seyn, fro the heved of Pisces; and thus have I 3 degrees by-twixe bothe prikkes; thanne sette I the degree of the longitude up-on the orisonte. Tho tok I my label, and leide it fix upon the degree of the longitude; tho sette I the point of A on my label, evene over the ecliptik lyne, in the ende evene of the degree of the longitude, and sette the point of F endlang in my label the space of 3 degrees of the latitude fro the zodiak, this is to seyn, southward fro the ecliptik, toward the bordure; and turned my riet til the prikke of F sat up-on the orisonte; thanne saw I wel that the body of Iuppiter, in his latitude of 3 degrees meridional, ascended with 14 degrees of Pisces in horoscopo. And in this manere maistow wirke with any latitude meridional, as I first seide, save in Capricorne. And yif thou wolt pleye this craft with the arysing of the mone, loke thou rekne wel hir cours houre by houre; for she ne dwelleth nat in a degree of hir longitude but a litel whyle, as thou wel knowest; but natheles, yif thou rekne hir verreye moeving by thy tables houre after houre,
[the original manuscript ends in mid-sentence at this point. The sentence was completed in some manuscripts by later scribes with, “thou shalt do wel ynow “- you will do well enough.] thou shalt do wel y-now
Notes
  1. John Somer. (return)
  2. Nicholas of Lynn. (return)
  3. Chaucer describes the back of the astrolabe first. (return)
  4. That is, the horizon. (return)
  5. The time required to walk a mile ~ 20 minutes. (return)
  6. Chaucer uses the term ‘noumbres of augrym’, that is, numbers used in arithmetic, to draw a distinction between Arabic numbers and Roman numerals. (return)
  7. of longitude. (return)
  8. al-Qabisi, c. 950, Aleppo, author of “Introduction to Astrology”, a highly regarded text at the time. (return)
  9. of longitude. (return)
  10. This is not a correct statement of the calendar reforms enacted during the reign of Julius Caesar. (return)
  11. The dominical numbers of the holy days. (return)
  12. Chaucer has the names of the scales reversed. The horizontal scale is used for shadows cast on the ground by a vertical gnomon and is called the umbra recta. The vertical scale is used for shadows cast by a horizontal gnomon on a wall and is called umbra versa. It is understandable that Chaucer might confuse the two since recta is the Latin word for ‘upright’, but it is the gnomon that is upright, not the scale. (return)
  13. This device is usually called the alidade. (return)
  14.  20 minutes. (return)
  15. That is, the beginning of the sign of Cancer. (return)
  16. It is not clear what value Chaucer used for the obliquity of the ecliptic because the numerical examples vary between editions. The actual value was about 23° 31′. In my opinion, he probably used the Toledan value of 23° 33′. (return)
  17. It is not clear whether Chaucer means a globe or the more common armillary sphere. Either context works since they are both three dimensional. (return)
  18. Chaucer uses the term ‘cenyth’ which is the point on the horizon corresponding to an azimuth angle. This is not exactly hour angle, but it is probably what was meant. (return)
  19. What Chaucer is trying to say is that the ecliptic on the astrolabe rete has the ecliptic arc itself as the border to the ecliptic circle and the northern six degrees of the zodiac are inside the ecliptic. The southern six degrees of the zodiac are not shown on the astrolabe. (return)
  20. More commonly called the ‘rule’. (return)
  21. From the Arabic ‘al muri’ – the pointer or index. (return)
  22. Alidade (return)
  23. It is pretty obvious that Chaucer ‘cooked’ the data in all of his examples by working backward from the answer, probably using tables. It is not realistic to be as accurate with a small astrolabe as his examples demonstrate. The results are, however, pretty close. (return)
  24. This problem is worked correctly for an astrolabe made for 52° 18′ N latitude. The latitude of Oxford is 51° 46′ N. Not bad accuracy. (return)
  25. i.e. Sirius, 1391 Right Ascension 6:45, Declination -16° 43′. (return)
  26. i.e. 9:40 PM. (return)
  27. This example is somewhat less accurate than the previous one. The altitude of Sirius at 9:40 PM on March 12, 1391 was about 9°. Chaucer’s result is about 25 minutes later than the actual time when Sirius was at 12° in altitude at Oxford. On the other hand, the answer is correct if calculated for a latitude of 47°. Note also that it is very hard to take an altitude for a star that is that low in the sky and that the moon was nearly half full on the night of March 12, 1391 which might not be bright enough to affect a star as bright as Sirius, but it might make it harder to find. I think that Chaucer chose his examples for ease in explanation and never actually made the observations. This is not a criticism by any means since his treatise was intended as a general educational tool. The examples are fine for that purpose. (return)
  28. i.e. the Sun’s altitude does not change enough when it is near culmination to get an accurate altitude reading. (return)
  29. i.e. within 15° of the meridian. (return)
  30. The horoscope is the degree of the ecliptic that is rising. (return)
  31. We are getting to fairly complicated material here related to the astrological houses. Several methods of defining the astrological houses have been used. The one used by Chaucer divides the angle from the point where the ecliptic crosses the eastern horizon to the meridian into three equal sections measured on the equator. The points where these angles cross the ecliptic are three of the houses. Another set of angles to the west of the meridian to the descendent (the point where the ecliptic crosses the horizon in the west) defines three more houses of a different angular width than the first three. The area below the horizon to the northern meridian is divided by into three different angles and three more are defined from the northern meridian to the descendent. The twelve houses thus defined are numbered from I to XII counterclockwise from the ascendant. Houses I, II and III have the same angular size as houses VII, VIII and IX and are in opposite quadrants. Similarly, houses X, XI and XII and IV, V and VI are the same size. The houses are particularly easy to determine on an astrolabe. Some astrologers sometimes defined the first house as beginning five degrees above the horizon (measured on the ecliptic) so a planet in the first house would be visible. This is the convention adopted by Chaucer in the next, rather tortuous paragraph. North offers a much more detailed and scholarly interpretation. (return)
  32. i.e. in the first house. (return)
  33. The brightest star in the constellation Scorpio. (return)
  34. I’m not confident that this paragraph is rendered correctly. (return)
  35. Horoscopes? (return)
  36. That is, to interpolate between almucantars, which were drawn for each two degrees on Chaucer’s instrument. (return)
  37. The problem is to find when the Sun is 18° below the horizon. Many astrolabes have a special almucantar for this purpose, but Chaucer’s apparently didn’t. (return)
  38. The point on the ecliptic opposite the sun. (return)
  39. Note that Chaucer is counting the signs of the zodiac inclusively, as was the custom in the Middle Ages. (return)
  40. The term artificial day is apparently used to signify that this length does not actually correspond to the length of daylight since there is considerable light during morning and evening twilight. (return)
  41. This item is a bit terse. The question raised is actually, “How long is a day in equal hours?”. The answer is to find the number of degrees in the day and divide by 15. Thus, if the Sun is above the horizon for the 200°, the day is 13 hours, 20 min long in equal hours. (return)
  42. It is not clear why this problem is included because the unequal hour can be found directly using the unequal hour arcs described in Part I.20. Either Chaucer’s astrolabe did not actually have the unequal hour arcs or this item was included for theoretical completeness. (return)
  43. In equal hours. (return)
  44. This is because the unequal hour arcs are drawn only below the horizon. Thus, the Sun’s actual position in the zodiac shows the unequal hour at night when the Sun is below the horizon. The point on the ecliptic that is opposite the Sun (the Sun’s nadir) is used during the day when the Sun is above the horizon. (return)
  45. The next rather complex paragraph attempts to explain the astrological concept of the planetary control of days and hours. Basically, each day of the week is said to ruled by a particular planet (of the seven classical planetary bodies) as follows: Saturday is ruled by Saturn, Sunday by the Sun, Monday/Moon, Tuesday/Mars, Wednesday/Mercury, Thursday/Jupiter, Friday/Venus. For each day, the first unequal hour of the day is ruled by the day’s planet and each subsequent hour by other planets (the moon being a planet in this context) in the order of their distance from the Earth according to Ptolemaic astronomy; Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon. The cycle of the planet ruling an hour cycles three times in 24 hours plus three planets. The ruling planet of the first hour of the next day falls in this sequence, which continues unbroken through the entire week, month, etc. This cycle repeats 24 times in a week so each hour of each day of each week is ruled by the same planet. (return)
  46. This would occur in 1389. (return)
  47. Chaucer is pointing out that the first hour of the day is named for the day’s planet and that the unequal hours of the day are found using the Sun’s nadir. (return)
  48. That is, the Sun rules the first hour of the day on Sunday. (return)
  49. Chaucer labels this item, “To know the degre of the sonne by thy ryet, for a maner curiosite”. In other words, “at your pleasure” or “just because you are curious”. (return)
  50. This can be done using either the rete or the calendar scale on the back. (return)
  51. This item has been modified considerably from the original. The original statement of the proposition was, “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.” The problem is the use of term ‘longitude’. The normal definition of celestial longitude is the angle of a celestial body on the ecliptic from the vernal equinox. Lines of equal longitude originate at the ecliptic pole. Celestial latitudes are angles above or below the ecliptic with 90° latitude at the ecliptic pole. In the Middle Ages, celestial positions were often specified using declination and a measure called mediation (coeli mediatio in Latin, literally ‘measure of the sky’). The definition of declination was the same then as now. The mediation of a celestial object is the point on the ecliptic that passes the meridian at the same instant as the star. Mediation is measured from the celestial pole to the ecliptic and is not the same as longitude. It is likely that the adoption of mediation as a celestial coordinate was because it is so obvious on an astrolabe; simply a line from the center of the instrument (the north celestial pole) to the ecliptic. The word ‘longitude’ has been replaced by ‘mediation’ in the following discussion. (return)
  52. This is intended to establish the time of the first observation. (return)
  53. This is intended to give a second time. The two times are supposed to be equal times before and after meridian passage of the unknown star; difficult to do in practice with an astrolabe. (return)
  54. This step is supposed to define the instant of meridian passage for the unknown star but it is wrong. The points on the ecliptic do not represent equal angles and the error is meaningful. Chaucer should have used the almuri or other index on the border scale to find an angle halfway between the observations instead of using the ascendant. The observational accuracy of this proposition is questionable in any case. (return)
  55. Basically, this is just the definition of mediation. (return)
  56. This is a rather difficult problem to solve analytically, but is quite simple on the astrolabe. (return)
  57. This step is intended to find the southern altitude of the equator and is not needed if the equator is drawn on the astrolabe plate. (return)
  58. The equinoxes. (return)
  59. i.e. the zenith distance of the equator is equal to the latitude. Presumably, Chaucer intends the equinoxes to be positioned on the meridian, but he does not say it specifically here, but see proposition 25 below. (return)
  60. This proposition tells you to measure the altitude of a star when it is directly above and below the pole and take the point halfway between as the pole. The method described is theoretically sound, if difficult to do accurately with an astrolabe. A finely divided and well sited quadrant would be better. One infers that the suggestion for making the measurements in the winter is because the measurement requires 12 hours and a long night is needed to complete the process. Chaucer was apparently aware that measuring the altitude of Polaris was not sufficiently accurate in the 14th century. Polaris is much closer to the celestial pole now. (return)
  61. This article seems to be identical to 23. (return)
  62. It is not clear what Chaucer means by ‘north or south’. The zenith distance of the southern culmination of the equator equals the latitude. The northern extreme of the equator is below the horizon for all northern latitudes. (return)
  63. i.e. at an equinox. (return)
  64. This is not strictly true. The Sun’s latitude is zero at the instant of the equinox, which is generally not at noon. The Sun will almost always have some latitude, either plus or minus, at noon on the day of the equinox. The maximum solar declination at noon on the day of an equinox is about ¼ degree.  (return)
  65. The latitude of the center of Oxford is 51° 46′. (return)
  66.  i.e. the local zenith. (return)
  67. Globe or armillary sphere. (return)
  68. The equator. (return)
  69. Latitudes not on the equator. These terms predate Ptolemy and are prominent in Ptolemy’s work. (return)
  70. Ptolemy et al? (return)
  71. i.e. at the equator. (return)
  72. This last statement is totally wrong. The almucantars for an astrolabe made for a 0° latitude are arcs of circle, as they are for all latitudes. The horizon is, however, a straight line. (return)
  73. To find the rising time you would divide the angle by 15. (return)
  74. After dividing by 15. (return)
  75. i.e. east or west. (return)
  76. This article is not quite correct. Instead of noting the angle of the rule on the border, you should note the Sun’s azimuth using the azimuth arcs on the plate and set the alidade on the back to the Sun’s azimuth angle. It is difficult to read the azimuth very accurately since there are usually few azimuth arcs. This method works best if the Sun’s altitude when it is on a marked azimuth is predetermined and then wait until the Sun reaches that altitude. (return)
  77. The terms used in this article have been significantly changed from the original. Chaucer refers to the ecliptic in this context as the wey of the sonne. Strictly speaking, the wey of the sonne is the path of the Sun in the sky for a given day. (return)
  78. This article works only in part. It is true that you can use the astrolabe with a normal plate to determine if the latitude of a planet is north (positive) or south (negative). You cannot, however, determine the amount of the planet’s latitude directly from the almucantars on an ordinary astrolabe plate. The problem is that latitudes are measured from the ecliptic plane to the ecliptic pole and the almucantars are based on the angle from the horizon to the zenith or nadir of a place. The alumcantars are in a different coordinate system than latitudes and calculating the latitude as Chaucer suggests gives the wrong answer. In any case, it would be asking too much from and astrolabe to suggest that a very accurate latitude could be measured at all. Some astrolabes were equipped with a special plate for the latitude of the arctic circle that was used for working with latitudes. It is possible to calculate the latitude from an observed altitude and azimuth using spherical trigonometry. (return)
  79. The meridian. (return)
  80. Chaucer mixes his terminology a bit here. The mariner’s compass rose divides the winds into 32 parts named, for example, N, N by E, NNE, NE by N, NE, etc. Chaucer begins to incorrectly apply the mariner’s terms to the azimuths but does not continue, so it is possible he was not certain of this point. (return)
  81.  i.e. in the east. (return)
  82. Planetary motions can be quite complex and this proposition does not work for any but the most elementary. Specifically, the time when the planet is stationary in its position is not covered and there are times when the planet’s latitude can change that do not match the conditions noted. One can use an astrolabe to determine if a planet is in direct or retrograde motion with only two observations under many, but not all circumstances. Many observations conducted over an extended period can be used to define the approximate movement of the moon and planets. (return)
  83. North covers this proposition and the next in detail on pp. 76-85. (return)
  84. The beginning of the 4th house. (return)
  85. This item clearly has nothing to do with astrolabes. Apparently, Chaucer felt it had sufficient educational value to justify including it anyhow. (return)
  86. Chaucer seems to be referring to the ‘climates’ defined by Ptolemy where the northern hemisphere was divided by latitudes where the length of the longest day varied by a half hour. Chaucer seems a bit vague in this proposition. Perhaps his knowledge was weak, this was just a draft to be edited later or he was running out of steam by this point in his treatise. (return)
  87. Chaucer appears to be estimating two degrees in latitude by measuring two degrees in longitude along the ecliptic. The approximation is actually not too bad because of the characteristics of he stereographic projection. (return)
  88. Chaucer seems to miss a minor point that the planet will not be above its longitude point on the ecliptic, but will be displaced toward the ecliptic pole. The error is not great for small latitudes, but is meaningful for larger values. (return)