Little Lowis my son, I have perceived well by certain evidences your ability to learn sciences touching numbers and proportions; and as well I consider your busy preyer in special to learn the Treatise of the Astrolabe.
Then, for as mach as a philosopher says, "he wraps him in his frend, that condescends to the rightful preyers of his frend," therefore I have given you a sufficient Astrolabe as for our horizon, compounded after the latitude of Oxford; upon which, by mediation of this little treatise, I purpose to teach you a certain number of conclusions appertaining to the same instrument.
（訳注：哲学者の言葉について、スキートは校注で、キケロ（*前106〜†前43）「Laelius de Amicitia（友情について）」44節の冒頭「Haec igitur prima lex amicitiae sanciatur, ut ... amicorum causa honesta faciamus（そこで次のことを友情の第一の法と定めよう、（中略）友人には誠実なことをなすべきだ）」であろうと推定している）
I say a certain of conclusions, for three causes.
The first cause is this: trust well that all the conclusions that have been found, or else possibly might be found in so noble an instrument as an Astrolabe, are unknown perfectly to any mortal man in this region, as I suppose.
Another cause is this; that truly, in any treatises of the Astrolabe that I have seen, there are some conclusions that will not in all things perform their behests; and some of them are to hard to your tender age of ten year to conceive.
This treatise, divided in five parts, I will show you under full light rules and naked words in English; for you can not yet Latin but little, my little son.
But nevertheless, these true conclusions in English suffice to you, as well as these same conclusions in Greek suffice to these noble scholars Greekes, and to Arabians in Arabic, and to Jews in Hebrew, and to the Latin folk in Latin; which Latin folk have them first out of other diverse languages, and written in their own tongue, that is to say, in Latin.
And god knows, that in all these languages, and in many more, these conclusions have been sufficiently learned and taught, and yet by diverse rules, right as diverse paths lead diverse folk the right wey to Rome.
Now I will prey meekly every discreet person that reads or hears this little treatise, to have my rude composing for excused, and my superfluity of words, for two causes.
The first cause is, for that curious composing and hard sentence is full heavy at once for such a child to learn.
And the second cause is this, that seems truly me better to write unto a child twice a good sentence, than he forget it once.
And Lowis, if so be that I show you in my light English as true conclusions touching this matter, and not only as true, but as many and as subtle conclusions as are showed in Latin in any common treatise of the Astrolabe, great me the more thank; and prey god save the king, that is lord of this language, and all that surely bears and obeys him, each in its degree, the more and the less.
But consider well, that I never claim to have found this work of my labor or of my skill.
I am not but a lewd compilator of the labor of old Astrologers, and have translated it in my English only for your doctrine; and with this sword I shall slay envy.
The first part of this treatise shall rehearse the figures and the members of your Astrolabe, because that you shall have the greater knowing of your own instrument.
The second part shall teach you the very practical work of the aforesaid conclusions, as far forth and as narrow as may be shown in so small an portable instrument about.
For every astrologer know well that smallest fractions will not be shown in an so small instrument, as in subtle tables calculated for a cause.
The third part shall contain diverse tables of longitudes and latitudes of fixed stars for the Astrolabe, and tables of declinations of the sun, and tables of longitudes of cities and of towns; and as well for the governance of a clock as for to find the altitude meridian; and many another notable conclusion, after the calendars of the reverent clerks, frere I. Somer and frere N. Lenne.
（訳注：ジョン・ソマーは14世紀後半に活動していた修道士で、チョーサーは彼の書いた「Kalendarium of John Somer」という天文年表を所持していた。
リンのニコラス（1386〜1411に活躍）も、天文学（占星学）分野の研究で著名だったカルメル会の修道士。オックスフォードで活動していた。 念のため言っとくとこの時代は宗教改革前（宗教改革は16世紀）なんでこの人ら確実にカトリックですねん。牧師とか訳しちゃう奴pgrやぞ）
（第4部：天体の動き・月の動き）
The fourth part shall be a theory to declare the moving of the celestial bodies with the causes.
The which fourth part in special shall shows a table of the very moving of the moon from hour to hour, every day and in every sign, after your almanac; upon which table there follows a canon, sufficient to teach as well the manner of the working of that same conclusion, as to know in our horizon with which degree of the zodiac that the moon arises in any latitude; and the arising of any planet after its latitude from the ecliptic line.
The fifth part shall be an introductory after the statute of our doctors, in which you may learn a great part of the general rules of theory in astrology.
In which fifth part you shall find tables of equations of houses after the latitude of Oxford; and tables of dignities of planets, and other useful things, if god and his mother the maiden will vouchsafe, more than I promise, &c.
PART I.
Here begins the description of the Astrolabe.
これよりアストロラーベの解説を始める。
（リング）
Your Astrolabe has a ring to put on the thumb of your right hand in taking the height of things.
And take keep, for from henceforth, I will call the height of any thing that is taken by your rule, the altitude, without more words.
This ring runs in a manner swivel, fast to the mother of your Astrolabe, in so wide a space that it doesn't disturb the instrument to hang after its right center.
The Mother of your Astrolabe is the thickest plate, pierced with a large hole, that receives in their womb the thin plates compound for diverse climates, and your rete shapes in manner of a net or of a web of a spider; and for the more declaration, lo here the figure.
（訳注：スキートが主な底本としたケンブリッジ大学所蔵の写本（写本番号Dd. 3. 53）には、この「and for the more declaration, lo here the figure」の文章と共に大量の図が追加されている。
ここではスキートによる図版や本文の記述を元に、新たに図を描き下ろした）
This mother is divided on the back-half with a line, that comes descending from the ring down to the lowest border.
The which line, from the aforesaid ring unto the center of the large hole amid, is called the south line, or else the meridional line.
And the rest of this line down to the border is called the north line, or else the line of midnight.
And for the more declaration, lo here the figure.
アストロラーベのマーテルの裏側は、リングから下の縁まで引かれた線で分けられる。
このリングから中央の大きな穴の中心へと引かれた線は「南の線」または「子午線」と呼ばれる。
この線の下の縁までの残りの部分は「北の線」または「真夜中の線」と呼ばれる。
より詳しくは図で示す。
（訳注：解説は裏面から始まる）
（東の線・西の線）
Across this aforesaid long line, there crosses that another line of the same length from east to west.
Of the which line, from a little cross + in the border unto the center of the large hole, is called the East line, or else the line Orientale; and the remnant of this line from the aforesaid + unto the border, is called the West line, or the line Occidentale.
Now you have divided here the four quarters of your Astrolabe, after the four principal regions or quarters of the firmament.
And for the more declaration, lo here your figure.
The east side of your Astrolabe is called the right side, and the west side is called the left side.
Do not Forget this, little Lowis.
Put the ring of your Astrolabe upon 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 rule general, as well on the back as on the womb-side.
Upon the end of this east line, as I first said, is marked a little +, whereas everemore generaly is considered the entering of the first degree in which the sun arises.
And for the more declaration, lo here the figure.
From this little + up to the end of the meridional line, under the ring, you shall find the border divided with 90 degrees; and by that same proportion every quarter of your Astrolabe is divided.
Over the which degrees there are numbers of algorism, that divide that same degrees from five to five, as shown by long strokes between.
Of which long strokes the space between contains a mile-way.
And every degree of the border contains four minutes, that is to say, minutes of an hour.
And for more declaration, lo here the figure.
Under the compass of that degrees the names of the Twelve Sign is writen, as Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricornus, Aquarius, Pisces; and the numbers of the degrees of those signs are writen in algorism above, and with long divisions, from five to five; divided from time that the sign enters unto the last end.
But understand well, that these degrees of signs are each of them considered of 60 minutes, and every minute of 60 secondes, and so forth into small fractions infinit, as Alkabucius says.
And therefore, know well, that a degree of the border contains four minutes, and a degree of a sign contains 60 minutes, and have this in mind.
And for the more declaration, lo here your figure.
Next this follows the Circle of the Days, that is figured in manner of degrees, that contains in number 365; divided also with long strokes from five to five, and the numbers in algorism written under that circle.
And for more declaration, lo here your figure.
Next the Circle of the Days, follows the Circle of the names of the Months; that is to say, Januarius, Februarius, Martius, Aprilis, Maius, Junius, Julius, Augustus, September, October, November, December.
The names of these months were called in Arabians, some for their properties, and some by decrees of lords, some by other lords of Rome.
Moreover of these months, as liked to Julius Caesar and to Caesar Augustus, some were compound of diverse numbers of days, as July and August.
Then January has 31 days, February 28, March 31, April 30, May 31, June 30, July 31, August 31, September 30, October 31, November 30, December 31.
Nevertheless, although that Julius Caesar took 2 days out of February and put them in his month of July, and Augustus Caesar called the month of August after his name, and ordered it of 31 days, yet trust well, that the sun dwells therefore never the more nor less in one sign than in another.
Then the names of the Holidays in the Calendar follow, and next them the letters of the A, B, C, ... on which they follow.
And for the more declaration, lo here your figure.
Next the aforesaid Circle of the A,B,C,..., under the cross-line, the scale is marked, in manner of two squares, or else in manner of ladders, that serves by these 12 points and this divisions of full many a subtle conclusion.
Of this aforesaid scale, from the cross-line unto the very angle, is called Umbra Versa, and the lower part is called the Umbra Recta, or else Umbra Extensa.
And for the more declaration, lo here the figure.
Then you have a broad Rule, that has on either end a square plates pierced with a certain holes, some more and some less, to receive the stream of the sun by day, and also by mediation of your eye, to know the altitude of stars by night.
And for the more declaration, lo here your figure.
Then there is a large Pin, in manner of an axis, that goes through the hole that halt the tables of the climates and the rete in the womb of the Mother, through which Pin there goes a little wedge which that is called "the horse," that strains all these parts together; this aforesaid great Pin, in manner of an axis, is imagined to be the Pole Arctic in your Astrolabe.
And for the more declaration, lo here the figure.
The womb-side of your Astrolabe is also divided with a long cross in four quarters from east to west, from south to north, from right side to left side, as the back-side is.
And for the more declaration, lo here your figure.
The border of which womb-side is divided from the point of the east line unto the point of the south line under the ring, in 90 degres; and by that same proportion is every quarter divided as the back-side is, that amounts 360 degrees.
And understand well, that degrees of this border are answering and concentric to the degrees of the Equinoctial, that is divided in the same number as every other circle is in the high heaven.
This same border is divided also with 23 letters capitals and a small cross + above the south line, that show the 24 hours equals of the clock; and, as I have said, 5 of these degrees makes a mile-way, and 3 mile-way makes an hour.
And every degree of this border contains 4 minutes, and every minute 60 seconds; now have I told you twice.
And for the more declaration, lo here the figure.
The plate under your rete is described with 3 principal circles; of which the least is called the circle of Cancer, because that the head of Cancer turns evermore concentric upon the same circle.
In this head of Cancer, declination northward of the sun is the greatest.
And therefore it is called the Solstice of Summer; which declination, after Ptolemy, is 23 degrees and 50 minutes, as well in Cancer as in Capricorn.
This sign of Cancer is called the Tropic of Summer, of tropos, that is to say "turning"; for then the sun begins to pass away from us.
And for the more declaration, lo here the figure.
The middle circle in wideness, of these 3, is called the Equinoctial Circle; upon which the heads of Aries and Libra turn evermore.
And understand well, that evermore this Equinoctial Circle turns justly from very east to very west; as I have shown you in the sphere solid.
This same circle is called also the Weigher, equator, of the day; for when the sun is in the heads of Aries and Libra, then the days and the nights are equal of length in all the world.
And therefore these two signs are called the Equinoxes.
And all that moves within the heads of these Aries and Libra, its moving is called northward; and all that moves without these heads, its moving is called southward as from the equinoctial.
Take keep of these latitudes north and south, and do not forget it.
By this Circle Equinoctial is considered the 24 hours of the clock; for evermore the arising of 15 degrees of the equinoctial makes an hour equal of the clock.
This equinoctial is called the girdle of the first moving, or else of the angulus primi motus vel primi mobilis.
And observe, that first moving is called "moving" of the first movable of the 8 sphere, which moving is from east to west, and after again into east; also it is called "girdle" of the first moving, for it departs the first movable, that is to say, the sphere, in two equal parts, even-distance from the poles of this world.
この天の赤道は「原動天の帯域」または「angulus primi motus（プリムム・モビーレの領域）もしくは primi mobilis（プリムム・モビーレ）」と呼ばれる。
The widest of these three principal circles is called the Circle of Capricorn, because that the head of Capricorn turns evermore concentric upon the same circle.
In the head of this aforesaid Capricorn is the greatest declination southward of the sun, and therefore it is called the Solstice of Winter.
This sign of Capricorn is also called the Tropic of Winter, for then begins the sun to come again toward us.
And for the more declaration, lo here your figure.
Upon this aforesaid plate is planned certain circles that is named Almucantars, of which some of them seems perfect circles, and some seems imperfect.
The center that stands amid the narrowest circle is called the Zenith; and the
lowest circle, or the first circle, is colled the Horizon, that is to say, the circle that divides the two hemispheres, that is, the part of the heaven above the earth and the part beneath.
These Almucantars are composed by two and two, although so that on diverse Astrolabes some Almucantars are divided by one, and some by two, and some by three, after the quantity of the Astrolabe.
This aforesaid zenith is imagined to be the very point over the crown of your head; and also this zenith is the very pole of the horizon in every region.
And for the more declaration, lo here your figure.
From this zenith, as it seems, there come a manner crooked strokes like to the claws of a spider, or else like to the work of a woman's caul, in crossing across the Almucantars.
And these same strokes or divisions are called Azimuths.
And they divide the horizon of your Astrolabe in twenty four divisions.
And these Azimuths serve to know the direction of the firmament, and to other conclusions, as for to know the cenyth of the sun and of every star.
And for more declaration, lo here your figure.
Next these azimuths, under the Circle of Cancer, there are twelve oblique divisions, much like to the shape of the azimuths, that show the spaces of the hours of planets; and for more declaration, lo here your figure.
The Rete of your Astrolabe with your zodiac, shapes in manner of a net or of a spider-web after the old description, which you may turn up and down as yourself like, contains certain number of fixed stars, with their determined longitudes and latitudes; if so be that the maker has not erred.
The names of the stars are written in the margin of the rete there as they sits; of which stars the small point is called the Center.
And understand also that all stars sitting within the zodiac of your Astrolabe are called "stars of the north," for they arise by north the east line.
And all the rest fixed, out of the zodiac, are called "stars of the south;" but I do not say that they arise all by south the east line; witness on Aldebaran and Algomeysa.
Generally understand this rule, that those stars that are called stars of the north arise sooner than the degree of their longitude, and all the stars of the south arise after the degree of their longitude; this is to say, fixed stars in your Astrolabe.
The measure of this longitude of stars is taken in the ecliptic line of heaven, under which line, when that the sun and the moon are in an exact line or else in the immediate neighbourhood of this line, then is the eclipse of the sun or of the moon; as I shall declare, and eke the cause why.
But truly the Ecliptic Line of your zodiac is the outermost border of your zodiac, there are marked the degrees.
Your Zodiac of your Astrolabe is shapes as a compass which that contains a large breadth, as after the quantity of your Astrolabe; in example that the zodiac in heaven is imagined to be a surface containing a latitude of twelve degrees, whereas all the rest of circles in the heaven is imagined very lines without any latitude.
Amid this celestial zodiac a line is imagined, which that is called the Ecliptic Line, under which line is evermore the way of the sun.
Thus there are six degrees of the zodiac on that on side of the line, and six degrees on that other.
This zodiac is divided in twelve principal divisions, that divide the twelve signs.
And, for the narrowness of your Astrolabe, then every small division is in a sign divided by two degrees and two; I mean degrees containing sixty minutes.
And this aforesaid heavenly zodiac is called the Circle of the Signs, or the Circle of the Beasts; for zodia in language of Greek sounds "beasts" in Latin tongue; and in the zodiac is the twelve signs that have names of beasts; or else, for when the sun enters in any of the signs, it takes the property of such beasts; or else, for that the stars that are fixed there are disposed in signs of beasts, or shapes like beasts; or else, when the planets are under these signs, they cause us by their influence operations and effects like to the operations of beasts.
And understand also, that when an hot planet comes into an hot sign, then increases its heat; and if a planet is cold, then lessens its coldness, because of the hotly sign.
And by this conclusion you may take example in all the signs, are they moist or dry, or movable or fixed; reckoning the quality of the planet as I first said.
And each of these twelve signs has respect to a certain part of the body of a man and has it in governance; as Aries has your heaed, and Taurus your neck and your throat, Gemini your armholes and your arms, and so forth; as shall be shown more crearly in the fifth part of this treatise.
This zodiac, which that is part of the eighth sphere, closses the equinoctial; and it closses it again in equal part; and that on half declines southward, and that other northward, as plainly declares the treatise of the sphere.
And for more declaration, lo here your figure.
Then you have a label, that is shape like a rule, save that it is narrow and has no plates on either end with holes; but, with the small point of the aforesaid label, you shall calculate your equations in the border of your Astrolabe, as by your almury.
And for the more declaration, lo here your figure.
Your Almury is called the Denticle of Capricorn, or else the Calculater.
This same Almury sit fixed in the head of Capricorn, and it serves of many a necessary conclusion in equations of things, as shall be shown; and for the more declaration, lo here your figure.
PART II. Here begin the Conclusions of the Astrolabe.
これよりアストロラーベの使い方を始める。
太陽の軌道からその日の太陽の黄経を求める。
To find the degree in which the sun is day by day, after its course about. [Hic incipiunt Conclusiones Astrolabii; et prima est ad inveniendum gradus solis in quibus singulis diebus secundum cursum sol est existens.]
Reckon and know which is the day of your month; and lay your rule up that same day; and then the very point of your rule will sit in the border, upon the degree of your sun.
example as thus; the year of our lord 1391, the 12 day of March at midday, I would know the degree of the sun.
I sought in the back side of my Astrolabe, and found the circle of the days, the which I know by the names of the months written under the same circle.
Then I laid my rule over this aforesaid day, and the point of my rule in the border found upon the first degree of Aries, a little within the degree; and thus I know this conclusion.
Another day, I would know the degree of my sun, and this was at midday in the 13 day of December; I found the day of the month in manner as I said; then I laid my rule upon this aforseid 13 day, and the point of my rule found in the border upon the first degree of Capricorn, a little within the degree; and then I had of this conclusion the full experience.
And for the more declaration, lo here your figure.
To know the altitude of the sun, or of other celestial bodies. [De altitudine solis et aliorum corporum supra celestium.]
Put the ring of your Astrolabe upon your right thumb, and turn your left side against the light of the sun.
And move your rule up and down, till that the streams of the sun shine through both holes of your rule.
Look then how many degrees your rule is arisen from the little cross upon your east line, and take it the altitude of your sun.
And in this same way you may know by night the altitude of the moon, or of bright stars.
This chapter is so general ever in one, that there needs no more declaration; but do not forget it.
And for the more declaration, lo here the figure.
To know every time of the day by light of the sun, and every time of the night by the stars fix, and eke to know by night or by day the degree of any sign that ascends on the East Horizon, which that is called commonly the Ascendant, or else Horoscope. [Ad cognoscendum quodlibet tempus diei per solis indicacionem, et quodlibet tempus noctis per quasdam stellas in celo fixas; ac eciam ad inveniendum et cognoscendum signum super orizontem qui communiter vocatur ascendens.]
Take the altitude of the sun when you choose, as I have said; and set the degree of the sun, in case that it be before the middle of the day, among your almucantars on the east side of your Astrolabe; and if it be after the middle of the day, set the degree of your sun upon the west side; take this manner of setting for a general rule, once for ever.
And when you have set up the degree of your sun as many almucantars of height as was the altitude of the sun taken by your rule, lay over your label, upon the degree of the sun; and then the point of your label will sit in the border, upon the very time of the day.
Example as thus: the year of our lord 1391, the 12 day of March, I would know the time of the day.
I took the altitude of my sun, and found that it was 25 degrees and 30 of minutes of height in the border on the back side.
Then I turned my Astrolabe, and because that it was before midday, I turned my rete, and set the degree of the sun, that is to say, the 1 degree of Aries, on the right side of my Astrolabe, upon that 25 degrees and 30 of minutes of height among my almucantars; then I laid my label upon the degree of my sun, and found the point of my label in the border, upon a capital letter that is called an X; then I reckoned all the capital letters from the line of midnight unto this aforesaid letter X, and found that it was 9 of the clock of the day.
Then I looked down upon the east horizon, and there found the 20 degree of Gemini ascending; which that I took for my ascendant.
And in this way I had the experience for always in which manner I should know the time of the day, and eke my ascendant.
Then I would know the same night following the hour of the night, and worked in this way.
Among a heap of stars fix, it liked me for to take the altitude of the fair white star that is called Alhabor; and found it sitting on the west side of the line of midday, 18 degrees of height taken by my rule on the back-side.
Then I set the center of this Alhabor upon 18 degrees among my almucantars, upon the west side; because that it was found on the west side.
Then I laid my label over the degree of the sun that was descended under the west horizon, and reckoned all the letters capitals from the line of midday unto the point of my label in the border; and found that it was passed 8 of the clock the space of 2 degrees.
Then I looked down upon my east horizon, and found there 23 degrees of Libra ascending, which I took for my ascendant; and thus I learned to know once for ever in which manner I should come to the hour of the night and to my ascendant; as verily as may be taken by so small an instrument.
But nevertheless, in general, I would warn you forever, not make you never bold to have take a just ascendant by your Astrolabe, or else to have set justly a clock, when any celestial body by which that you expect govern that things are near the south line; for trust well, when that the sun is near the meridional line, the degree of the sun runs so long concentric upon the almucantars, that truly you shall err from the just ascendant.
The same conclusioun I say by the center of any fixed star by night; and moreover, by experience, I know well that in our horizon, from 11 of the clock unto one of the clock, in taking of a just ascendant in a portable Astrolabe, it is to hard to know.
I mean, from 11 of the clock before the hour of noon till one of the clock next following.
And for the more declaration, lo here your figure.
Special declaration of the ascendant. [Specialis declaracio de ascendente.]
The ascendant truly, as well in all nativities as in questions and elections of times, is a thing which that these astrologers greatly observe; wherefore seems me convenient, since that I speak of the ascendant, to make of it special declaration.
The ascendant truly, to take it at the largest, is that degree that ascends at any of those aforesaid times upon the east horizon; and therefore, if that any planet ascends at that same time in that aforesaid degree of its longitude, men say that the planet is in horoscopo.
But truly, the house of the ascendant, that is to say, the first house or the east angle, is a thing more broad and large.
For after the statutes of astrologers, what celestial body that is 5 degrees above that degree that ascends, or within that number, that is to say, near the degree that ascends, yet they reckon that planet in the ascendant.
And what planet that is under that degree that ascends the space of 25 degrees, yet they say that the planet is like to him that is in the house of the ascendant; but truly, if it passes the bounds of those aforesaid spaces, above or beneath, they say that the planet is failing from the ascendant.
Those astrologers say it, that the ascendant, and eke the lord of the ascendant, may be shaped for to be fortunate or unfortunate, as thus: they call a fortunate ascendant when that no wicked planet, as Saturn or Mars, or else the Tail of the Dragon, is in the house of the ascendant, nor that no wicked planet have no aspect of enmity upon the ascendant; but they will cast that they have a fortunate planet in their ascendant and yet in this felicity, and then they say that it is well.
Furthermore, they say that the unfortunate of an ascendant is the contrary of those aforesaid things.
The lord of the ascendant, they say, that it is fortunate, when it is in good place from the ascendant as in angle; or in a succedent, where as it is in its dignity and comforted with friendly aspects of planets and well received, and also that it may see the ascendant, and that it do not retrograde nor combust, not joined with no shrew in the same sign; not that it is not in its descention, nor joined with no planet in its discention, not have upon it no unfortunate aspect; and then they say that it is well.
Nevertheless, these are observances of judicial matters and rites of pagans, in which my spirit has no faith, nor knowing of its horoscopum; for they say that every sign is divided in 3 even parts by 10 degrees, and that portion they call a Face.
And although that a planet have a latitude from the ecliptic, yet some folk say, so that the planet arise in that same sign with any degree of the aforesaid face in which its longitude is reckoned, that yet the planet is in horoscopo, it is in nativity or in election, &c.
And for the more declaration, lo here the figure.
To know the very equation of the degree of the sun, if so that is it fall between your almucantars. [Ad cognoscendum veram equacionem de gradu solis, si contigerit fore in duas Almicanteras.]
For as much as the almucantars in your Astrolabe are compounded by two and two, whereas in various Astrolabes some almucantars are compounded by one and one, or else by two and two, it is necessary to your learning to teach you first to know and work with your own instrument.
Wherefore, when that the degree of your sun falls between two almucantars, or else if your almucantars are engraved with over great a point of a compass, (for both these things may cause error as well in knowing of the time of the day as of the very ascendant), you must work in this way.
Set the degree of your sun upon the higher almucantars of both, and watch well where as your almury touches the border, and set there a prick of ink.
Set down again the degree of your sun upon the lower almucantars of both, and set there another prick.
Remove then your almury in the border even amid both pricks, and this will lead justly the degree of your sun to sit between both almucantars in its right place.
Lay then your label over the degree of your sun; and find in the border the very time of the day or of the night.
And as verily you shall find your ascendant upon your east horizon.
And for more declaration, lo here your figure.
To know the spring of the dawn and the end of the evening, the which is called the two crepusculis: [Ad cognoscendum ortum solis et eius occasum, que vocatur vulgariter crepusculum.]
Set the nadir of your sun upon 18 degrees of height among your almucantars on the west side, and lay your label on the degree of your sun, and then shall the point of your label show the spring of day.
Also set the nadir of your sun upon 18 degrees of height among your almucantars on the east side, and lay over your label upon the degree of the sun, and with the point of your label find in the border the end of the evening, that is, very night.
The nadir of the sun is that degree that is opposite to the degree of the sun, in the seventh sign, as thus: every degree of Aries by order is nadir to every degree of Libra by order; and Taurus to Scorpio; Gemini to Sagittarius; Cancer to Capricorn; Leo to Aquarius; Virgo to Pisces; and if any degree in your zodiac is dark, its nadir shall declare it.
And for the more declaration, lo here your figure.
To know the arc of the day, that some folk call the artificial day, from the sun arising till it go to rest. [Ad cognoscendum archum diei, quem vulgus vocat diem artificialem, in hoc, ab ortu solis usque ad occasum.]
Set the degree of your sun upon your east horizon, and lay your label on the degree of the sun, and at the point of your label in the border set a prick.
Turn then your rete about till the degree of the sun sit upon the west horizon, and lay your label upon the same degree of the sun, and at the point of your label set another prick.
Reckon then the quantity of time in the border between both pricks, and take there your arc of the day.
The remnant of the border under the horizon is the arc of the night.
Thus you may reckon both arcs, or every portion, of whether that you like.
And by this manner of working you may see how long that any fixed star dwells above the earth, from time that it rises till it go to rest.
But the natural day, that is to say 24 hours, is the revolution of the equinoctial with as much part of the zodiac as the sun of its proper moving passes in the meanwhile.
And for the more declaration, lo here your figure.
To turn the unequal hours in equal hours. [Ad convertendum horas inequales in horas equales.]
Know the number of the degrees in the unequal hours, and divide it by 15, and take it your equal hours.
And for the more declaraciun, lo here your figure.
To know the quantity of the vulgar day, that is to say, from spring of the day unto very night. [Ad cognoscendum quantitatem diei vulgaris, viz. ab ortu diei usque ad noctem.]
Know the quantity of your crepusculis, as I have taught in the chapter before, and add it to the arc of your artificial day; and take it the space of all the whole vulgar day, unto very night.
The same manner you may work, to know the quantity of the vulgar night.
And for the more declaration, lo here the figure.
To know the quantity of unequal hours by day. [Ad cognoscendum horas inequales in die.]
Understand well, that these unequal hours are called hours of planets, and understand well that sometime they are longer by day than by night, and sometime the contrary.
But understand well, that evermore, generally, the unequal hour of the day with the unequal hour of the night contain 30 degrees of the border, which border is evermore answering to the degrees of the equinoctial; wherefore the arc of the artificial day divide in 12, and take it the quantity of the unequal hour by day.
And if you abate the quantity of the unequal hour by day out of 30, then the remnant that leave shall perform the hour unequal by night.
And for the more declaracioun, lo here the figure.
To know the quantity of equal hours. [Ad cognoscendum quantitatem horarum inequalium.]
The quantity of equal hours, that is to say, the hours of the clock, are divided by 15 degrees already in the border of your Astrolabe, as well by night as by day, generally forever.
What needs more declaration?
Wherefore, when you list to know how many hours of the clock are passed, or any part of any of these hours that are passed, or else how many hours or part of hours are to come, from switch a time to switch a time, by day or by night, know the degree of your sun, and lay your label on it; turn your rete about jointly with your label, and with the point of it reckon in the border from the sun arise unto the same place there you desire, by day as by night.
I will declare this conclusion in the last chapter of the 4 part of this treatise so openly, that there shall lack no word that needs to the declaration.
And for the more declaration, lo here the figure.
Special declaration of the hours of planetes. [Specialis declaracio de horis planetarum.]
Understand well, that evermore, from the arising of the sun till it go to rest, the nadir of the sun shall show the hour of the planet, and from that time forward all the night till the sun arise; then the very degree of the sun shall show the hour of the planet.
Example as thus.
The 13 day of March fill upon a Saturday perchance, and, at the arising of the sun, I found the second degree of Aries sitting upon my east horizon, although that it was but little; then I found the 2 degree of Libra, nadir of my sun, descending on my west horizon, upon which west horizon every day generally, at the sun arises, the hour of any planet enters, after which planet the day bears its name; and ends in the next stroke of the plate under the aforesaid west horizon; and ever, as the sun climbs upper and upper, so its nadir goes downer and downer, teaching by such strokes the hours of planets by order as they sit in the heaven.
The first hour unequal of every Saturday is to Saturn; and the second, to Jupiter; the 3rd, to Mars; the 4th, to the Sun; the 5th, to Venus; the 6th, to Mercury; the 7th, to the Moon; and then again, the 8th is to Saturn; the 9th, to Jupiter; the 10th, to Mars; the 11th, to the Sun; the 12th, to Venus; and now my sun is gone to rest as for that Saturday.
Then the very degree of the sun shows the hour of Mercury entering under my west horizon at evening; and next it succeeds the Moon; and so forth by order, planet after planet, in hour after hour, all the night long till the sun arise.
Now the sun resets that Sanday by the morning; and the nadir of the sun, upon the west horizon, shows me the entering of the hour of the aforesaid sun.
And in this manner succeeds planet under planet, from Saturn unto the Moon, and from the Moon up again to Saturn, hour after hour generally.
And thus I know this conclusion.
And for the more declaration, lo here the figure.
To know the altitude of the sun in middle of the day, that is called the meridian altitude. [Ad cognoscendum altitudinem solis in medio diei, que vocatur altitudo meridiana.]
Set the degree of the sun upon the meridional line, and reckon how many degrees of almucantars are between your east horizon and the degree of the sun.
And take them your altitude meridian; this is to say, the highest of the sun as for that day.
So you may know in the same line, the highest course that any fixed star climbs by night; this is to say, that when any fixed star is passed the meridional line, then it begins to descend, and so the sun does.
And for the more declaration, lo here your figure.
To know the degree of the sun by your rete, for a manner curious, &c. [Ad cognoscendum gradum solis curiose.]
Seek busily with your rule the highest of the sun in middle of the day; then turn your Astrolabe, and mark with a prick of ink the number of that same altitude in the meridional line.
Turn then your rete about till you find a degree of your zodiac according with the prick, this is to say, sitting on the prick; and in truth, you shall find but two degrees in all the zodiac of that condition; and yet that two degrees are in diverse signs; then you may lightly know the sign in which that is the sun by the season of the year.
And for the more declaration, lo here your figure.
To know which day is like to which day as of length, &c. [Ad cognoscendum quales dies in longitudine sunt similes.]
Look which degrees are alike far from the heads of Cancer and Capricorn; and look, when the sun is in any of that degrees, then the days are alike of length.
This is to say, that as long is that day in that month, as was such a day in such a month; there varying but little.
Also, if you take two days naturally in the year alike far from either point of the equinoctial in the opposite parts, then as long the artificial day of is that on day as is the night of that other, and the contrary.
And for the more declaration, lo here youe figure.
This chapter is a manner declaration to conclusions that follow. [Illud capitulum est quedam declaracio ad certas conclusiones sequentes.]
Understand well that your zodiac is divided in two half circles, as from the head of Capricorn unto the head of Cancer; and backward from the head of Cancer unto the head of Capricorn.
The head of Capricorn is the lowest point, where as the sun goes in winter; and the head of Cancer is the highest point, in which the sun goes in sommer.
And therefore understand well, that any two degrees that are alike far from any of these two heads, trust well that the two degrees are of alike declination, it is southward or northward; and the days of them are alike of length, and the nights also; and the shadows alike, and the altitudes alike at midday forever.
And for more declaration, lo here your figure.
To know the very degree of any manner strange or not strange star after its longitude, though it is indeterminate in your Astrolabe; truly to the truth, thus it shall be know. [Ad cognoscendum verum gradum alicuius stelle aliene secundum eius longitudinem, quamvis sit indeterminata in astrolabio; veraciter isto modo.]
Take the altitude of this star when it is on the east side of the meridional line, as near as you may guess; and take an ascendant immediately by some manner fixed star which that you know; and do not forget the altitude of the first star, and your ascendant.
And when that this is done, spy diligently when this same first star passes anything the south westward, and have it immediately in the same number of altitude on the west side of this meridional line as it was caught on the east side; and take a new ascendant immediately by some manner fixed star which that you know; and do not forget this secound ascendant.
And when that this is done, then reckon how many degrees are between the first ascendant and the second ascendant, and reckon well the middle degree between both ascendants, and set that middle degree upon your east horizon; and then wait what degree that sit upon the meridional line, and take it the very degree of the ecliptic in which the star stands for the time.
For in the ecliptic the longitude of a celestial body is reckoned, exactly from the head of Aries unto the end of Pisces.
And its latitude is reckoned after the quantity of its declination, north or south toward the poles of this world; as thus.
If it is of the sun or of any fixed star,its latitude or its declination reckon from the equinoctial circle; and if it is of a planet, reckon then the quantity of its latitude from the ecliptic line.
Although so that the declination or the latitude of any celestial body may be reckoned from the equinoctial, after the site north or south, and after the quantity of its declination.
And right so the latitude or the declinacion of any celestial body may, save only of the sun, after its site north or south, and after the quantity of its declination, be reckoned from the ecliptic line; from which line all planets sometime decline north or south, save only the aforesaid sun.
And for the more declaration, lo here your figure.
To know the degrees of the longitudes of fixed stars after that they are determined in your Astrolabe, if so is that they are truly set. [Ad cognoscendum gradus longitudinis de stellis fixis que determinantur in astrolabio, sicut in suis locis recte locentur.]
Set the center of the star upon the meridional line, and take keep of your zodiac, and look what degree of any sign that sit on the same meridional line at that same time, and take the degree in which the star stands; and that same star comes with that same degree unto that same line from the horizon.
And for more declaration, lo here your figure.
To know with which degree of the zodiac any fixed star in your Astrolabe arises upon the east horizon, althogh its dwelling is in another sign. [Ad cognoscendum cum quibus gradibus zodiaci que stella fixa in astrolabio ascendit super orizontem orientalem, quamvis eius statio sit in alio signo.]
Set the center of the star upon the east horizon, and look what degree of any sign that sit upon the same horizon at that same time.
And understand well, that with that same degree arises that same star; and this marvellous arising with a strange degree in another sign is because that the latitude of the fixed star is either north or south from the equinoctial.
But truly the latitudes of planets are commonly reckoned from the ecliptic, because that none of it declines but few degrees out from the breadth of the zodiac.
And take good keep of this chapter of arising of the celestial bodies; for trust well, that neither moon nor star as in our oblique horizon arises with that same degree of its longitude, save in one case; and that is, when they have no latitude from the ecliptic line.
But nevertheless, sometime each of these planets is under the same line.
And for more declaracioun, lo here your figure.
To know the declination of any degree in the zodiac from the equinoctial circle, &c. [Ad cognoscendum declinacionem alicuius gradus in zodiaco a circulo equinoctiali.]
Set the degree of any sign upon the meridional line, and reckon its altitude in almucantars from the east horizon up to the same degree set in the aforesaid line, and set there a prick.
Turn up then your rete, and set the head of Aries or Libra in the same meridional line, and set there another prick.
And when that this is done, consider the altitudes of them both; for truly the difference of that altitudes is the declination of that degree from the equinoctial.
And if so is that the degree is northward from the equinoctial, then it is declination north; if it is southward, then it is south.
And for the more declaration, lo here your figure.
To know for what latitude in any region the almucanters of any table are compounded. [Ad cognoscendum pro qua latitudine in aliqua regione almicantre tabule mee sunt composite.]
Reckon how many degrees of almucanters, in the meridional line, are from the equinoctial circle unto the zenith; or else from the arctic pole unto the north horizon; and for so a great latitude or for so a small latitude is the table compounded.
And for more declaration, lo here your figure.
To know in the special latitude of our country, I mean after the latitude of Oxford, and the height of our pole. [Ad cognoscendum specialiter latitudinem nostri regionis, scilicet latitudinem Oxonie, et altitudinem poli nostri.]
Understand well, that the head of Aries or Libra in the equinoctial from our horizon is as far as is the zenith from the arctic pole; and the arctic pole from the horizon is as high, as the equinoctial is far from the zenith.
I prove it thus by the latitude of Oxford.
Understand well, that the height of our arctic pole from our north horizon is 51 degrees and 50 minutes; then the zenith from our arctic pole is 38 degrees and 10 minutes; then the equinoctial from our zenith is 51 degrees and 50 minutes; then is our south horizon from our equinoctial 38 degrees and 10 minutes.
Understand well this reckoning.
Also do not forget that the zenith is 90 degrees of height from the horizon, and our equinoctial is 90 degrees from our arctic pole.
Also this short rule is true, that the latitude of any place in a region is the distance from the zenith unto the equinoctial.
And for more declaration, lo here your figure.
To prove evidently the latitude of any place in a region, by the prove of the height of the arctic pole in that same place. [Ad probandum evidenter latitudinem alicuius loci in aliqua regione, per probacionem altitudinis de polo artico in eodem loco.]
In some winter's night, when the firmament is clear and thickly covered with star, wait a time till that any fixed star sit exactly in a perpendicular line over the arctic pole, and call that star A.
And wait another star that sit exactly in a line under A, and under the pole, and call that star F.
And understand well, that F is not considered but only to declare that A sit exactly over the pole.
Take then immediately the altitude of A from the horizon, and do not forget it.
Let A and F go farewell till against the dawn a great while; and come then again, and abide till that A is exactly under the pole and under F; for truly, then F will sit over the pole, and A will sit under the pole.
Take then soon after the altitude of A from the horizon, and note as well its second altitude as its first altitude; and when that this is done, reckon how many degrees that the first altitude of A exceeds its second altitude, and take half that portion that is exceeded, and add it to its second altitude; and take it the elevation of your pole, and also the latitude of your region.
For these two are of a number; this is to say, as many degrees as your pole is elevated, is so much the latitude of the region.
Example as thus: peradventure, the altitude of A in the evening is 56 degrees of height.
Then its second altitude or the dawn will be 48; that is 8 less than 56, that was its first altitude at even.
Take then the half of 8, and add it to 48, that was its second altitude, and then you have 52.
Now you have the height of your pole, and the latitude of the region.
But understand well, that to prove this conclusion and many another fair conclusion, you must have a plummet hanging on a line higher than your head on a perch; and that line must hang exactly perpendicular between the pole and your eye; and then you shall see if A sit exactly over the pole and over F at exactly; and also if F sit exactly over the pole and over A or day.
And for more declaration, lo here your figure.
Another conclusion to prove the hight of the arctic pole from the horizon. [Alia conclusio ad probandum altitudinem de polo artico ab orizonte.]
Take any fixed star that never descends under the horizon in that region, and consider its highest altitude and its lowest altitude from the horizon; and make a number of both these altitudes.
Take then and abate half that number, and take it the elevation of the arctic pole in that same region.
And for more declaration, lo here your figure.
Another conclusion to prove the latitude of the region, &c. [Alia conclusio ad probandum latitudinem regionis.]
Understand well that the latitude of any place in a region is verily the space between the zenith of it that dwells there and the equinoctial circle, north or south, taking the measure in the meridional line, as shown in the almucantars of your Astrolabe.
And that space is as much as the arctic pole is high in the same place from the horizon.
And then the depression of the antarctic pole is, that is to say, then the antarctic pole is beneath the horizon, the same quantity of space, neither more nor less.
Then, if you desire to know this latitude of the region, take the altitude of the sun in the middle of the day, when the sun is in the heads of Aries or of Libra; (for then the sun moves in the equinoctial line); and abate the number of that same sun's altitude out of 90, and then the remnant of the number is that leaves the latitude of the region.
As thus: I suppose that the sun is that day at noon 38 degrees and 10 minutes of hight.
Abate then these degrees and minutes out of 90; so there leaves 51 degrees and 50 minutes, the latitude.
I do not say this but for example; for I know well the latitude of Oxford is certain minutes less, as I might prove.
Now if so is that you seem to long a tarrying, to abide till that the sun is in the heads of Aries or of Libra, then wait when the sun is in any other degree of the zodiac, and consider the degree of its declination from the equinoctial line; and if it is so that the sun's declinacion is northward from the equinoctial, then abate the number of its declination from the sun's altitude at noon, and then you have the height of the heads of Aries and Libra.
As thus: my sun is, peradventure, in the first degree of Leo, 58 degrees and 10 minutes of height at noon and its declination is almost 20 degrees northward from the equinoctial; abate then that 20 degrees of declination out of the altitude at noon, than leaves you 38 degrees and odd minutes; lo there the head of Aries or Libra, and your equinoctial in that region.
Also if so is that the sun's declination is southward from the equinoctial, add then that declination to the altitude of the sun at noon; and take there the heads of Aries and Libra, and your equinoctial.
Abate then the height of the equinoctial out of 90 degrees, and then there leaves the distance of the pole, 51 degrees and 50 minutes, of that region from the equinoctial.
Or else, if you lust, take the highest altitude from the equinoctial of any fixed star that you know, and take its lower elongation extending from the same equinoctial line, and work in the manner aforesaid.
And for more declaracion, lo here your figure.
Declaration of the ascension of signs, &c. [Declaracio de ascensione signorum.]
The excellence of the solid sphere, among other noble conclusions, shows manifest the diverse ascensions of signs in diverse places, as well in the right circle as in the oblique circle.
These authors write that the sign is called of right ascension, with which ascends more part of the circle equinoctial and less part of the zodiac; and that sign ascends oblique, with which ascends less part of the equinoctial and more part of the zodiac.
Moreover they say, that in that country where as the zenith of them that dwells there is in the equinoctial line, and their horizon passing by the poles of this world, that folk have this right circle and the right horizon; and evermore the arc of the day and the arc of the night there is alike long, and the sun twice every year passing through the zenith of their head; and two summers and two winters in a year this aforesaid people have.
And the almucantars in their Astrolabes are straight as a line, so as shown in this figure.
The utility to know the ascensions in the right circle is this: trust well that by mediation of that ascensions these astrologers, by their tables and their instruments, know verily the ascension of every degree and minute in all the zodiac, as shall be shown.
And observe, that this aforesaid right horizon, that is called orison rectum, divides the equinoctial into right angles; and the oblique horizon, where as the pole is enhanced upon the horizon, closses the equinoctial in oblique angles, as shown in the figure.
And for the more declaration, lo here the figure.
This is the conclusion to know the ascensions of signs in the right circle, that is, circulus directus, &c. [Ad cognoscendum ascenciones signorum in recto circulo, qui vocatur circulus directus.]
Set the head of what sign you lust to know its ascending in the right circle upon the meridional line; and observe where your almury touches the border, and set there a prick.
Turn then your rete westward till that the end of the aforesaid sign sits upon the meridional line; and soon after observe where your almury touches the border, and set there another prick.
Reckon then the number of degrees in the border between both pricks, and take the ascension of the sige in the right circle.
And thus you may work with every portion of your zodiac, &c.
And for the more declaration, lo here your figure.
To know the ascensions of signs in the oblique circle in every region, I mean, in circulo obliquo. [Ad cognoscendum ascenciones signorum in circulo obliquo, in omni regione.]
Set the head of the sign which as you lust to know its ascension upon the east horizon, and observe where your almury touches the border, and set there a prick.
Turne then your rete upward till that the end of the same sign sit upon the east horizon, and observe soon after where as your almury touches the border, and set there another prick.
Reckon then the nuumber of degrees in the border between both pricks, and take it the ascension of the sign in the oblique circle.
And understand well, that all signs in your zodiac, from the head of Aries unto the end of Virgo, are called signs of the north from the equinoctial; and these signs arise between the very east and the very north in our horizon generaly forever.
And all signs from the head of Libra unto the end of Pisces are called signs of the south from the equinoctial; and these signs arise evermore between the very east and the very south in our horizon.
Also every sign between the head of Capricorn unto the end of Gemini arises on our horizon in less than two equal hours; and these same signs, from the head of Capricorn unto the end of Gemini, are called "tortuous signs" or "crooked signs," for they arise oblique on our horizon; and these crooked signs are obedient to the signs that are of right ascension.
The signs of right ascension are from the head of Cancer to the end of Sagittarius; and these signs arise more upright, and they are called also sovereign signs; and each of them arises in more space than in two hours.
Of which signs, Gemini obeys to Cancer; and Taurus to Leo; Aries to Virgo; Pisces to Libra; Aquarius to Scorpio; and Capricorn to Sagittarius.
And thus evermore two signs, that are alike far from the head of Capricorn, obey each of them till other.
And for more declaration, lo here the figure.
To know justly the four quarters of the world, as east, west, north, and south. [Ad cognoscendum evidenter quatuor partes mundi, scilicet, orientem, austrum, aquilonem, et occidentem.]
Take the altitude of your sun when you lust, and note well the quarter of the world in which the sun is for the time by the azimuth.
Turn then your Astrolabe, and set the degree of the sun in the almucantars of its altitude, on that side that the sun stands, as is the manner in taking of hours; and lay your label on the degree of the sun, and reckon how many degrees of the border are between the meridional line and the point of your label; and note well that number.
Turn then again your Astrolabe, and set the point of your great rule, there you take your altitudes, upon as many degrees in its border from its meridional as was the point of your label from the meridional line on the womb-side.
Take then your Astrolabe with both hands deeply and subtly, and let the sun shine through both holes of your rule; and subtly, in that shining, let your Astrolabe lay down evenly upon a smooth ground, and then the very meridional line of your Astrolabe will lay evenly south, and the east line will lay east, and the west line west, and north line north, so that you work softly and advisedly in the laying; and thus you have the 4 quarters of the firmament.
And for the more declaration, lo here the figure.
To know the altitude of planets from the way of the sun, whether so they are north or south from the aforesaid way. [Ad cognoscendum altitudinem planetarum a cursu solis, utrum sint in parte australi vel boreali a cursu supra dicto.]
Look when that a planet is in the meridional line, if that its altitude is of the same height that is the degree of the sun for that day, and then the planet is in the very way of the sun, and have no latitude.
And if the altitude of the planet is higher than the degree of the sun, then the planet is north from the way of the sun such a quantity of latitude as shown by your almucantars.
And if the altitude of the planet is less than the degree of the sun, then the planet is south from the way of the sun such a quantity of latitude as shown by your almucantars.
This is to say, from the way where as the sun went that day, but not from the way of the sun in every place of the zodiac.
And for the more declaration, lo here the figure.
To know the cenith of the arising of the sun, this is to say, the part of the horizon in which that the sun arises. [Ad cognoscendum signum de ortu solis, scilicet, illam partem orientis in qua oritur sol.]
You must first consider that the sun arises not always very east, but sometime by north the east, and sometime by south the east.
Truly, the sun arises nevermore very east in our horizon, but it is in the head of Aries or Libra.
Now your horizon is departed in 24 parts by your azimuth, in signification of 24 parts of the world; although so that shipmen reckon that parts in 32.
Then there is no more but observe in which azimuth that your sun enters at its arising; and take there the cenith of the arising of the sun.
The manner of the division of your Astrolabe is this; I mean, as in this case.
First it is devided in 4 principal regions with the line that goes from east to west, and then with another line that goes from south to north.
Then it is divided in small parts of azimuth, as east, and east by south, where as is the first azimuth above the east line; and so forth, from part to part, till that you come again unto the east line.
Thus you may understand also the cenith of any star, in which part it rises, &c.
And for the more declaration, lo here the figure.
To know in which part of the firmament the conjunctioun is. [Ad cognoscendum in qua parte firmamenti sunt coniuncciones solis et lune.]
Consider the time of the conjunction by your calender, as thus; look how many hours that conjunction is from the midday of the precedent day, as shown by the canon of your calender.
Reckon then that number of hours in the border of your Astrolabe, as you are wont to do in knowing of the hours of the day or of the night; and lay your label over the degree of the sun; and then the point of your label will sit upon the hour of the conjunction.
Look then in which azimuth the degree of your sun sits, and in that part of the firmament the conjunctioun is.
And for the more declaration, lo here your figure.
To know the cenith of the altitude of the sun, &c. [Ad cognoscendum signa de altitudine solis.]
This is no more to say but any time of the day the altitude of the sun take; and by the azimuth in which it stands, you may see in which part of the firmament it is.
And in the same way you may see, by the night, of any star, whether the star sit east or west or north, or any part between, after the name of the azimuth in which the star is.
And for the more declaration, lo here the figure.
To know truly the degree of the longitude of the moon, or of any planet that has no latitude for the time from the ecliptic line. [Ad cognoscendum veraciter gradum de longitudine lune, vel alicuius planete qui non habet longitudinem pro tempore causanto linea ecliptica.]
Take the altitude of the moon, and reckon your altitude up among your almucantars on which side that the moon stand; and set there a prick.
Take then immediately, upon the moon's side, the altitude of any fixed star which that you know, and set its center upon its altitude among your almucantars there the star is found.
Observe then which degree of the zodiac touches the prick of the altitude of the moon, and take there the degree in which the moon stands.
This conclusioun is very true, if the stars in your Astrolabe stands after the truth; of common, treatise of Astrolabe do not make exception whether the moon have latitude, or not; nor on whether side of the moon the altitude of the fixed star is taken.
And observe, that if the moon shows itself by light of day, then you may work this same conclusion by the sun, as well as by the fixed star.
And for the more declaration, lo here your figure.
This is the working of the conclusion, to know if that any planet is direct or retrograde. [Hec conclusio operatur ad cognoscendum si aliqua planeta sit directa vel retrograda.]
Take the altitude of any star that is called a planet, and note it well.
And take also soon the altitude of any fixed star that you know, and note it well also.
Come then again the third or the fourth night next following; for then you shall perceive well the moving of a planet, whether so it move forward or backward.
Await well then when that your fixed star is in the same altitude that it was when you took it first altitude; and take then soon after the altitude of the aforesaid planet, and note it well.
For trust well, if so is that the planet is on the right side of the meridional line, so that its second altitude is less than its first altitude was, then the planet is direct.
And if it is on the west side in that condition, then it is retrograde.
And if so is that this planet is upon the east side when its altitude is taken, so that its second altitude is more than its first altitude, then it is retrograde, and if it is on the west side, then it is direct.
But the contrary of these parts is of the course of the moon; for truly, the moon moves the contrary from other planets as in its epicycle, but in no other manner.
And for the more declaration, lo here your figure.
The conclusions of equations of houses, after the Astrolabe, &c. [Conclusio de equacione domorum.]
Set the beginning of the degree that ascends upon the end of the unequal 8 hour; then the beginning of the 2 house will sit upon the line of midnight.
Remove then the degree that ascends, and set it on the end of the unequal 10 hour; and then the beginning of the 3 house will sit upon the midnight line.
Bring up again the same degree that ascends first, and set it upon the horizon; and then the beginning of the 4 house will sit upon the line of midnight.
Take then the nadir of the degree that first ascends, and set it on the end of the unequal 2 hour; and then the beginning of the 5 house will sit upon the line of midnight; set then the nadir of the ascends on the end of the 4 hour, then the beginning of the 6 house will sit on the midnight line.
The beginning of the 7 house is nadir of the ascendent, and the beginning of the 8 house is nadir of the 2; and the beginning of the 9 house is nadir of the 3; and the beginning of the 10 house is the nadir of the 4; and the beginning of the 11 house is nadir of the 5; and the beginning of the 12 house is nadir of the 6.
And for the more declaration, lo here the figure.
Another manner of equatious of houses by the Astrolabe. [De aliqua forma equacionis domorum secundum astrolabium.]
Take your ascendant, and then you have your 4 angles; for well you know that the opposite of your ascendant, that is to say, your beginning of the 7 house, sit upon the west horizon; and the beginning of the 10 house sit upon the meridional line; and its opposite upon the line of midnight.
Then lay your label over the degree that ascends, and reckon from the point of your label all the degrees in the border, till you come to the meridional line; and depart all that degrees in 3 even parts, and take the even equation of 3; for lay your label over each of 3 parts, and then you may see by your label in which degree of the zodiac is the beginning of each of these same houses from the ascendant: that is to say, the beginning of the 12 house next above your assendent; and then the beginning of the 11 house; and then the 10, upon the meridional line; as I first said.
The same way you work from the ascendant down to the line of midnight; and then thus you have other 3 houses, that is to say, the beginning of the 2, and the 3, and the 4 houses; then the nadir of these 3 houses are the beginning of the 3 houses that follow.
And for the more declaration, lo here your figure.
To find the meridional line to dwell fixedly in any certain place. [Ad inveniendum lineam meridionalem per subtiles operaciones.]
Take a round plate of metal; for warping, the broader the better; and make there upon a just compass, a little within the border; and lay this round plate upon an even ground, or on an even stone, or on an even fixed stock in the ground; and lay it even by a level.
And in center of the compass stick an even pin or a wire upright; the smaller the better.
Set your pin by a plumb rule evenly upright; and let this pin be no longer than a quarter of the diameter of your compass, from the center.
And wait busily, about 10 or 11 of the clock and when the sun shines, when the shadow of the pin enters anything within the circle of your plate an hair-part, and mark there a prick with ink.
await then still waiting on the sun after 1 of the clock, till that the shadow of the wire or of the pin passes anything out of the circle of the compass, be it never so little; and set there another prick of ink.
Take then a compass, and measure evenly the middle between both pricks; and set there a prick.
Take then a rule, and draw a strike, evenly align from the pin unto the middle prick; and take there your meridional line for evermore, as in that same place.
And if you draw a cross-line across the compass, justly over the meridional line, then you have east and west and south; and, in consequence, then the nadir of the south line is the north line.
And for more declaration, lo here your figure.
Description of the meridional line, of longitudes, and latitudes of cities and towns from one to another of climates.
This meridional line is but a manner description of imagined line, that passes upon the poles of this world and by the zenith of our head.
And it is called the meridional line; for in what place that any manner man is at any time of the year, when that the sun by moving of the firmament comes to its very meridian place, then it is very midday, that we call our noon, as to that man; and therfore it is called the line of midday.
And nota, for evermore, of 2 cities or of 2 towns, of which that one town approachs more toward the east than does that other town, trust well that these towns are diverse meridians.
Nota also, that the arc of the equinoctial, that is contained or bounded between the 2 meridians, is called the longitude of the town.
And if so is that two towns have alike meridian, or one meridian, then the distance of them both is alike far from the east; and the contrary.
And in this manner they do not change their meridian, but truly they change their almucantars; for the elevation of the pole and the distance of the sun.
The longitude of a climate is a imagined line from east to west, alike distance between them all.
The latitude of a climate is a imagined line from north to south the space of the earth, from the beginning of the first climate unto the very end of the same climate, evenly direct against the arctic pole.
Thus say some authors; and some of them says that if men call the latitude, they mean the meridian arc that is contained or intercept between the zenith and the equinoctial.
Then they say that the distance from the equinoctial unto the end of a climate, evenly against the arctic pole, is the latitude of a climate for truth.
And for more declaration, lo here your figure.
To know with which degree of the zodiac that any planet ascends on the horizon, whether so that its latitude is north or south.
Know by your almanac the degree of the ecliptic of any sign in which that the planet is reckoned for to be, and that is called the degree of its longitude; and know also the degree of its latitude from the ecliptic, north or south.
And by these following samples in special, you may work for truth in every sign of the zodiac.
The degree of the longitude, peradventure, of Venus or of another planet, was 6 of Capricorn, and the latitude of it was northward 2 degrees from the ecliptic line.
I took a subtle compass, and called that one point of my compass A, and that other point F.
Then I took the point of A, and set it in the ecliptic line evenly in my zodiac, in the degree of the longitude of Venus, that is to say, in the 6 degree of Capricorn; and then I set the point of F upward in the same sign, because that the latitude was north, upon the latitude of Venus, that is to say, in the 6 degree from the head of Capricorn; and thus I have 2 degrees between my two pricks.
Then I laid down softly my compass, and set the degree of the longitude upon the horizon; then I took and waxed my label in manner of a pair of tables to receive distinctly the pricks of my compass.
Then I took this aforesaid label, and laid it fixed over the degree of my longitude; then I took up my compass, and set the point of A in the wax on my label, as even as I could guess over the ecliptic line, in the end of the longitude; and set the point of F along in my label upon the space of the latitude, inward and over the zodiac, that is to say, northward from the ecliptic.
Then I laid down my compass, and looked well in the way upon the prick of A and of F; then I turned my rete till that the prick of F sat upon the horizon; then I saw well that the body of Venus, in its latitude of 2 degrees northern, ascended, in the end of the 6 degree, in the head of Capricorn.
And nota, that in the same manner you may work with any northern latitude in all signs; but truly the meridional latitude of a planet in Capricorn may not be take, because of the little space between the ecliptic and the border of the Astrolabe; but truly, in all other signs it may.
Also the degree, peradventure, of Jupiter or of another planet, was in the first degree of Pisces in longitude, and its latitude was 3 degrees meridional; then I took the point of A, and set it in the first degree of Pisces on the ecliptic, and then I set the point of F downward in the same sign, because that the latitude was 3 degrees south, that is to say, from the head of Pisces; and thus I have 3 degrees between both pricks; then I set I the degree of the longitude upon the horizon.
Then I took my label, and laid it fixed upon the degree of the longitude; then I set the point of A on my label, evenly over the ecliptic line, in the end evenly of the degree of the longitude, and the point of F set along in my label the space of 3 degrees of the latitude from the zodiac, this is to say, southward from the ecliptic, toward the border; and turned my rete till the prick of F sat upon the horizon; then I saw well that the body of Jupiter, in its latitude of 3 degrees meridional, ascended with 14 degrees of Pisces in horoscopo.
And in this manner you may work with any meridional latitude, as I first said, save in Capricorn.
And if you will play this craft with the arising of the moon, look you reckon well its course hour by hour; for it does not dwells in a degree of its longitude but a little while, as you well know; but nevertheless, if you reckon its very moving by your tables hour after hour,
[you shall do well enough].
Explicit tractatus de Conclusionibus Astrolabii, compilatus per Galfridum Chauciers ad Filium suum Lodewicum, scolarem tunc temporis Oxonie, ac sub tutela illius nobilissimi philosophi Magistri N. Strode, etc.
Umbra Recta.
If it is so that you will work by umbra recta, and you may come to the base of the tower, in this manner you shall work.
Take the altitude of the tower by both holes, so that your rule lay even in a point.
Example as thus: I see through it at the point of 4; then I measure the space between me and the tower, and I find it 20 feet; then I behold how 4 is to 12, so right the space between you and the tower is to the altitude of the tower.
For 4 is the third part of 12, so the space between you and the tower is the third part of the altitude of the tower; then three 20 feet is the height of the tower, with adding of your own person to your eye.
And this rule is so general in umbra recta, from the point of one to 12.
Umbra Versa.
Another manner of working, by umbra versa.
If so is that you may not come to the base of the tower, I see it through the number of 1; I set a prick there at my foot; then I near to the tower, and I see it through at the point of 2, and there I set another prick; and I behold how 1 has it to 12, and there I find that it has that twelve times; then behold I how 2 has it to 12, and you shall find that six times; then you shall find that as 12 above 6 is the number of 6, the space between your two pricks is right so the space of 6 times your altitude.
And note, that at the first altitude of 1, you set a prick; and afterward, when you see it at 2, there you set another prick; then you find between two pricks 60 feet; then you shall find that 10 is the 6 part of 60.
And then 10 feet is the altitude of the tower.
For other points, if it fill in umbra versa, as thus: I set case it fill upon 2, and at the second upon 3; then you shall find that 2 is 6 parts of 12; and 3 is 4 parts of 12; then 6 passes 4, by number of 2; so the space between two pricks is twice the height of the tower.
And if the difference were three, then it should be three times; and thus you may work from 2 to 12; and if it is 4, 4 times; or 5, 5 times; et sic de ceteris.
Umbra Recta.
Another manner of working by umbra recta.
If it is so that you may not come to the base of the tower, in this manner you shall work.
Set your rule upon 1 till you see the altitude, and set at your foot a prick.
Then set your rule upon 2, and behold what is the difference between 1 and 2, and you shall find that it is 1.
Then measure the space between two pricks, and that is the 12 part of the altitude of the tower.
And if there were 2, it were the 6 part; and if there were 3, the 4 part; et sic deinceps.
And note, if it were 5, it were the 5 part of 12; and 7, 7 part of 12; and note, at the altitude of your conclusion, add the stature of your height to your eye.
Another manner conclusion, to know the mean motion and the argument of any planet.
To know the mean motion and the argument of every planet from year to year, from day to day, from hour to hour, and from small infinite fractions. [Ad cognoscendum medios motus et argumenta de hora in horam cuiuslibet planete, de anno in annum, de die in diem.]
In this manner you shall work: consider your root first, the which is made the beginning of the tables from the year of our lord 1397, and enter it into your slate for the last midday of December; and then consider the year of our lord, what is the date, and behold whether your date be more or less than the year 1397.
And if it is so that it is more, look how many years it passes, and with so many enter into your tables in the first line there as is written anni collecti et expansi.
And look where the same planet is written in the head of your table, and then look what you find in direct of the same year of our lord which is passed, by it 8, or 9, or 10, or what number that ever it is, till the time that you come to 20, or 40, or 60.
And write that you find in direct in your slate under your root, and add it together, and that is your mean motion, for the last meridian of the December, for the same year which that you has purposed.
次の方法で使う。
最初に1397年の天文表の冒頭から「基準位置（訳注：原文では「根」）」を定め、それを12月末日の正午の位置としてメモする。
それから求める日付と西暦を決めて、その日が1397年より前か後かを確認する。
1397年以降であれば、何年経過しているかを確認し、最初の行に「anni collecti et expansi（訳注：短期・長期年表）」と書かれている表を参照する。
そして表の見出しから求める惑星について書かれた欄を見て、8年先、9年先、10年先、あるいは20年先、40年先、60年先など、求める西暦に当たる欄を探す。
そしてその欄に書かれた値を、メモした基準位置の下の欄に書き込み、基準位置に足し合わせると、それが求める年の12月末日正午の平均運動となる。
And if it is so that it passes 20, consider well that from 1 to 20 are anni expansi, and from 20 to 3000 are anni collecti; and if your number passes 20, then take that you find in direct of 20, and if it is more, as 6 or 18, then take that you find in direct thereof, that is to say, signs, degrees, minutes, and seconds, and add together unto your root; and thus to make roots; and note, that if it is so that the year of our lord is less than the root, which is the year of our lord 1397, then you shall write in the same way first your root in your slate, and after enter into your table in the same year that is less, as I taught before; and then consider how many signs, degrees, minutes, and seconds your entering contains.
And so that is there are 2 entries, then add them together, and after withdraw it from the root, the year of our lord 1397; and the reminder that leaves is your mean motion from the last midday of December, the which you have purposed;
and if it so is that you will know your mean motion for any day, or for any fraction of day, in this manner you shall work.
Make your root from the last day of December in the manner as I have taught, and afterward behold how many months, days, and hours are passed from the midday of December, and with that enter with the last month that is full passed, and take that you find in direct of it, and write it in your slate; and enter with as many days as is more, and write that you find in direct of the same planet that you work for; and in the same way in the table of hours, for hours that are passed, and add all these to your root; and the reminder is the mean motion for the same day and the same hour.
Another manner to know the mean motion.
When you will make the mean motion of any planet to be by Arsechieles' tables, take your root, the which is for the year of our lord 1397; and if so is that your year is passed the date, write that date, and then write the number of the years.
Then withdraw the years out of the years that are passed that root.
Example as thus: the year of our lord 1400, I would know, precise, my root; then I wrote first 1400.
And under that number I wrote a 1397; then I withdraw the last number out of that, and then I found the residue was 3 year; I knew that 3 year was passed from the root, the which was written in my tables.
Then afterward I sought in my tables the annis collectis et expansis, and among my expanse years I found 3 year.
Then I took all the signs, degrees, and minutes, that I found direct under the same planet that I worked for, and wrote so many signs, degrees, and minutes in my slate, and afterward I added to signs, degrees, minutes, and seconds, the which I found in my root the year of our lord 1397; and kept the residue; and then I had the mean motion for the last day of December.
And if you would know the mean motion of any planet in March, April, or May, other in any other time or month of the year, look how many months and days are passed from the last day of December, the year of our lord 1400; and so with months and days enter into your table there you find your mean motion written in months and days, and take all the signs, degrees, minutes, and seconds that you find written in direct of your months, and add to signs, degrees, minutes, and seconds that you find with your root the year of our lord 1400, and the residue that leaves is the mean motion for that same day.
And note, if it is so that you would know the mean motion in any year that is less than your root, withdraw the number of so many years as it is less than the year of our lord a 1397, and keep the residue; and so many years, months, and days enter into your tables of your mean motion.
And take all the signs, degrees, and minutes, and seconds, that you find in direct of all the years, months, and days, and write them in your slate; and above that number write the signs, degrees, minutes, and seconds, the which you find with your root the year of our lord a 1397; and withdraw all the lower signs and degrees from the signs and degrees, minutes, and seconds of other signs with your root; and your residue that leaves is your mean motion for that day.
For to know at what hour of the day, or of the night, shall be flood or ebb.
First you know certainly, how that haven stands, that you lust to work for; that is to say in which place of the firmament the moon being, makes see full.
Then you observe quickly in what degree of the zodiac that the moon at that time is in.
Bring forth then the label, and set the point thereof in that same coast that the moon makes flood, and you set there the degree of the moon according with the edge of the label.
Then afterward observe where is then the degree of the sun, at that time.
Remove you then the label from the moon, and bring and set it justly upon the degree of the sun.
And the point of the label shall then declare to you, at what hour of the day or of the night shall be flood.
And there also you may know by the same point of the label, whether it is, at that same time, flood or ebb, or half flood, or quarter flood, or ebb, or half or quarter ebb; or else at what hour it was last, or shall be next by night or by day, then you shall know easily, &c.
Furthermore, if it is so that you happen to work for this matter about the time of the conjunction, the degree of the moon with the label bring forth to that coast as it is before said.
But then you shall understand that you may not bring forth the label from the degree of the moon as you did before; because the sun is then in the same degree with the moon.
And so you may know at that time by the point of the unremoved label the hour of the flood or of the ebb, as it is before said, &c.
And evermore as you find the moon passes from the sun, so you remove the label then from the degree of the moon, and bring it to the degree of the sun.
And you work then as you did before, &c.
Or else you know what hour it is that you are in, by your instrument.
Then you bring forth from then the label and ley it upon the degree of the moon, and thereby you may know also when it was flood, or when it will be next, it is night or day; &c.
[The following sections are spurious; they are numbered so as to show what propositions they repeat.]
（以下のセクションは疑わしい（訳注：正確な解説ではない）。重複する解説の番号を当てている）
41a. 正接の目盛り（Umbra Recta）その2
41a. Umbra Recta.
If your rule fall upon the 8 point on right shadow, then make your figure of 8; then look how much space of feet is between you and the tower, and multiply that by 12, and when you have multiplied it, then divide it is the same number of 8, and keep the reminder; and add thereto up to your eye to the reminder, and that shall be the very height of the tower.
And thus you may work on the same way, from 1 to 12.
41b. Umbra Recta.
Another manner of working upon the same side.
Look upon which point your rule falls when you see the top of the tower through two little holes; and measure then the space from your foot to the base of the tower; and right as the number of your point has itself to 12, right so the measure between you and the tower has itself to the height of the same tower.
Example: I set case your rule fall upon 8; then 8 is two-third parts of 12; so the space is the two-third parts of the tower.
42a. Umbra Versa.
To know the height by your points of umbra versa.
If your rule fall upon 3, when you see the top of the tower, set a prick there as your foot stand; and go near till you may see the same top at the point of 4, and set there another like prick.
Then measure how many foot is between the two pricks, and add the length up to your eye thereto; and that shall be the height of the tower.
And note, that 3 is [the] fourth part of 12, and 4 is the third part of 12.
Now 4 passes the number of 3 is the distance of 1; therefore the same space, with your height to your eye, is the height of the tower.
And if it is so that there is 2 or 3 distance in the numbers, so the mesures between the pricks should be two or three the height of the tower.
43a. Ad cognoscendum altitudinem alicuius rei per umbram rectam.
To know the height of things, if you may not come to the base of a thing.
Set your rule upon what you will, so that you may see the top of the thing through the two holes, and make a mark there your foot stands; and go near or farther, till you may see through another point, and mark there another mark.
And look then what the difference is between the two points in the scale; and right as that difference has it to 12, right so the space between you and the two marks has it to the height of the thing.
Example: I set case you see it through a point of 4; after, at the point of 3.
Now the number of 4 passes the number of 3 is the difference of 1; and this difference 1 has right as itself to 12, right so the measure between the two marks has it to the height of the thing, putting to the height of yourself to your eye; and thus you may work from 1 to 12.
42b. Per umbram versam.
Furthermore, if you will know in umbra versa, by the craft of umbra recta, I suppose you take the altitude at the point of 4, and make a mark; and you go near till you have it at the point of 3, and than make you there another mark.
Then you must divide 144 by each of the aforesaid points, as thus: if you divide 144 by 4, and the number that comes thereof shall be 36, and if you divide 144 by 3, and the number that comes thereof shall be 48, then look what the difference between 36 and 48 is, and there you shall find 12; and right as 12 has it to 12, right so the space between two pricks has it to the altitude of the thing.
