Severus Sebokht, Description of the Astrolabe, in R.T.Gunther, Astrolabes of the World, Oxford (1932) pp.82-103.
3. To find the hour during the night, by the help of the moon.
4. To find, by the help of the astrolabe, the ἐποχή, that is to say, the position of the sun.
6. To find the ἐποχή of ascension and descent, that is to say, the latitude of the moon.
8. How we should test, whether the pointer is accurate and well made.
15. How one can find the difference of the meridian in two towns.
16. How we can find out the ascensions of the right sphere, of which Ptolemy has written.
17. How we can know in which climate we are, from the sun or one of the fixed stars.
19. How we can know, by the help of the astrolabe, the longitude and latitude of the fixed stars.
Chapters 20 and 21 are lost
by
SEVERUS SABOKT
ca. A.D. 650
[Translated by Jessie Payne Smith Margoliouth]
[There is no Heading to the Syriac text.]
BY the help of God, Lord of All, we write the Treatise (σχόλιον) on the Astrolabe. On what the brazen astrolabe is; How it is composed; What and of what kind are its different parts; What are the names of the parts and of the figures upon it.
Before we happen to read the Treatise on the astrolabe, how it is to be used for determining the hour, and the other results which may be understood from it, we should know its composition and its form. I say, how and of what it is composed, how all its parts are arranged, and what the positions and signs on it are called; why tablets,1 circles, and different numbers must appear on it, and what is the number that gives the longitude of the heavenly spheres, and what is that which shows their latitude; how the four regions, east, west, north, and south are represented on it; which is the upper side or hemisphere above the earth and which is under it; with many other like things represented on the astrolabe.
This reasonable art is taught us by rules; but first we inquire as to the subject and manner of the astrolabe, and of what it is composed. I will take into consideration, O friend of learning, every necessary question, and accordingly I first mention in a few words the composition and the form of the astrolabe, as I have said above, and even before that I will give the definition of it, then I will explain it, and give notes upon the treatise to the best of my ability. In this way the understanding of this science will be easy and light.
Now an astrolabe is a skilfully constructed instrument, by the aid of which are determined the stars, the hours, the risings (of heavenly bodies), the tropical zones, in a word, the double movement of the celestial sphere, i. e. longitude and latitude, and the change of climes (or the various climes).
It is called skilful (or made by art) to distinguish it from 'natural'; compound, to distinguish it from 'simple'; by the aid of which the stars |83 &c. are determined, to distinguish from it the instruments of other arts. I mean, of geometry, of music, of medicine, and of all the manual arts.
The material of it is brass, the form round and flat, it is composed of three or four tablets.2 If they are raised, they are all found to be round, flat, and equal to each other. They are placed one upon another within one which encloses them all. This last has a rim like a case, which encloses and contains all of them. Above all these and within is placed the circle called the zodiac because the ζῴδια, that is to say the signs of the zodiac are marked on it with their names and degrees, which are 30 in number (for each sign). The astrolabe may be bipartite (διπλοῦς) when one inscribed degree represents two of them, or even tripartite (τριπλοῦς) when an inscribed degree represents three.3 It bears the names (of the signs) and all round the names of the most brilliant and best known of the fixed stars of the celestial sphere; their names being written above them. And all this structure of the signs of the zodiac of the fixed stars of which we have just spoken was called by the philosopher who constructed the astrolabe ἀράχνη, that is to say 'spider', because the attachments of its grooves are like the filaments or threads of a spider's web, plus all round it a round flat circle.
Next, as best they can, they mark on a quadrant 90 degrees, that is to say the quarter of the measure of a circumference, that is to say on one of the quarters of the outside tablet which encloses and contains all the rest. These degrees give the altitude for the upper hemisphere, which can go as far as 90°, to the point situated above the centre of the earth, that is to say, above the head of each one of us. So they divide this tablet of which we are speaking into four parts, by means of two straight lines, one drawn from the top to the bottom and the other from east to west in the revered form of the cross. On the upper part of the surface of this tablet are represented the 90 degrees of which we have spoken; the beginning, i.e. the first degree, is where the upper part of the hemisphere begins, that is to say, on the horizon near the earth and the 90th degree is at the (zenith) that is to say, at the point of the middle of the sky. Upon this tablet is attached a 'ruler' whose arms are sharpened to a point. On these latter are fixed two very small vanes, their height as their width is about an inch, and in each one of |84 them a hole is pierced. These two holes are set exactly opposite one another, so that if one is set directly opposite the sun, moon, or a star, the ray passes directly through the two, that is to say, the ray when it first falls on one vane passes directly to the other. The length 4 of this ruler is that of the diameter of the tablet, so that one of its heads may always pass or fall on the degrees of the quarter-circle. Its width is about an inch.
This ruler of which we have spoken, on which are fixed the two little vanes pierced by the two holes opposite each other, is called 'dioptron' by geometers because by it we see in a straight line a ray of the sun or of some other luminary. The heads of this dioptron, which are, as we have said, sharpened to points,5 are both called pointers of the degrees 6 because they show us in which degree of the quadrant, that is to say, of the quarter of the heaven, is to be found the sun, or some star at the moment of observing when a ray of the star passes through the dioptron.
At the middle of this dioptron, at the middle of all the above-mentioned tablets and of the spider's web is adjusted a hole, equal in each of them, in which is set a nail after the tablets have been arranged exactly one above the other. This nail marks the place (projection) of the North Pole, that is to say, the northern extremity of the axis of the world, and holds together all the parts of the astrolabe so that they shall not get lost.
On each side of the said tablets the clime is indicated by name, and [the tablet is] divided into degrees of its latitude and the hours of its longest day. Each tablet is also divided into four parts by means of two lines, as we have said, in the case of the outside tablet. But on this latter there are indicated only the degrees of altitude of one quadrant or 90°, whilst on the tablets are indicated those of the upper hemisphere from the southern horizon to the northern horizon, i.e. 180°. These 180 degrees begin at the horizon which strictly separates the upper half of the sphere from the lower, which is understood to be the further limits of the earth. On it are defined the east and the west, the north and the south, as well as the rising and setting of all luminaries, stars, and planets. And these reckoned from diameter to diameter in whatever direction desired, amount to 180 degrees, while as far as the point situated above our heads (zenith) are only 90°. Hence it is evident that these tablets of the astrolabe, relative to any clime will always |85 bear from one degree to 90 degrees from the southern quarter or region, as far as the point (σημεῖον) of the middle of the sky, that is to say, to the centre immediately above our head (zenith), in whatever clime we may be.
The philosopher has indicated the southern region not only because the latitude of the sphere or of the world begins thence, but because it is on this side that the circle of the zodiac passes above the horizon and that the greater number of the stars rise and set. On this side too are the three tropical zones whence are known the divers relative latitudes of the climes, and the meridian circle which owes to it its name. The 180 degrees, or rather, the 90 circles are called parallels, i.e. 'close to one another' or after one another.7 Whether reckoned from the east or from the west, but all meet in the circle of the 90 degrees on a straight line which is in truth (the meridian). They are not counted from the East and from the West, that is to say, on the celestial sphere, for such is not the intention of the philosopher who constructed the astrolabe, but from the south, straight along the meridian. The philosopher who constructed the astrolabe, limited its size for every clime, to the tropic of winter, as the figure shows; also, all parallels which precede the tropic of winter are interrupted as soon as they arrive at this zone and no further to the south (read to the north) because there is no more room or surface on the tablet. Hence those degrees or parallels to the south of the winter tropic could not be engraved for there is no room. It is necessary to engrave (them) from the eastern horizon towards the west; but it is evident that if we observe the sun, the moon, or one of the stars in the first degree of the said parallels, or in the 5th or in the 10th (as we shall learn from the Treatise on the Astrolabe), that is, before it reaches the parallel of the winter tropic which is the thirtieth in the fourth clime,8 it will matter little whether the luminary be in the east or in the west, we shall always say that it is at the altitude of that degree to the south of the winter tropic, because, as we have said, the parallels serve to measure the altitude of the sun, and not its longitude.9 |86
For the longitude of the entire heaven which is measured from east to west is 360°. These degrees are engraved on the edge or rim of the exterior tablet which encloses and contains all the others. These same 360° are divided into four parts of 90 degrees each; and these quadrants start from the equator. Thus the whole sphere is doubly divided by the parallels of longitude and of latitude, all the movement of all the spheres and of all the luminaries are within the same, i.e. the longitude and latitude. It was necessary that this double movement should be known, for the knowledge of it is useful to us for many exact researches and especially for the variations of the climes, and the distinction of the five zones, namely: the three tropical zones, the arctic and antarctic zones. The philosopher contrived to engrave for each climate, on the said tablets the latitude which goes from south to north, and in like manner to write the longitude which goes from east to west,10 and the same on the rim of the outer tablet as we have said above.11 He next taught how to ascertain both together by the rotation of the arachne and of the index of degrees which is fixed above, as we shall learn later. On each of these said tablets, the east and the west are again indicated by their names. The middle of the sky, or 'the point of the middle of the sky' is determined by a line which goes from top to bottom, intersecting all the parallels at right-angles, and passing the 90th degree which is called the meridian, as we have said. It is evident that from this 90th degree till we reach the end of the tablet on the side which the parallels intersect; it is named the south region, and from this same 90th degree towards the opposite side where the parallels stop, we shall have the north region. The last side, beneath where the twelve hours are marked, is called the place under the earth, and the meridian line which passes through it at right-angles is called 'centre of the place beneath the earth', or again, 'of the fathers'. The east is called, 'centre of life', and the west, 'centre of nuptials'.12 The three circles described on each tablet for every clime above and below the earth signify the 'tropics'. That which is at the extremity of all the tablets, and always bears the beginning of Capricorn, indicates the 'winter tropic'. The middle circle on which the beginnings of Aries and Libra constantly move is the |87 'equinoctial'; and finally, the innermost circle, on which the beginning of Cancer always moves, is the 'summer tropic'.
Further, we must most carefully mention that all the circles described on the astrolabe by the philosopher, as those of the tropical zones, the meridian and the parallels, all the four points and the eight places that are spoken of between them,13 the horizons of the seven climes, the axis (ἄξων) and the poles on which its ends rest, the circle of the middle of the zodiac, the arctic and antarctic zones situated above and below the earth and many other analogous things are to be perceived by the mind alone, but not by the senses. And so, the philosopher represented them in the air beneath the sphere of heaven. He considered them with his mind, and saw them on the sphere that bears them quite as clearly as the rest of the luminaries, planets, and stars.
But I think that I have sufficiently shown, concisely what is borne on the quarter of the outer tablet (i.e. the back). The diopter, the parallels which appear on each tablet, their points, the latitude and longitude of the whole sphere, the meridian and the plate beneath the earth, and the tropical zones; and that we must not seek to see by the senses, but by the mind.
I add a few words, O studious friend, on that which is called the web.14 As we have said above, it is placed above all the tables, that is to say, on the parallels of any clime that can occupy us. We can turn it round, and make it rise and lift it gradually to the middle of the heaven, and then make it drop as far as the west and beneath the earth. On that said quarter where there are 90 degrees, we observe among the signs of the zodiac on which degree the head of the diopter, which is the index, falls. After that we look and determine this same degree in the parallels of the corresponding clime, in which it is, then as we have to learn in the Treatise on the Astrolabe, we arrive little by little at what we are trying to find out. This brief recapitulation by way of introduction, on the construction and composition of the astrolabe, before arriving at the Treatise itself, will, I hope, be sufficient. |88 It is time then, for thee, O friend of study, our spiritual son, beloved in the Lord, to approach the Treatise. We will recount it as best we can, and we will divide it into distinct rules, so that he who comes across them may apprehend them easily. I will therefore begin:
End of the Introduction to the Treatise on the Astrolabe.
1. To find during the day, with the help of the astrolabe, the solar hour; then to find for this hour the degree (of the zodiac) that is in the ascendant, which star rises and sets, is in the descendant, which is in the middle of the heaven (at the meridian) and which is beneath the earth.15
We look first at the true position of the sun, and in what sign of the zodiac it is; then, at the hour that we want, we turn the whole instrument facing the sun until a ray passes through the two holes pierced opposite each other in the diopter. It is evident that if we place one point of the diopter called the 'index' on the quadrant, that is on the quarter of the whole celestial sphere which is 90 degrees only, we shall see how many degrees the index moves on the quadrant. We note the degree thence thus obtained. Then we turn the astrolabe to the other side, and turn the zone of the zodiac which is in the middle of the spider's web on to the clime which we want, and on to the intersections of the parallels, that is to say, next to one another, until we place the degree where the sun is, on the intersection of these parallels at the very degree where we first observed it by the help of a solar ray passing through the two holes of the diopter.16 Then we look under the earth for the degree diametrically opposed to the sun on the zodiac and how many hours it moves among the hours engraved underneath; and how this solar hour is to be found. Here is clear to us the degree 'of life', that 'of nuptials', that of the middle of the heaven and that of the underpart of the earth, for the degree and the sign found on the eastern horizon of the clime at the hour observed will be said to be 'at the life', that which is diametrically opposed on the western horizon will be said to be 'at the nuptials', |89 that which is at the summit of the clime, i.e. on the meridian line is 'in the middle of the heaven' and that which is diametrically opposed beneath the earth is 'at the fathers'.
For example, let us suppose that, in the fourth clime the index of the diopter is on the 30th degree, and that the sun is in the first degree of Cancer. Let us turn the web until the first degree of Cancer is on the eastern horizon, then, continue to turn the web till we bring it above as far as the first degree of Cancer on the 30th parallel where the index was, then look for the degree of the zodiac diametrically opposite to Cancer which is the first degree of Capricorn. This is situated beneath the earth at the third hour. That is, I say, the solar hour. From this we know both the four centres; for we find them by observing their places in the fourth clime which rises in the 5th degree of Leo, it sets in the same degree of Aquarius, again the Ram stands in mid-heaven in the 24th degree and beneath the earth Libra is in the same (degree). To know the ascensions from the beginning of the Ram to the point which rises at this hour we note the position of the index of the web which is the beginning of Capricorn, counting the degrees from that point of the middle of the heavens (the meridian) as far as the point where the beginning of Capricorn is, and we find 112 degrees for these ascensions in the fourth clime. We find also that Leo rises and that Aquarius sets in the 5th degree. When we carry this number over to the right sphere, we find that the Ram is in the middle of the heavens in the 24th degree: it is evident that Libra is under the earth in the same degree. From the first hour until the sixth the sun is on the parallels which precede the middle of the day, from the sixth until the twelfth it is on the parallels which follow the middle of the day. One recognizes the position of the sun, if it is before or after midday, from the index. If the degrees indicated by the index increase for two successive observations the sun is mounting towards the middle of the day. If the degrees diminish the sun is descending from the middle of the heavens. It is the same for any star.
First we observe on the instrument the fixed star we seek from those marked on the network, as we have already done for the sun, by the number or degree of the diopter. Then turn the observed star, and place it on that number of the parallels which we have found by the help of the diopter, then we look under the earth in which hour falls the degree in which the |90 sun is situated: we shall say that that is the night hour with its fractions. It is evident also that we shall, from this, know the degree 'of life', that of the middle of the heavens and those which are diametrically opposite to them.
3. To find the hour during the night, by the help of the moon.
First we find out, exactly, in which sign and in which degree the moon moves. When we know this, we find the moon by help of the diopter, as we have done for the sun, in what degrees of the quadrant the moon is situated; then we turn the rete, that is to say, the true place of the moon, and set it on the number of these parallels in agreement with that number where the diopter has shown us that the moon was. We then look beneath the earth in what hour is the degree where the sun then is; that will show us the hours already past. But, by day or night, you must first of all know if the sun, the moon, or the star under consideration are before the meridian; then you look for them on the parallels that precede the middle of the day, or, if after the meridian, on the parallels that follow the middle of the day. It is evident that here again we know 'the centres' of which we have spoken.
4. To find, by the help of the astrolabe, the ἐποχή, that is to say, the position of the sun.
To find the position of the sun, we lift up the instrument a little before the sixth hour 17 of the day so that a ray of the sun may pass through the two holes of the alidade together; then, little by little, in proportion as the sun mounts, we also raise the alidade so that the ray of the sun may always pass through the two holes. When we see that the sun is no longer mounting, but is beginning to go down again, we say that it is the middle of the day. Then we look on which degree of the quadrant the alidade falls; then, turning the instrument round, we cause the zone of the zodiac to turn; and the degree of the zodiac, which we see coinciding with a certain number of the inner intersection of these parallels equal to the degree observed by the help of the alidade when the ray of the sun passed through it, shows us in which sign and in which degree the sun travels for that day. We shall say that the sun is in that degree, and in the sign which contains it.
But, first we must know in which of the four tropics and seasons of the year we are, so as to search only in the three signs which correspond to that season, and to avoid all error. |91
5. To find, by the help of the astrolabe, the ἐποχή, that is to say, the position of the moon and of the five planets.18
First we take one of the fixed stars marked on the rete, and find out on the quadrant by the help of the diopter in what number (i.e. degree of altitude) it is found. We turn the rete until the star arrives on the same degree of the inner intersection of the parallels: we then fix the rete in this position. We next find out by the help of the pointer of the alidade in which degree of the quadrant the moon is (to be found), then we turn the instrument round, and we seek on the parallels the same number that the alidade has given us. The sign and the degree which correspond to the intersection of the parallels equal to the degree of the alidade give us the position of the moon for that night (or rather: the degree of the zodiac which has the same height. We observe and obtain in like manner as for the moon, and so for the ἐποχή or position of the five planets.
6. To find the ἐποχή 19 of ascension and descent, that is to say, the latitude of the moon.
It is possible to know the degrees of ascension ἀναβιβάζων or the latitude of the moon from the astrolabe, thus: we determine, as usual, the night hour from the fixed stars; in like manner we determine carefully, as we have said,20 the degrees of the moon.21 If both times agree we say that the moon is at the place of the eclipses, i.e. in the διάμεσον of the zodiac. If the time given by the stars is less, and that given by the moon be greater, and if the latter is at the meridian, we say that the moon is to the north of the ecliptic. If the time given by the stars is greater than the time given by the moon,22 and if the latter has not yet arrived at the meridian, it is evident that it is in the ἐποχή. If the time given by the stars is less, we ought to know that the moon is to the south of the ecliptic; if the time given by the stars is greater, we shall say that the moon is to the north of the ecliptic, or to the north of the plane which passes to the middle of the zone of the zodiac. |92
Let us suppose, for instance, that we are in the fourth climate and that the sun is in the first degree of Aries, we then turn the rete so as to bring this first degree of Aries on to the eastern horizon; at the same time we look how many degrees are marked by the pointer which is on the rete. Suppose that it is then at the middle of the heavens. Next turn the rete until the degree opposite to that of the sun, which is the first degree of Libra also arrives on the horizon. Then let us see the number of the risings (a0nafora&j) that the pointer of the degrees on the rete has travelled from the middle of the heaven, since the place where the first degree of Aries was placed on the eastern horizon, until that when the point diametrically opposed to the degree of the sun has arrived there, we shall find here 180 (if the astrolabe is well constructed) and we write them on one side.23 After that, multiply by 12 hours the number of the times 24 of an hour opposite the first degree of Aries on the third table σελίδιον for the fourth climate in the canon given by Ptolemy, and add the number of the ascensions placed opposite the degree of the sun for this same fourth climate, in the second table. If the number drawn from the canon is equal to the number given by the pointer of the rete, degrees of the astrolabe is true; if there is a difference of two or three degrees it is evident that the astrolabe is untrue.
We can know it also by the help of the canon made by Ptolemy for the right sphere, i.e. the amount by which the pointer of the rete has moved from the degree or sign of the middle of the heaven, is equal to the number of risings on the right sphere of this degree of the middle of the sky. We can know this for any degree, or any sign. And when we are thus seeking for the risings of any sign and for the risings of the right sphere, it is evident that if we turn the rete as far as the point diametrically opposite to that for which we seek, and if we look at the same time how far the pointer of the rete has moved from the middle of the heaven, since we compared the canon to the astrolabe and did not find the same number we ought to conclude that the canon, or else the astrolabe is badly made, and we ought to examine the two, for the canon of Ptolemy is made from the astrolabe. |93
8. How we should test, whether the pointer is accurate and well made.
In every climate we must first observe in which degree and in which sign the sun is, then we set in place the plate of that clime which is occupying our attention; then we turn the rete until the degree of the sign where the sun is, is in the middle of the heaven (we then note its height). Then, towards the sixth hour, we observe the ray of the sun through the two holes of the alidade until the number of the degrees no longer increases but begins to diminish; and if the number then indicated by the pointer of the alidade is the same as the number obtained when the sun holds the middle of the heaven (by the help of the rete) we say that the pointer is well made and true; if not, we shall know that it is not accurate.
9. How, with the help of any astrolabe we can know how many are the ascensions of each sign in any climate 25 whether to the centre of life, or to that of the middle of the heaven, and what are the 'descents' 26 to the centre 'of nuptials' and to that which is beneath the earth.27
We observe the numbers of the degrees of life and those of the middle of the heaven in the climate which we are investigating, and thus, as a consequence we place the indicator of the degrees of the rete on whichever of the degrees of ascension it stands. After having put the beginning of the sign which is occupying us, on the eastern horizon, we make it revolve on (or to) the parallels, and while this sign is rising we count the degrees of |94 ascension which the indicator of the degrees of the rete describes from when the beginning of the sign was on the eastern horizon until the whole sign has risen: the number obtained gives us the ascensions of this sign for this climate.
So that when the first degree of Aries is on the Eastern horizon, which is (the centre) of life, the pointer of the rete which is the beginning of Capricorn, will be found in the middle of the heaven; and when the whole of Aries rises into the fourth climate, the said pointer of the rete will move about thirty degrees from the middle of the heaven; such will be the ascensions of Aries in the fourth climate. And if we wish to know the ascensions of Taurus, we count the road traversed by the pointer of the rete from the place where it was at first as far as the place where the whole of the sign Taurus has risen above the eastern horizon: this will be the number of the ascensions of Taurus, and so we do for the rest of the signs.
We work again in the same way on the right sphere for the sign and the degrees that we wish to know. Then we place in the middle of the heaven (i.e. on the meridian) the beginning of the sign for whose ascensions we are looking, we then make it pass completely to the middle of the heaven; and the amount by which the pointer of the rete moves from the point where it was when we placed the beginning of the sign which is occupying us in the middle of the heaven, gives us the ascensions of this sign on the right sphere; that is to say, to the middle of the heaven.
After having written what is the number of ascensions to the degree 'of life' and to the middle of the heaven for any sign and for any climate, we must speak of 'the descents' to the west, that is to say, to the degree of conjunction, and about those of the middle of the earth (on the lower half of the meridian). We place the beginning of the sign which is occupying us on the western horizon, then note where the pointer is (to be found), and turn the rete round until the whole sign goes down beneath the horizon; the pointer has travelled a certain distance from when the sign has begun to descend until the moment when it has completely set; if we then count the degrees travelled by the pointer they give us the descents of this sign in the climate which is occupying us. We will proceed in the same way for finding the descents to the middle of the earth; placing the beginning of the sign in the middle of the centre 'of the fathers', i.e. the earth, then we turn the rete towards the eastern horizon until the whole sign has passed through the point of the middle of the earth, and the number of the degrees travelled |95 by the pointer of the rete during this time will give us the number of the descents of this sign to the middle of the earth.
10. To find how many ascensions there are from the beginning of Aries to that of the rising, that is to say, to the Horoscope.
If we want to know how many ascensions there are from the beginning of Aries to the horoscope, that is to say, to the degree of the zodiac which is rising at the hour under consideration, whether diurnal or nocturnal, we place the degree of the zodiac which is occupying us, whether diurnal or nocturnal, on the eastern horizon; then we count how many degrees the pointer, which is at the beginning of Capricorn is distant from the middle of the heaven: we say that the number thus found gives the ascensions from the beginning of Aries to the degree which is rising at the hour which we seek.
We can also find the ascensions by taking in Ptolemy's canon the number written in the second column opposite the degree which we have placed on the eastern horizon, in the proper climate which is occupying us.28 This number of (the) ascensions is also to be found in the table for the right sphere.
11. How one may know by the help of the astrolabe the composition of the hours of the day or the night, or the length or shortness of the day or of the night which is occupying us,29 that is to say (the greatest or smallest distance) of the degree 'of life' or of the degree 'of nuptials'.
We have given the rules for finding the ascensions; it is now well to look for the hours (equinoctials) and the equatorial degrees of an hour (temporal) for all climates. To find the length and the degrees of an hour of a certain day, we place the sun's degree on the eastern horizon, then we note the place where the pointer of the rete falls. Next we turn the sun's degree above the earth upon the parallels until it arrives at the western horizon; after which we count how many degrees the pointer of the rete has advanced since the sun's degree began to move from the eastern horizon until it rests on the western. If we are looking for the (equinoctial) hours (of the day) we divide |96 this number of degrees by 15, so many as we subtract so are the horary times (?) (= temporal hours) of that solar or diurnal degree. When we divide the remainder by 12 we know the parts or minutes which are inserted after them (i. e. intercalary).
If we are seeking to know the amount of hours and the horary times of the night, we place the degree (of the zodiac) opposite (to the sun) on the eastern horizon, then we turn it until it arrives on the western horizon. Calculate the advance or course of the pointer of the rete, as we have said before; then, if we want the hours, divide this number of degrees by 15, and we shall have the equinoctial hours of that night; if we are looking for the horary times, divide by 12, and we shall have the degrees of an hour diametrically opposite to the sun. If we subtract the hours of the day from those of the night, the lesser number from the greater, the remainder will give us the excess of the night over the day, or of the day over the night.
Again, we can proceed in another way to find more easily the number of the hours and the degrees of an hour. When we have found, by the method indicated above, the hours and the degrees of an hour which correspond either to the degree of the sun, or else to the point diametrically opposite, that is to say, reckoning from the degree of life, or else from the degree of nuptials,30 we shall subtract from twenty-four the hours that we have found whether for the day or for the night and the remainder will give us the hours of the night or of the day for that day. As for the degrees of an (equinoctial) hour we shall subtract from 30 31 the degrees of the diurnal or nocturnal hour that we have found for the sun or for the point diametrically opposite, and the remainder are those of that other degree of life or of nuptials or of a nocturnal or diurnal hour.
13. How we can know by the help of the astrolabe which is the more northerly and the more southerly of two cities under consideration.
When the sun is in the first degree of Aries, at the sixth hour we shall find out, with the help of the alidade, what is the meridian height in the city. |97 We observe how many are the degrees of this height on the quadrant (which is on the back of the astrolabe), then we go to the other city which we want to compare to the former and, at the sixth hour, when the sun is in this same first degree of Aries, we take its meridian height in the same way. If, in passing from the first town to the second, the pointer of the degrees of the quadrant on the back of the astrolabe indicates a higher number, by the number of the degrees it has added is the second city more southerly than the first; and if it indicates less degrees the second town is by so much more northerly than the first. It is not necessary for the sun to stand in Aries; it may be in Libra, or in any other sign. You can also use fixed stars, proceeding as we have done for the sun. By the help of the alidade we take the meridian height of the star, and when the pointer indicates more degrees, the corresponding town is more southerly; when it indicates less degrees, the town is more northerly. In this way also we find in which climate we are. We can, again, by means of another method, arrive at the same result: Take a style of iron, or of reed, or of wood, or of any other material, and, when it is exactly six o'clock in the town where we are, find out how many feet there are in the shadow of the style we have set up; then we shall do the same in the other town, the same month, the same day, at the same hour (with a style of the same length); when the number of feet in the shadow is greater we shall say that the corresponding town is more northerly; when this number is smaller, we shall say that the town is more southerly, for the shadow is by so much the longer as the sun is more distant from us about midday and by so much the shorter as we are nearer to it.32
14. How one may know the longitude of one town with regard to another, which is the more easterly and which is the more westerly.
We can know this by the eclipses of the moon or of the sun. By the help of the astrolabe, we take the (degree of the zodiac which is at the) middle of the heaven in both cities, at the beginning or at the end of obscuration or during the whole time of the eclipse; then we send (the result found on) the astrolabe from one town to the other of which we want to know the relative position, east or west. It is written above how we take the degree of the middle of the heaven in the two towns, then we compare the degree of the alidade found (at the same moment) in the two towns. When the number |98 indicated by the alidade is greater, we say that the corresponding town is more easterly than the other for which the pointer indicates a smaller number.33
15. How one can find the difference of the meridian in two towns.
Next, we find in the following manner the difference of the meridians in the two towns. We subtract the smallest number of the indicator of the degrees of the alidade from the greatest and we divide the difference by 15: the number obtained represents (some) equinoctial hours, and we shall say that the distance from one town to the other, to the east or to the west, is equal to the number of those hours. It will be midday first in the town which is more easterly.
Thus, when it is three o'clock at Carthage it is six at Arbela, because the difference of midday between Carthage and Arbela is three hours, and this latter town is three hours more easterly than the former. For example, the longitude of Arbela is 80 degrees and that of Carthage 35 degrees 34; therefore, if we subtract the smaller number from the greater we get 45 remaining degrees which, divided by 15 gives us three equinoctial hours.
16. How we can find out the ascensions of the right sphere, of which Ptolemy has written.
For each climate we look for the sign and the degree that is occupying us, then we multiply the number of the degrees of an hour which is written opposite this degree by the six hours which go from the degree 'of life' to the middle of the heaven. Next we add the ascensions written opposite this sign on the second table and thus obtain the ascensions on the right sphere.
Thus, in the fourth climate, opposite the first degree of Cancer, are written the degrees of an hour, namely: 18 degrees and 7 minutes. If we multiply them by 6 hours, we obtain 108° 42'; then, if we add the ascensions written opposite, which are 72° 22', 35 we obtain 180 degrees 36 for the right sphere, in the first degree of Cancer in our climate. |99
We shall proceed likewise, with the same method, for the other climates and for any sign and degree.
17. How we can know in which climate we are, from the sun or one of the fixed stars.
We observe the sun by the help of the alidade, until it no longer mounts, to the moment when it reaches the middle of the day. We then write the degree that was marked by the pointer of the alidade at the sixth hour. There we take the degree of the sun (in the tables and carry it over to the meridian by turning the rete on the third climate until the degree of the sun and the degree of the pointer of the diopter both intersect the meridian. If, on the meridian the sun intersects the circle of height corresponding to the number indicated by the pointer we say that we are in the third climate, if not we shall have to look in the fourth climate or in the fifth or in one of the others until the coincidence occurs. When that happens we shall say that the corresponding climate is ours.
The latitude begins on the southern straightness or directness (i.e. the equator) and so it is divided into 90 degrees, that is to say the half of the 180 degrees which are on the horizon of the heaven. We turn the rete into each one of the climates until the first degree of Aries is on the meridian.37 Then we take those degrees written on the parallels of the middle of the heaven (the degree of height) which correspond to the first of Aries, then we subtract them from 90 degrees and we say that the remainder is the latitude of the climate which is occupying us, starting from the south (from the equator).
19. How we can know, by the help of the astrolabe, the longitude and latitude of the fixed stars.
To know the latitude of the fixed stars 38 we turn the rete round until the star which is occupying us arrives on the southern sign = σημεῖον i.e. |100 on the meridian. Then we observe how many degrees of latitude this star is distant from the zone of the zodiac towards the north or towards the south. For the longitude . . .
(A sheet is missing here.)
. . . each of these fixed stars and how many degrees is its distance in latitude as far as the fixed stars, by the help of the astrolabe.
For the latitude, we turn the rete round, as aforesaid until the star which is occupying us stays at the middle of the heaven; then we see how many parallels are to be found both the zone of the zodiac and the star which is occupying us. We take the distance from the zones of the zodiac to the stars and find how many degrees distant in latitude to the north or to the south. Likewise, always using the zodiac and placing (the star) on the eastern horizon, we find on what degree of the longitude of the zone and with what sign this star rises. By this means, we find, in addition whether this star appears 39 to the east or to the west of the sun. A star is visible when it is 25 degrees to the east or to the west of the sun.
22. How, by the help of the astrolabe, we can know the declination of every sign of the zodiac from the equator,40 to the north or to the south for each climate, and in what place is either of the three tropical zones.
The declination of the signs from the zone of the equator is found in the following manner: We take the instrument and turn the rete round until the first degree of Aries is at the point beneath the earth (on the inferior meridian). Thence we know the position of the equator in whatever climate it may be: it is enough to look in what degree of the parallels is (to be found) the first degree of Aries 41 and to make a mark there; then we turn the rete round until the first degree of Cancer comes to the meridian which is the middle of the heaven, and we take the number of the degree of the parallels where the first degree of Cancer falls as well as the degree of the parallels noted before; we subtract the lesser from the greater and the degrees which remain give us the declination of Cancer on the southern equator, that is to say, the zone of winter. This same inquiry gives us 24 degrees for the declination of Cancer to the north, that is to say of the zone of summer from the equator.42 |101 In the same manner we shall find 24 degrees for the declination of Capricorn from the southern side or the zone of winter on to the first degree of Aries from the equator. We shall do the same for any degree and for any sign that we like and shall thus find its declination from the equator to the north or to the south. We should do the same for the sun as we are about to learn.
23. How we can know the declination of the sun from the equator to the north or to the south in every sign and in every degree.
We turn the rete round until the degree of the sun, in whatever sign it may be arrives at the mark of the meridian, then we look to see how many degrees the degree of the sun occupies on the parallels.43 If this number is less than that which corresponds to those of the equator we shall say that the difference indicates the declination of the sun from the equator towards the south, whether it is rising or going down. If this number is greater than that of the equator we shall subtract those of the equator from that of the solar degree on the parallels, and shall say that the remainder represents the declination of the sun to the north of the equator, whether it is rising or going down. The sun rises from Capricorn to Cancer, and goes down from Cancer to Capricorn.
24. 24. Of the measure in latitude of the hemisphere, i.e. of the 180 degrees (which extend) from the north to the south or the division and relative distance of the various zones.
The latitude of the sphere is measured from north to south in the following manner.44 As aforesaid, we measure by the help of the astrolabe on the meridian starting from the first degree of Cancer which is the zone of summer as far as the 90th degree (as far as the zenith in the fourth climate); there are 12 degrees. And from the equator as far as the same 90th degree there are 36 degrees. From the same 90th degree as far as the zone of winter, which is the place of the first degree of Capricorn (we find) 60 degrees. And as far as the southern (zone) called 'antarctic' which is constantly |102 hidden, there are 90 degrees. And from the extreme north of the zone called 'arctic' which is constantly visible, as far as the point which is the centre, that is to say the north pole, through which passes the northern extremity of the axis (of the world) there are 36 degrees. And from this said centre (north pole) as far as the southern extremity (as opposed to the arctic zone), there are again 36 degrees. And from the zone constantly visible, i.e. the arctic, as far as the middle of the heaven (zenith) there are 18 degrees. These (last degrees added) together give 90 degrees, for if we add to (both the width of the arctic zone which is constantly visible as far as the middle of the heaven (zenith) we find 90 degrees. And from the middle of the heaven as far as that which is constantly hidden, that is to say antarctic, we find 90 degrees: hence the whole latitude gives 180 degrees.
There exists another division in five zones made by the philosopher. The first zone called 'arctic' is cold and uninhabitable. Its latitude is 36 degrees from the north pole towards the south. The second is called 'tropic of summer' and counts 30 degrees. The third is called 'equatorial tropic' and counts 48 degrees (of which 24 degrees are) to the north of the equator and the other 24 to the south. The fourth is called 'tropic of winter' (and counts) 30 degrees. The fifth is called 'antarctic' (and also again counts) 36 degrees, namely from its extremity as far as the south pole: in all 180 degrees.
There is further another division made by the astronomer Ptolemy. First the arctic (zone) of 36° 9'. Second (the zone) of summer of 30 degrees. Third the equatorial zone which is 23° 51' to the north (of the equator) and as much to the south. 45 The fourth is (the zone) of winter of 30 degrees. The fifth is the antarctic (zone) of 36° 9'. That makes in all 180 degrees; it is evident that here again this philosopher teaches us to measure the latitude from the north pole as far as the south pole.
The poles are points or positions on which we conceive to be situated the two extremities of the axis which we imagine drawn obliquely from top to bottom, that is to say, from north to south, passing directly to the middle of the centre of the earth, which is also placed equally in the middle of the sphere. |103
25. How, in every climate, we can ascertain the ascensions of the sign which is in the east, and which is called 'the sign of life', and those of the sign which is in the middle of the heaven.
We take the ascensions of the degree of life as we have already shewn.46 First we take the degree of this sign on the eastern horizon, and the western degree on the western horizon. Then we observe on which degree the pointer of the degrees of the rete falls, then we make the whole sign rise above the horizon and observe by how many degrees the pointer of the degrees has advanced, and the degrees of the movement of the pointer of the degrees of the rete and those (which it marked at the beginning) of this sign, we substract the smaller number from the greater, the remainder gives us the ascensions of this sign, and its power over the number of the years.47 In the same way, in working to the middle of the heaven, we find how many hours a sign takes to go to the middle of the heaven, because the various signs do not rise equally above the eastern horizon and in the position of the right sphere. For example, when in the fourth climate we take the ascensions of the degrees of the ascendants, as we have seen above,48 we then look how many degrees the pointer of the degrees of the rete has advanced, then we turn the rete round until the degree of life is on the meridian and we look how many degrees the pointer of the degrees of the rete has advanced, we subtract the degrees of life from the degrees of the middle of the heaven, and in the remainder we find the degrees of an hour for the point of life.
End of the Treatise on the Astrolabe composed by the Abbot Mar Severus of Nisibis, that is to say Sabokt. Pray for him who wrote it.
[Footnotes moved to the end and renumbered]
1. 1 These tablets, one for each region, were called by the Arabs saphiahs. The Greeks called them τύμπανοι. Cf. Philopon, chapter 2, p. 62. (This and other notes on Sabokt are by Nau.)
2. 1 A different tablet is needed for each climate. Unfortunately the Syriac text contains no figures of them.
3. 2 Philopon calls these astrolabes διμοιριαῖι and τριμοιριαῖοι (p. 62).
4. 1 [Syriac] signifies in this treatise 'length, geographical longitude, horary angle'.
5. 2 This is the correct sense of the Greek κέντρον although in Syriac more often it means 'centre'. Severus also uses it in the sense of 'point' (the zenith).
6. 3 τὸ μοιρογνωμόνιον (Philopon). Cf. inscription on p. 58.
7. 1 It is here a question of parallels to the horizon, or circles of height. The Arabs have translated this word by almuqanterat, that is to say, according to M. Sedillot, circuit progressionum (Mémoire, p. 154).
8. 2 Because, for Sabokt the winter tropic is at 24° from the equator (cf. p. 101 note) and the colatitude of the fourth climate is 54°. The difference, which gives the meridian height of the winter tropic, is obviously 30 degrees.
9. 3 Word for word 'latitude' and 'longitude'. But it is not a question here of ecliptic co-ordinates. The latitude which is seen and which is carried over to the right south is the height. The longitude which is counted on the outside edge is certainly the horary angle. It will, however, be noticed, that it is always a question of meridian height. One can, therefore, as soon as one knows the latitude of the place of observation, immediately deduce the declension from it. It is probably this which leads our author sometimes to confuse height and declension.
10. 1 This must be the azimuth which is reckoned on the horizon.
11. 2 On the edge of the outside tablet the horary angle is certainly measured distinct from the azimuth. Sabokt calls all the angles (azimuth, horary angle and longitude) by the same word.
12. 3 Cf. the four 'pivots' of the Arabs in Sedillot (Mémoire, p. 96) and Prolegomena of the astronomical tables by Ulugh Beg, translation, p. 195. Cf. Fermicus Maternus II, xiii and xiv quoted below (p. 93).
13. 1 These are the twelve 'celestial houses'. Cf. Sedillot, Prolegomena, and Firm. Mat. loc. cit. (v. infra, probl. ix).
14. 2 This name ἀράχνη is found for the first time in Vitruvius. This writer cites the inventors of the various clocks and sun-dials and adds, 'Arachnen Eudoxus astrologus, nonnulli dicunt Apollonium'. Eudoxus, the astronomer, or according to some, Apollonius (invented) the spider. M. Letronne wrote on this subject, 'M. Ideler conjectures with much appearance of reason that it is a question of a horizontal quadrant, thus named because of the numerous lines starting from the vertical pin as centre and describing a spider's web' (Journal des Savants, 1840-41). In reality this conjecture is false, as Nau has shown at length in his introduction. Cf. p. 54.
15. 1 Literally return and revolution.
16. 2 The sun being thus placed all the astral bodies and all the circles are also set in their true positions. The face of the astrolabe thus represents the position of the heavens at a definite moment, and, to know the hour, it is enough to look at the sign which is at the horizon.
17. 1 It is a matter of finding the meridian height, or the culmination of the sun: that is to say, the point where the sun ceases to rise higher above the horizon before sinking again.
18. 1 The title denotes, as in the preceding article, the meridian height although this is not specified.
19. 2 Word for word: 'the retrogressions'. But then it would be a matter only of finding the maximum and minimum of the latitude of the moon, whereas the demonstration seems to give the sense of the latitude at some epoch.
21. 4 That is to say, the degree of the zodiac which has the same height.
22. 5 The meaning seems to require here the clause: 'we shall say that the moon is to the south of the ecliptic'.
23. 1 It is a matter of estimating directly the ascensions of a certain number of signs, then of comparing this number given by the astrolabe with that given by a table constructed by Ptolemy (called the author), and analogous, probably to those which occur in the Almagest in Bk. II, ch. vii.
24. 2 'The times of an hour' are the equatorial degrees which correspond to an hour; they are found by dividing by twelve the equatorial arc included between the points of sunrise and sunset.
25. 1 We call 'ascensions (ἀναφοραί) to the centre of life' (on the eastern horizon), which correspond to a sign, the number of the degrees of the equator which are mounting above the horizon while this sign itself mounts completely above the horizon (Cf. Ptolemy, Mathematical Composition, Bk. II, ch. vii, and Bar Hebraeus, Course of Astronomy, Bk. II, ch. iii, sects. 1, 2, 3, 4). The moving of the rete reproduces the diurnal movement; the degrees of the equator are noted on the edge of the astrolabe.
26. 2 καταφοραί, as opposed to 'ascensions' ἀναφοραί.
27. 3 The signification of these four so-called 'centres' is as follows: centre 1, is on the eastern horizon; 2, on the upper meridian; 3, on the western horizon; 4, on the lower meridian. The four places called 'centres' by Severus were also called 'pivots', which is a translation of the word 'cardines' (geniturarum) used by Firmicus Maternus II, xiii.
Each one of the intervals was again divided into three parts, these are the twelve loci of Fermicus II, xvii, or the twelve 'houses' of Severus, for each of these places lodges a sign of the zodiac and some planet. The first house begins at the eastern horizon, and continues towards the lower meridian until the thirtieth degree. 'In hoc loco vita hominum et spiritus continetur.' F. M. xvii, 2. The fourth house begins at the lower meridian. 'Quartus locus, id est imum coelum, . . . ostendit nobis "parentes", patrimonium.' F. M. II, xvii, 5. The seventh house begins at the western meridian (appellatur occasus a nobis, a graecis vero δύσις . . . Ex hoc loco qualitatem et quantitatem quaeramus "nuptiarum").' F. M. II, xvii, 8. The tenth house begins at the upper meridian, 'a nobis medium coelum a graecis μεσουράνημα appellatur ' F. M. xvii, 11.
28. 1 In the Almagest, Bk. II, ch. viii, the ascensions of the signs of the zodiac are given for every 10 degrees for the various climates.
29. 2 They distinguish two sorts of hours: 1, the temporal hours ὥρας καιρικάς. There are always twelve of these from the rising to the setting of the sun; and so they differ in length according to the season; 2, the equinoctial hours, these latter correspond to the 15 degrees of the equator; and so they are equal to each other, but the days contain more or fewer of them according to the season. Cf. Bar Hebraeus, Course of Astronomy, Bk. II, ch. v, sect. 1.
30. 1 That means that we calculate the time taken by the sun to pass from the eastern horizon to the western horizon and vice versa.
31. 2 This is accurate, for if the parallel described by the sun has n degrees above the horizon, and as twelve temporal hours of the day correspond to these n degrees, each hour of the day will contain n/12 degrees. But the same parallel will have 360-n degrees below the horizon to which will correspond the twelve hours of the night. Each hour of the night will therefore contain (360-n)/12 degrees, or, as Severus expresses it 30 ( -n/12).
32. 1 This latter method is classic, but has no reference to the astrolabe; the former, if one uses the sun, implies an interval of six months between the two observations, according to the account that Severus gives of it.
33. 1 In reality the degrees of the signs of the zodiac go on increasing from the west towards the east.
34. 2 These longitudes are counted starting from the Island of Ferro and are even a little exaggerated. Longitudes were also counted, starting from the continent, which was 10 degrees east of the Island of Ferro (cf. Bar Hebraeus, Cours d'astronomie, Bk. II, ch. i, sect. 1). This explains how the longitude of Cairo could be 55 degrees as M. Marcel maintained, although it ought to be 65 degrees according to M. Sedillot (Mémoires de l'Acad. des Insc. t. 1, 1844, p. 59). Both numbers are accurate, the origin of the longitudes is different.
35. 3 We can deduce this number from the figures given by Ptolemy in the Almagest, for the parallel of the Hellespont (Ed. Halma, p. 106).
37. 1 The first degree of Aries being on the equator, its height gives the colatitude of the corresponding place. It is a question here, obviously, only of those countries for which the plates of the astrolabe have been constructed. This rule is given by Macarius Hieromonachus (Rhein. Mus. p. 159). But he does not assume that the first degree of Aries is indicated on the astrolabe: he tells us to observe the sun at the moment when it is at the first degree of Aries or of Libra and to take its meridian height. Here the astrolabe is of no use. We use only the rete.
38. 2 Again, it is a question only of the stars represented on the astrolabe; they are usually few in number, thirty at the most. Cf. Sedillot, loc. cit., p. 167.
39. 1 Bar Hebraeus, Treatise of Astronomy, p. 77
40. 2 It is a question of the declension of the degrees of the zodiac. Bar Hebraeus, Course of Astronomy, pp. 17-18).
41. 3 The first degree of Aries always marks the equator.
42. 4 The author takes a round number for the obliquity of the ecliptic, or rather he borrows his figure from an extremely ancient author. For it was in the time of Aristotle that Eudemus represented the obliquity by one side of a polygon of 15 faces (Letronne, Les écrits et les travaux d'Eudoxe de Cnide, ap. Journal des Savants, 1840-1). If we divide 360 by 15, we find that 24 degrees corresponded to one side of a polygon of 15 faces. It is remarkable that John Philopon describing the planispheric astrolabe from sources analogous to those of Severus, also takes 24 degrees for the obliquity of the ecliptic.
43. 1 Again it is a question of the parallels of height.
44. 2 In the first paragraph the latitude seems related to the zenith of the observer.
45. 1 In the Almagest, Bk. I,ch. x, Ptolemy says that the distance of the two tropics is included between 47° 40' and 47° 45'. If we take 47° 42' we obtain 23° 51' for the obliquity of the ecliptic.
47. 2 Cf. Firm. Mat. II, xxv, De distributione temporum.
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