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The Sphere of Sarcrobosco
An early 13th century treatise on astronomy, by
Iohannes de Sacrobosco.
Translated by Lynn Thorndike, 1949.
CONTENTS OF THE FOUR
CHAPTERS
The treatise on the sphere we
divide into four chapters, telling,
FIRST, what a sphere is, what its
center is, what the axis of a sphere is, what the pole of the world is,
how many spheres there are, and what the shape of the world is.
IN THE SECOND we give information
concerning the circles of which this material sphere is composed and that
supercelestial one, of which this is the image, is understood to be
composed.
IN THE THIRD we talk about the
rising and setting of the signs, and the diversity of days and nights
which happens to those inhabiting diverse localities, and the division
into climes.
IN THE FOURTH the matter concerns
the circles and motions of the planets, and the causes of eclipses.
SPHERE DEFINED. -- A sphere is thus described by Euclid: A sphere is
the transit of the circumference of a half-circle upon a fixed diameter
until it revolves back to its original position. That is, a sphere is such
a round and solid body as is described by the revolution of a semicircular
arc.
By Theodosius a sphere is described thus: A sphere is a solid body
contained within a single surface, in the middle of which there is a point
from which all straight lines drawn to the circumference are equal, and
that point is called the "center of the sphere." Moreover, a straight line
passing through the center of the sphere, with its ends touching the
circumference in opposite directions, is called the "axis of the sphere."
And the two ends of the axis are called the "poles of the world."
SPHERE DIVIDED. -- The sphere is divided in two ways, by substance and
by accident. By substance it is divided into the ninth sphere, which is
called the "first moved" or the primum mobile; and the sphere of
the fixed stars, which is named the "firmament"; and the seven spheres of
the seven planets, of which some are larger, some smaller, according as
they the more approach, or recede from, the firmament. Wherefore, among
them the sphere of Saturn is the largest, the sphere of the moon the
smallest, as is shown in the accompanying figure.
By accident the sphere is divided into the sphere right and the sphere
oblique. For those are said to have the sphere right who dwell at the
equator, if anyone can live there. And it is called "right" because
neither pole is elevated more for them than the other, or because their
horizon intersects the equinoctial circle and is intersected by it at
spherical right angles. Those are said to have the sphere oblique who live
this side of the equator or beyond it. For to them one pole is always
raised above the horizon, and the other is always depressed below it. Or
it is because their artificial horizon intersects the equinoctial at
oblique and unequal angles.
THE FOUR ELEMENTS. -- The machine of the universe is divided into two,
the ethereal and the elementary region. The elementary region, existing
subject to continual alteration, is divided into four For there is earth,
placed, as it were, as the center in the middle of all, about which is
water, about water air, about air fire, which is pure and not turbid there
and reaches to the sphere of the moon, as Aristotle says in his book of
Meteorology. For so God, the glorious and sublime, disposed. And these
are called the "four elements" which are in turn by themselves altered,
corrupted and regenerated. The elements are also simple bodies which
cannot be subdivided into parts of diverse forms and from whose commixture
are produced various species of generated things. Three of them, in turn,
surround the earth on all sides spherically, except in so far as the dry
land stays the sea's tide to protect the life of animate beings. All, too,
are mobile except earth, which, as the center of the world, by its weight
in every direction equally avoiding the great motion of the extremes, as a
round body occupies the middle of the sphere.
THE HEAVENS. -- Around the elementary region revolves with continuous
circular motion the ethereal, which is lucid and immune from all variation
in its immutable essence. And it is called "Fifth Essence" by the
philosophers. Of which there are nine spheres, as we have just said:
namely, of the moon, Mercury, Venus, the sun, Mars, Jupiter, Saturn, the
fixed stars, and the last heaven. Each of these spheres incloses its
inferior spherically.
THEIR MOVEMENTS. -- And of these there are two movements. One is of the
last heaven on the two extremities of its axis, the Arctic and Antarctic
poles, from east through west to east again, which the equinoctial circle
divides through the middle. Then there is another movement, oblique to
this and in the opposite direction, of the inferior spheres on their axes,
distant from the former by 23 degrees. But the first movement carries all
the others with it in its rush about the earth once within a day and
night, although they strive against it, as in the case of the eighth
sphere one degree in a hundred years. This second movement is divided
through the middle by the zodiac, under which each of the seven planets
has its own sphere, in which it is borne by its own motion, contrary to
the movement of the sky, and completes it in varying spaces of time -- in
the case of Saturn in thirty years, Jupiter in twelve years, Mars in two,
the sun in three hundred and sixty-five days and six hours, Venus and
Mercury about the same, the moon in twenty-seven days and eight hours.
REVOLUTION OF THE HEAVENS FROM EAST TO WEST. -- That the sky revolves
from east to west is signified by the fact that the stars, which rise in
the east, mount gradually and successively until they reach mid-sky and
are always at the same distance apart, and, thus maintaining their
relative positions. they move toward their setting continuously and
uniformly. Another indication is that the stars near the North Pole, which
never set for us, move continuously and uniformly, describing their
circles about the pole, and are always equally near or far from one
another. Therefore, from those two continuous movements of the stars, both
those that set and those which do not, it is clear that the firmament is
moved from east to west.
THE HEAVENS SPHERICAL. -- There are three reasons why the sky is round:
likeness, convenience, and necessity. Likeness, because the sensible world
is made in the likeness of the archetype, in which there is neither end
nor beginning; wherefore, in likeness to it the sensible world has a round
shape, in which beginning or end cannot be distinguished. Convenience,
because of all isoperimetric bodies the sphere is the largest and of all
shapes the round is most capacious. Since largest and round, therefore the
most capacious. Wherefore, since the world is all-containing, this shape
was useful and convenient for it. Necessity, because if the world were of
other form than round -- say, trilateral, quadrilateral, or many-sided --
it would follow that some space would be vacant and some body without a
place, both of which are false, as is clear in the case of angles
projecting and revolved.
A FURTHER PROOF. -- Also, as Alfraganus says, if the sky were flat, one
part of it would be nearer to us than another, namely, that which is
directly overhead. So when a star was there, it would be closer to us than
when rising or setting. But those things which are closer to us seem
larger. So the sun when in mid-sky should look larger than when rising or
setting, whereas the opposite is the case; for the sun or another star
looks bigger in the east or west than in mid-sky. But, since this is not
really so, the reason for its seeming so is that in winter and the rainy
season vapors
rise between us and the sun or other
star. And, since those vapors are diaphanous, they scatter our visual rays
so that they do not apprehend the object in its true size, just as is the
case with a penny dropped into a depth of limpid water, which appears
larger than it actually is because of a like diffusion of rays.
THE EARTH A SPHERE. -- That the earth, too, is round is shown thus. The
signs and stars do not rise and set the same for all men everywhere but
rise and set sooner for those in the east than for those in the west; and
of this there is no other cause than the bulge of the earth. Moreover,
celestial phenomena evidence that they rise sooner for Orientals than for
westerners. For one and the same eclipse of the moon which appears to us
in the first hour of the night appears to Orientals about the third hour
of the night, which proves that they had night and sunset before we did,
of which setting the bulge of the earth is the cause.
FURTHER PROOFS OF THIS. -- That the earth also has a bulge from north
to south and vice versa is shown thus: To those living toward the north,
certain stars are always visible, namely, those near the North Pole, while
others which are near the South Pole are always concealed from them. If,
then, anyone should proceed from the north southward, he might go so far
that the stars which formerly were always visible to him now would tend
toward their setting. And the farther south he went, the more they would
be moved toward their setting. Again, that same man now could see stars
which formerly had always been hidden from him. And the reverse would
happen to anyone going from the south northward. The cause of this is
simply the bulge of the earth. Again, if the earth were flat from east to
west, the stars would rise as soon for westerners as for Orientals. which
is false. Also, if the earth were flat from north to south and vice versa,
the stars which were always visible to anyone would continue to be so
wherever he went, which is false. But it seems flat to human sight because
it is so extensive.
SURFACE OF THE SEA SPHERICAL. -- That the water has a bulge and is
approximately round is shown thus: Let a signal be set up on the seacoast
and a ship leave port and sail away so far that the eye of a person
standing at the foot of the mast can no longer discern the signal. Yet if
the ship is stopped, the eye of the same person, if he has climbed to the
top of the mast, will see the signal clearly. Yet the eye of a person at
the bottom of the mast ought to see the signal better than he who is at
the top, as is shown by drawing straight lines from both to the signal.
And there is no other explanation of this thing than the bulge of the
water. For all other impediments are excluded, such as clouds and rising
vapors.
Also, since water is a homogeneous body, the whole will act the same
as its parts. But parts of water, as happens in the case of little drops
and dew on herbs, naturally seek a round shape. Therefore, the whole, of
which they are parts, will do so.
THE EARTH CENTRAL. -- That the earth is in the middle of the firmament
is shown thus. To persons on the earth's surface the stars appear of the
same size whether they are in mid-sky or just rising or about to set, and
this is because the earth is equally distant from them. For if the earth
were nearer to the firmament in one direction than in another, a person at
that point of the earth's surface which was nearer to the firmament would
not see half of the heavens. But this is contrary to Ptolemy and all the
philosophers, who say that, wherever man lives, six signs rise and six
signs set, and half of the heavens is always visible and half hid from
him.
AND A MERE POINT IN THE UNIVERSE. -- That same consideration is a sign
that the earth is as a center and point with respect to the firmament,
since, if the earth were of any size compared with the firmament, it would
not be possible to see half the heavens. Also, suppose a plane passed
through the center of the earth, dividing it and the firmament into equal
halves. An eye at the earth's center would see half the sky, and one on
the earth's surface would see the same half. From which it is inferred
that the magnitude of the earth from surface to center is inappreciable
and, consequently, that the magnitude of the entire earth is inappreciable
compared to the firmament. Also Alfraganus says that the least of the
fixed stars which we can see is larger than the whole earth. But that
star, compared with the firmament, is a mere point. Much more so is the
earth, which is smaller than it.
THE EARTH IMMOBILE. -- That the earth is held immobile in the midst of
all, although it is the heaviest, seems explicable thus. Every heavy thing
tends toward the center. Now the center is a point in the middle of the
firmament. Therefore, the earth, since it is heaviest, naturally tends
toward that point. Also, whatever is moved from the middle toward the
circumference ascends. Therefore, if the earth were moved from the middle
toward the circumference, it would be ascending, which is impossible.
MEASURING THE EARTH'S CIRCUMFERENCE. -- The total girth of the 700
stades for each of the 360 parts of the zodiac (sic). For let one take
earth by the authority of the philosophers Ambrose, Theodosius, and
Eratosthenes is defined as comprising 252,000 stades, which is allowing an
astrolabe on a clear starry night and, sighting the pole through both
apertures in the indicator, [1] note the number of degrees where it is.
Then let our measurer of the cosmos
proceed directly north until on another clear night, observing the pole as
before, the indicator stands a degree higher. After this let the extent of
his travel be measured, and it will be found to be 700 stades. Then,
allowing this many stades for each of 360 degrees, the girth of the earth
is found.
AND DIAMETER. -- From these data the diameter of the earth can be found
thus by the rule for the circle and diameter. Subtract the twenty-second
part from the circuit of the whole earth, and a third of the remainder --
that is, 80, 181 stades and a half and third part of one stade -- will be
the diameter or thickness of the terrestrial ball.
OF THE CIRCLES AND THEIR NAMES
CELESTIAL CIRCLES. -- Of these circles some are larger, some smaller,
as sense shows. For a great circle in the sphere is one which, described
on the surface of the sphere about its center, divides the sphere into two
equal parts, while a small circle is one which, described on the surface
of the sphere, divides it not into two equal but into two unequal
portions.
THE EQUINOCTIAL. -- Of the great circles we must first mention the
equinoctial. The equinoctial is a circle dividing the sphere into two
equal parts and equidistant at its every point from either pole. And it is
called "equinoctial" because, when the sun crosses it, which happens twice
a year, namely, in the beginning of Aries and in the beginning of Libra,
there is equinox the world over. Wherefore it is termed the "equator of
day and night," because it makes the artificial day equal to the night.
And 'tis called the "belt of the first movement."
THE TWO MOVEMENTS AGAIN. -- Be it understood that the "first movement"
means the movement of the primum mobile, that is, of the ninth
sphere or last heaven, which movement is from east through west back to
east again, which also is called "rational motion" from resemblance to the
rational motion in the microcosm, that is, in man, when thought goes from
the Creator through creatures to the Creator and there rests.
The second movement is of the firmament and planets contrary to this,
from west through east back to west again, which movement is called
"irrational" or "sensual" from resemblance to the movement of the
microcosm from things corruptible to the Creator and back again to things
corruptible.
THE NORTH AND SOUTH POLES. -- 'Tis called the "belt of the first
movement" because it divides the primum mobile or ninth sphere into
two equal parts and is itself equally distant from the poles of the world.
It is to be noted that the pole which always is visible to us is called "septentrional,"
"arctic," or "boreal." "Septentrional" is from septentrio, that is,
from Ursa Minor, which is derived from septem and trion,
meaning "ox," because the seven stars in Ursa move slowly, since they are
near the pole. Or those seven stars are called septentriones as if
septem teriones, because they tread the parts about the pole.
"Arctic" is derived from arthos, which is Ursa Major, for 'tis near
Ursa Major. It is called "boreal" because it is where the wind Boreas
comes from. The opposite pole is called "Antarctic" as opposed to
"Arctic." It also is called "meridional" because it is to the south, and
it is called "austral" because it is where the wind Auster comes from. The
two fixed points in the firmament are called the "poles of the world"
because they terminate the axis of the sphere and the world revolves on
them. One of these poles is always visible to us, the other always hidden.
Whence Virgil:
This vertex is ever above us, but that
Dark Styx and deep Manes hold beneath our feet. [2]
THE ZODIAC. -- There is another circle in the sphere which intersects
the equinoctial and is intersected by it into two equal parts. One half of
it tips toward the north, the other toward the south. That circle is
called "zodiac" from zoe, meaning "life," because all life in
inferior things depends on the movement of the planets beneath it. Or it
is derived from zodias, which means "animal," because, since it is
divided into twelve equal parts, each part is called a sign and has its
particular name from the name of some animal, because of some property
characteristic of it and of the animal, or because of the arrangement of
the fixed stars there in the outline of that kind of animal. That circle
in Latin is called signifer because it bears the "signs" or because
it is divided into them. By Aristotle in On Generation and Corruption
it is called the "oblique circle," where he says that, according to the
access and recess of the sun in the oblique circle, are produced
generations and corruptions in things below.
THE TWELVE SIGNS. -- The names, order, and number of the signs are set
forth in these lines:
There are Aries, Taurus, Gemini, Cancer, Leo, Virgo,
Libra and Scorpio, Architenens, Caper, Amphora, Pisces.
Moreover, each sign is divided into 30 degrees, whence it is clear that
in the entire zodiac there are 360
degrees. Also, according to astronomers, each degree is divided into 60
minutes, each minute into 60 seconds. each second into 60 thirds, and so
on. And as the zodiac is divided by astronomers, so each circle in the
sphere, whether great or small, is divided into similar parts.
While every circle in the sphere except the zodiac is understood to be
a line or circumference, the zodiac alone is understood to be a surface,
12 degrees wide of degrees such as we have just mentioned. Wherefore. it
is clear that certain persons in astrology lie who say that the signs are
squares, unless they misuse this term and consider square and quadrangle
the same. For each sign is 30 degrees in longitude, 12 in latitude.
THE ECLIPTIC. -- The line dividing the zodiac in its circuit, so that
on one side it leaves 6 degrees and on the other side another 6, is called
the "ecliptic," since when sun and moon are on that line there occurs an
eclipse of sun or moon. The sun always moves beneath the ecliptic, but all
the other planets decline toward north or south; sometimes, however, they
are beneath the ecliptic. The part of the zodiac which slants away from
the equinoctial to the north is called "northern" or "boreal" or "Arctic,"
and those six signs which extend from the beginning of Aries to the end of
Virgo are called "northern." The other part of the zodiac which tips from
the equinoctial toward the south is called "meridional" or "austral," and
the six signs from the beginning of Libra to the end of Pisces are called
"meridional" or "austral."
EXTENDED USES OF "SIGN." -- When it is said that the sun is in Aries or
in another sign, it should he understood that in is taken for
beneath according as we now accept sign. In another meaning a sign is
called a "pyramid," whose quadrilateral base is that surface which we call
a "sign," while its apex is at the center of the earth. And in this sense
we may properly say that the planets are in signs. "Sign" may be
used in a third way as produced by six circles passing through the poles
of the zodiac and through the beginnings of the twelve signs. Those six
circles divide the entire surface of the sphere into twelve parts, wide in
the middle but narrower toward the poles, and each such part is called a
"sign" and has a particular name from the name of that sign which is
intercepted between its two lines. And according to this usage stars which
are near the poles are said to be "in signs." Also think of a body whose
base is a sign in this last sense which we have accepted but whose edge is
on the axis of the zodiac. Such a body is called a "sign" in a fourth
sense, according to which usage the whole world is divided into twelve
equal parts, which are called "signs," and so whatever is in the world is
in some sign.
COLURES. -- There are two other great circles in the sphere which are
called "colures," whose function is to distinguish solstices and
equinoxes. "Colure" is derived from colon, which is a member, and
uros, which is a wild ox, because, just as the lifted tail of the
wild ox, which is its member, describes a semicircle and not a complete
circle, so a colure always appears to us imperfect because only one half
of it is seen.
The colure distinguishing the solstices passes through the poles of the
universe and through the poles of the zodiac and through the greatest
declinations of the sun, that is, through the first degrees of Cancer and
Capricorn. Wherefore, the first point of Cancer, where that colure
intersects the zodiac, is called the "point of the summer solstice,"
because, when the sun is in it, the summer solstice occurs and the sun
cannot approach further toward our zenith. The zenith is a point in the
firmament directly above our heads. The arc of the colure which is
intercepted between the point of the summer solstice and the equinoctial
point is called the "sun's greatest declination" and is, according to
Ptolemy, 23 degrees and 51 minutes, according to Almeon, 23 degrees and 33
minutes. Similarly, the first point of Capricorn is called the "point of
the winter solstice," and the arc of the colure intercepted between that
point and the equinoctial is called the "sun's greatest declination" and
is equal to the former.
The other colure passes through the poles of the universe and through
the points of Aries and Libra where are the two equinoxes, whence it is
called the "colure distinguishing the equinoxes." Those two colures
intersect at the poles of the world at spherical right angles. The signs
of the solstices and equinoxes are stated in these verses:
These two solstices make, Cancer and Capricorn,
But Aries and Libra equal the nights to days.
THE MERIDIAN. -- There are yet two other great circles in the sphere,
namely, the meridian and the horizon. The meridian is a circle passing
through the poles of the world and through our zenith, and it is called
"meridian" because, wherever a man may be and at whatever time of year,
when the sun with the movement of the firmament reaches his meridian, it
is noon for him. For like reason it is called the "circle of midday." And
it is to be noted that cities of which one is farther east than the other
have different meridians. The arc of the equinoctial intercepted between
two meridians is called the "longitude" of the city. If two cities have
the same meridian, then they are equally distant from east and from west.
THE HORIZON. -- The horizon is a circle dividing the lower hemisphere
from the upper, whence it is called "horizon," that is, "limiter of
vision."
It is also called the "circle of the hemisphere." Moreover, the horizon
is twofold -- that is, right, and oblique or slanting. Those have a right
horizon and right sphere whose zenith is on the equinoctial, since their
horizon is a circle passing through the poles of the world cutting the
equinoctial at right angles, wherefore it is called "right horizon" and
"right sphere." But those to whom the pole of the world is raised above
the horizon have an oblique or slanting horizon, since their horizon
intersects the equinoctial at unequal and oblique angles and is called
"oblique horizon" and the sphere "oblique" or "slanting." Moreover, the
zenith over our heads is always the pole of the horizon.
ELEVATION OF THE POLE. -- From these things it is evident that the
elevation of the pole of the world above the horizon is as great as the
distance of the zenith from the equator, which is shown in this way. Since
in every natural day either colure twice joins or becomes identical with
the meridian, whatever is true of one holds for the other. Take, then, a
fourth part of the colure distinguishing the solstices, which is from the
equinoctial to the pole. Take another fourth part of the same colure,
which is from zenith to horizon. Since the zenith is the pole of the
horizon, those two quarters, since they are quarters of one and the same
circle, are equal. But if equals are subtracted from equals, or the same
thing common to both is subtracted, the remainders will be equal.
Therefore, if we subtract the common arc, namely, that between the zenith
and the pole, the remainders will be equal, namely, the elevation of the
pole above the horizon and the distance of the zenith from the
equinoctial.
TROPICS OF CANCER AND CAPRICORN. -- Having told of the six great
circles, we must speak of the four smaller circles. Be it noted, then,
that the sun, when in the first point of Cancer or the summer solstice, as
it is carried by the firmament describes a circle, which is the one last
described by the sun in the direction of the Arctic pole. Wherefore it is
called the "circle of the summer solstice" for the reason aforesaid, or
the "summer tropic" from tropos, which is "turning," because then
the sun begins to turn toward the lower hemisphere and to recede from us.
The sun again, when in the first point of Capricorn or winter solstice, as
it is carried by the firmament describes another circle which is the one
last described by the sun in the direction of the Antarctic pole, whence
'tis called the "circle of the winter solstice" or the "winter tropic,"
because then the sun turns toward us.
ARCTIC AND ANTARCTIC CIRCLES. -- Since the zodiac slants from the
equinoctial, the pole of the zodiac will decline from the pole of the
world. Therefore, since the eighth sphere and the zodiac, which is a part
of it, are moved about the axis of
the world, the pole of the zodiac, too, will move about the pole of the
world. And that circle which the pole of the zodiac describes about the
Arctic pole of the world is called the "Arctic circle." And that circle
which the other pole of the zodiac describes about the Antarctic pole is
called the "Antarctic circle."
As great as is the maximum declination of the sun, so great is the
distance of the pole of the world from the pole of the zodiac, which is
shown in this way. Take the colure distinguishing the solstices which
passes through the poles of the world and the poles of the zodiac. Since
all quarters of one and the same circle are equal, the quarter of this
colure between equator and pole is equal to the quarter of the same colure
from the first point of Cancer to the pole of the zodiac. Then, if we
subtract from those equals the common arc from the first point of Cancer
to the pole of the world, the remainders will be equal, namely, the
maximum declination of the sun and the distance from the pole of the world
to the pole of the zodiac. Moreover, since the Arctic circle at every
point is equidistant from the pole of the world, it is evident that that
part of the colure which lies between the first point of Cancer and the
Arctic circle is almost double the maximum declination of the sun or the
arc of the same colure intercepted between the Arctic circle and the
Arctic pole, which is equal to the maximum declination of the sun. Since
that colure, like other circles in the sphere, has 360 degrees, a quarter
of it will be 90 degrees. Then, since the maximum declination of the sun
according to Ptolemy is 23 degrees and 51 minutes and of as many degrees
is the arc which is between the Arctic circle and the Arctic pole, if
those two combined, which make about 48 degrees, are subtracted from 90,
the remainder will be 42 degrees, as is the arc of the colure which lies
between the first point of Cancer and the Arctic circle. So it is clear
that that arc is almost double the maximum declination of the sun.
It is also to be noted that the equinoctial with the four small circles
are called "parallels," as it were equidistant, not that the first is as
far from the second as the second is from the third, because this is
false, as has already been shown, but because any two taken together are
equidistant at every point. They are called the "equinoctial parallel,"
the "parallel of the summer solstice," the "parallel of the winter
solstice," the "Arctic parallel", and the "Antarctic parallel." It is
further to be noted that the four minor parallels, namely, the two tropics
and the Arctic parallel and Antarctic parallel, distinguish five zones or
five regions in the heaven. Therefore, Virgil:
Five zones possess the sky, of which one is ever
Red from blazing sun and ever burnt by fire. [3]
Also a like number of zones is distinguished on earth directly beneath
the said zones. Wherefore, Ovid:
... and just as many zones are marked on earth. [4]
THE FIVE ZONES. -- That zone which lies between the tropics is said to
be uninhabitable because of the heat of the sun, which ever courses
between the tropics. Similarly, the zone of earth directly beneath it is
said to be uninhabitable because of the fervor of the sun, which ever
courses above it. But those two zones which are described by the Arctic
circle and the Antarctic circle about the poles of the world are
uninhabitable because of too great cold, since the sun is far removed from
them. The same is to be understood of the zones of earth directly beneath
them. But those two zones of which one is between the summer tropic and
the Arctic circle and the other between the winter tropic and the
Antarctic circle are habitable and tempered from the heat of the torrid
zone between the tropics and from the cold of the extreme zones which lie
about the poles. The same is to be understood of the stretches of earth
directly beneath them.
RISINGS AND SETTINGS OF THE SIGNS. -- The risings and settings of the
signs are taken in two ways, according to the poets and according to the
astronomers. The rising and setting of the signs according to the poets is
threefold, namely, cosmic, chronic, and heliacal.
COSMIC RISING. -- Cosmic or mundane rising takes place when sign or
star ascends above the horizon from the east by day. And albeit in each
artificial day six signs rise, yet antonomastically that sign is said to
rise cosmically with which and in which the sun rises in the morning. And
this is rising in the strict and chief and daily sense. Of this rising we
have an instance in the Georgics, where the planting of beans and
millet in springtime, when the sun is in Taurus, is taught thus:
The white bull with gilded horns opens the year,
And the dog, yielding to adverse star, sets. [5]
COSMIC SETTING. -- Cosmic setting is a matter of opposition. When the
sun rises with a sign, the opposite sign sets cosmically. This setting is
spoken of in the Georgics, where is taught the sowing of wheat in
late fall when the sun is in
Scorpio. For when Scorpio rises with the sun, Taurus, where the Pleiades
are, sets.
Ere Eoe Atlantides are hidden from you,
Consign the seed as you should to the furrow. [6]
CHRONIC RISING AND SETTING. -- Chronic or temporal rising takes place
when sign or star, after sunset, emerges above the horizon from the east
at night. It is called "temporal rising" because astronomical time begins
with sunset. Of this rising we have an example in Ovid's From Pontus,
where he complains of his prolonged exile, saying,
Pleias having risen makes four autumns, [7]
signifying by four autumns that four years had passed since he was sent
into exile. But Virgil made the Pleiades set in the autumn, so they seem
contradictory. But the explanation of this is that according to Virgil
they set cosmically and according to Ovid they rise chronically, which may
well happen on the same day but differently, since cosmic setting is with
respect to daytime, but chronic rising is in the evening.
Chronic setting is a matter of opposition. Hence Lucan:
Then the short night shot Thessalian arrows. [8]
HELIACAL RISING AND SETTING. -- Heliacal or solar rising occurs when
sign or star can be seen by departure of the sun from it, which previously
could not be seen because of the nearness of the sun. Ovid gives an
example of this in the Fasli, saying:
Now aged Aquarius sits below with urn inclined. [9]
And Virgil in the Georgics:
And the Gnosian Star of the burning crown descends, [10]
which star, being next to Scorpio, was not visible while the sun was in
Scorpio.
Heliacal setting takes place when the sun approaches a sign and by its
presence prevents it from being seen. An example of this is the following
verse:
And the dog, yielding to adverse star, sets. [11]
RIGHT ASCENSIONS. -- We next consider the rising and setting of the
signs according to the astronomers and first in the right sphere. It
should be remarked that the rising
or setting of a sign is nothing else than the rising of that part of the
equinoctial circle which rises with that sign, when it comes above the
horizon, or the setting of that part of the equinoctial which sets with
that sign when it sets, that is, moves westward below the horizon. A sign
is said to rise "vertically" when a larger part of the equator rises with
it, "obliquely" where a smaller part rises with it. The same is to be
understood of setting.
It should be known that in the right sphere the four quarters of the
zodiac beginning from four points, namely, from the two solstices and two
equinoxes, are equal in their ascensions, that is, as much time as a
quarter of the zodiac consumes in rising, so much time the quarter of the
equinoctial corresponding to it takes to rise; but the parts of those
quarters vary and do not have equal ascensions, as will now appear.
There is the rule that every two arcs of the zodiac opposite and equal,
equally distant from one of the four points already mentioned, have equal
ascensions. Whence it follows that opposite signs have equal ascensions.
And this is what Lucan says in speaking of the march of Cato into Libya
toward the equator:
They do not move obliquely, nor is Scorpio straighter
Than Taurus, or Aries give its time to Libra,
Or Astrea bid Pisces to descend slowly.
Chiron is par with Gemini, the same as burning Carcinos
Is humid Aegoceros, nor is Leo moved more than the Urn. [12]
Here Lucan says that to dwellers beneath the equinoctial opposite signs
have equal ascensions and settings. Moreover, the opposing signs are
indicated by this verse:
Sunt li. an. scor. tau. sa. gemi. cap. can. a. le. pis. vir.
Note that this argument does not hold: these two arcs are equal and
begin to rise together and always a greater part of one rises than of the
other; therefore, that arc rises more rapidly of which a larger part
always rises. An example of this argument is shown in the case of parts of
the aforesaid quarters. For if the fourth part of the zodiac is taken,
which extends from the beginning of Aries to the end of Gemini, a larger
part of the quarter of the zodiac always rises [13] than of the quarter of
the equinoctial corresponding to it. Yet those quarters complete their
rising simultaneously. The same is the case with the quarter of the zodiac
from the beginning of Libra to the end of Sagittarius. Also if the quarter
of the zodiac is taken which
extends from the beginning of Cancer to the end of Virgo, a larger part
will always rise of the quarter of the equinoctial than of the quarter of
the zodiac corresponding to it. Yet those two quarters complete their
rising simultaneously. The same is true of the quarter of the zodiac from
the first point of Capricorn to the end of Pisces.
OBLIQUE ASCENSIONS. -- In the oblique or slanting sphere, halves of the
zodiac equal their ascensions. I mean the halves which are taken from the
two equinoctial points, because the half of the zodiac which extends from
the beginning of Aries to the end of Virgo rises with the half of the
equinoctial corresponding to it. Similarly, the other half of the zodiac
rises with the other half of the equinoctial. But the parts of those
halves vary in their risings, since in the half of the zodiac from the
beginning of Aries to the end of Virgo a larger part of the zodiac always
rises than of the equinoctial. Yet those halves complete their rising
simultaneously. The opposite happens in the other half of the zodiac,
which extends from the beginning of Libra to the end of Pisces, for always
a larger part of the equinoctial rises than of the zodiac. Yet those
halves complete their rising simultaneously. So this case is clearly
against the argument aforesaid.
Moreover, the arcs which succeed Aries to the end of Virgo in the
oblique sphere lessen their ascensions compared to the ascensions in the
right sphere; and the arcs which succeed Libra to the end of Pisces in the
oblique sphere increase their ascensions over the ascensions of the same
arcs in the right sphere. That is, they increase by the same quantity as
the arcs succeeding Aries lessen.
From this it is evident that two equal and opposite arcs in the
slanting sphere have their combined ascensions equal to the ascensions of
the same arcs taken together in the right sphere, because as much as is
the diminution on the one hand, so much is the addition on the other.
The rule, indeed, is that any two arcs which are equal and equally
distant from either of the equinoctial points have unequal(?) ascensions.
INEQUALITIES OF DAYS. -- From the aforesaid it is also clear that
natural days are unequal; for a natural day is the revolution of the
equinoctial with as much as the sun covers meanwhile by its own movement
against the firmament. But, since the ascensions of those arcs are
unequal, as is evident from the foregoing, alike in right sphere as in
oblique, and natural days are reckoned according to the increase of those
ascensions, they will of necessity be unequal, in the right sphere for a
single reason -- the obliquity of the zodiac -- in the oblique sphere for
two reasons -- the obliquity of the zodiac and the obliquity of the
oblique horizon. Moreover, a third cause is wont to be assigned -- the
eccentricity of the sun's orbit.
MOVEMENT OF THE SUN. -- It also should be noted that the sun, moving
from the first point of Capricorn through Aries to the first point of
Cancer with the sweep of the firmament, describes 182 parallels, to which
parallels, although they are not really circles but spirals, since there
is no sensible error in this, no violence is done if they are called
"circles," of which number of circles are the two tropics and the
equinoctial. Also the sun describes these circles with the sweep of the
firmament as it descends from the first point of Cancer through Libra to
the first point of Capricorn; and those circles are called the "circles of
natural days." But the arcs above the horizon are the arcs of artificial
days, and the arcs below the horizon are the arcs of the nights.
In the right sphere the horizon, since it passes through the poles of
the world, divides all those circles into equal parts, whence the arcs of
days are the same as those of nights for persons living at the equator.
Hence it is evident that for persons living at the equator it is always
equinox, wherever the sun may be in the firmament.
But in the slanting sphere the oblique horizon divides the equinoctial
alone into two equal parts. Hence, when the sun is at either equinoctial
point, the arc of day equals the arc of night, and there is equinox the
world over. But the oblique horizon divides all the other circles into
unequal parts, so that in all the circles from the equinoctial to the
Tropic of Cancer and at the Tropic of Cancer itself the arc of day is
greater than that of night, that is, the arc above the horizon than that
below the horizon. Hence all the time that the sun is moved from the
beginning of Aries through Cancer to the end of Virgo, the days are longer
than the nights and so much the more as the sun comes closer to Cancer. In
all the other circles which are between the equinoctial and the Tropic of
Capricorn the arc is greater below the horizon than above. Hence the arc
of day is less than the arc of night; and, according to the proportion
between the arcs, the days grow less than the nights, and the closer the
circles get to the winter tropic, the more the days shorten.
DAY AND NIGHT. -- Wherefore it appears that, if two circles are taken
equidistant in their various parts from the equinoctial, as great as is
the arc of day in the one, so great is the arc of night in the other. From
this it seems to follow that if two natural days in the year are taken
equally remote from either equinoctial point in opposite directions, as
long as is the artificial day in one case, so long is the night in the
other, and conversely. But this is with reference to ordinary observation
in fixing the horizon. For reason determines more exactly by discounting
the movement of the sun contrary to the firmament in the obliquity of the
zodiac.
The more the pole is elevated above the horizon, so much more are the
days of summer lengthened when the sun is in the northern signs.
Conversely, when the sun is in the southern signs the days are so much
shorter than the nights.
RIGHT AND OBLIQUE ASCENSIONS. -- It is to be noted that the six signs
from the beginning of Cancer through Libra to the end of Sagittarius have
their combined ascensions greater than the ascensions of the other six
signs from the beginning of Capricorn through Aries to the end of Gemini.
Hence those six signs first mentioned are said to rise erect, but the
others obliquely. Wherefore the verses:
They rise aright, oblique descend from Cancer's star
Till Chiron ends, but the other signs
Are prone at birth, descend by a straight path.
And when we have the longest day of summer, when the sun is in the
beginning of Cancer, then six signs rise vertically by day but six
obliquely at night. Conversely, when we have the shortest day of the year,
when the sun is in the beginning of Capricorn, then those six signs which
rise by day do so obliquely, but by night the other six rise vertically.
When, moreover, the sun is at either equinoctial point, then by day three
signs rise vertically and three obliquely, and at night the same.
For the rule is: However short or long the day or night may be, six
signs rise by day and six by night, nor because of the length or brevity
of day or night do more or fewer signs rise.
From these facts it is gathered that, since a natural hour is the space
of time in which half a sign rises, there are twelve natural hours in each
artificial day, and so also in the night. Moreover, in all the circles
which parallel the equator to north or south, days or nights are
lengthened or shortened according as more or fewer signs rise vertically
or obliquely by day or night.
DWELLERS AT THE EQUATOR. -- Moreover, it is to be noted that in the
case of those whose zenith is in the equinoctial the sun twice a year
passes directly overhead, namely, when in the beginning of Aries and in
the beginning of Libra; and then there are two high solstices for them
when the sun passes directly overhead. Again there are two low solstices
for them when the sun is in the first points of Cancer and Capricorn, and
they are called "low" because then the sun is farthest removed from their
zenith. From what has been said it is clear that, while they always have
equinox, they will have in the course of a year four solstices, two high
and two low. It also is evident that they have two summers when the sun is
in either of the equinoctial points
or nearly so, and likewise two winters when the sun is in the first points
of Cancer and Capricorn or thereabouts. And this is why Alfraganus says
that for them summer and winter are of one and the same complexion, since
those two seasons which are winter and summer for us are for them two
winters, and the difference is made clear by these lines of Lucan:
'Tis understood this is the place where the circle
Of the high solstice hits that of the signs midway. [14]
Here Lucan calls the equinoctial "the circle of the high solstice," on
which two high solstices happen to those living at the equator. He calls
the zodiac "circle of the signs," which the equinoctial "hits," that is,
divides "midway," that is, halved or divided in two.
These also during the year have four shadows; for, when the sun is in
either equinoctial point, their shadow in the morning falls toward the
west, in the evening in the opposite direction. At noon their shadow is
perpendicular, when the sun is overhead. When the sun is in the northern
signs, their shadow lies toward the south; but when the sun is in the
southern signs, then their shadow falls toward the north.
For them, too, the stars which are near the poles rise and set, and for
others living near the equator. Hence Lucan:
Then Roman fury moves the remote Orestae
And Carmanian leaders whose ether, now turned
Southward, yet does not see Arcton quite submerged,
And there swift Boötes shines in scant night. [15]
Therefore it is setting and shines little. Ovid, too, says of the same
star:
The guardian of the Erimanthean bear is dipped in ocean
And with his star disturbs the waters of the sea. [16]
That is to say, it sets vertically. But in our locality those stars
never set. Wherefore Virgil:
This vertex is ever above us. [17]
And Lucan:
Axis never-setting, bright with both Bears. [18]
Also Virgil:
Arctos dreading to touch the ocean wave. [19]
BETWEEN THE EQUATOR AND TROPIC OF CANCER. -- To those whose zenith is
between the equinoctial and the Tropic of Cancer it happens twice a year
that the sun passes directly overhead, which is shown thus. Suppose a
circle parallel to the equinoctial passes through their zenith. That
circle will intersect the zodiac at two points equidistant from the
beginning of Cancer. Therefore, when the sun is at those two points it
passes through their zenith; wherefore they have two summers and two
winters, four solstices and four shadows, like those living at the
equator. And some say Arabia is so situated. Hence Lucan, speaking of the
Arabs coming to Rome to aid Pompey, says:
You Arabs have come to a world unknown to you
And marvel that the shade of trees is never leftward, [20]
since in their country shadows were sometimes to their right, sometimes
to their left, sometimes perpendicular, sometimes to the east, sometimes
to the west. But when they came to Rome beyond the Tropic of Cancer, then
the shadows were always northward.
AT THE TROPIC OF CANCER. -- To those whose zenith is at the Tropic of
Cancer it happens that the sun once a year passes through their zenith,
namely, when it is in the first point of Cancer, and then for one hour of
one day of the whole year their shadow is perpendicular. The city of Syene
Is said to be so situated. Hence Lucan:
Syene's never varying shadow. [21]
Understand this as applying to noon of a single day; for all the rest
of the year their shadow is northward.
BETWEEN THE TROPIC AND THE ARCTIC CIRCLE. -- But to those whose zenith
is between the Tropic of Cancer and the Arctic circle it happens that the
sun is never directly overhead and their shadow always lies toward the
north. Such is our situation. Also it is to be noted that, according to
some persons, Ethiopia or a part of it is this side of the Tropic of
Cancer. Hence Lucan:
And Ethiopia which alone is untouched
By any region of the sign-bearing pole,
Except the hoof tip of curvetting Taurus. [22]
For they say that sign is here taken equivocally, both for a twelfth
part of the zodiac and for the outline of the animal which, for the most
part, is within the sign to which it gives its name. Wherefore Taurus,
although it is, for the most part, within the zodiac, extends its foot
beyond the Tropic of Cancer and so touches Ethiopia, although no part of
the zodiac touches it. For if the foot of Taurus were extended toward the
equinoctial so that it was in the direction of Aries or another sign, then
it would be touched by Aries and Virgo or other signs, which is evident by
drawing a circle parallel to the equinoctial through the zenith of the
Ethiopians and Aries and Virgo or other signs. But, since philosophical
reason is opposed to this, for they would not be so black if they were
born in the temperate habitable zone, it must be said that that part of
Ethiopia of which Lucan is speaking is beneath the equinoctial circle and
that the foot of Taurus, of which he speaks, extends toward the
equinoctial. But there is a distinction between cardinal signs and
regions; for "cardinal signs" are the name for the two signs in which the
solstices occur and the two in which the equinoxes occur, while the
intermediate signs are called "regions." And in this way it becomes clear
that, although Ethiopia is at the equator, it is not touched by any region
but merely by two cardinal signs, namely, Aries and Libra.
AT THE ARCTIC CIRCLE. -- To those whose zenith is at the Arctic circle
it happens on every day of the year that their zenith is identical with
the pole of the zodiac, and then they have the zodiac or ecliptic as their
horizon. And this is what Alfraganus says, that there the circle of the
zodiac is bent over the circle of the hemisphere. But, since the firmament
is in continual motion, the circle of the horizon will intersect the
zodiac instantaneously, and, since they are great circles in the sphere,
they will intersect in equal parts. Hence one half of the zodiac rises
immediately above the horizon, and the other sinks below the horizon. And
this is what Alfraganus says, that six signs set suddenly there, and the
other six rise with the whole equinoctial. And, since the ecliptic is
their horizon, when the sun is in the first point of Cancer they will have
a day of 24 hours and a quasi-instant for night, since the sun touches the
horizon for an instant and straightway rises, and that amount of contact
is their night. The opposite happens when the sun is in the first point of
Capricorn, for then they have a night of 24 hours and a quasi-instant for
a day.
BETWEEN THE ARCTIC CIRCLE AND THE NORTH POLE. -- To those whose zenith
is between the Arctic circle and the North Pole, it happens that their
horizon will intersect the zodiac in two points equidistant from the
beginning of Cancer. And, as the firmament revolves, this intercepted
portion of the zodiac always remains above the horizon. Hence it is clear
that, so long as the sun is in that portion, there will be continuous day
without night. Therefore, if it is as much as one sign, there will be
continuous day there for one month without night. If the sun remains for
the extent of two signs, there will be continuous day without night for
two months, and so on. It likewise happens that the portion intercepted
between two points equidistant from the beginning of Capricorn is always
left below the horizon. Hence, when the sun is in that intercepted
portion, there will be one continuous night without day, short or long
according to the extent of the portion intercepted. Moreover, the
remaining signs which rise and set for them, rise and set preposterously.
They rise preposterously, as Taurus before Aries, Aries before Pisces,
Pisces before Aquarius. Yet the signs opposite these rise in right order.
They set preposterously, as Scorpio before Libra, Libra before Virgo,
<Virgo before Leo>. Yet the signs opposite these set vertically.
AT THE NORTH POLE. -- To those whose zenith is at the Arctic pole it
happens that the horizon is identical with the equinoctial. Hence, since
the equinoctial intersects the zodiac in equal parts, their horizon leaves
half of the zodiac above and half below it. Wherefore, while the sun is
moving through that half which extends from the beginning of Aries to the
end of Virgo, there will be one continuous day without night; and when the
sun is moving in the other half, which extends from the beginning of Libra
to the end of Pisces, there will be one continuous night without day.
Wherefore, one half of the whole year will be one artificial day, and the
other half one night. Hence there the whole year is one natural day. But
since there the sun is never more than 23 degrees below the horizon, it
seems that they have continuous day without night; for we speak of its
being day before the rise of the sun above the horizon. But this is
according to popular usage; for in a scientific sense it is not artificial
day except from the rising of the sun above the horizon to its setting
beneath the horizon. As for that argument again, that there ought to be
perpetual light there, it should be said that the air there is misty and
dense, for the rays of the sun there are feeble and raise more vapors than
they can consume, so that the air is not clear.
THE SEVEN CLIMES. -- Let a circle be imagined on the earth's surface
directly under the equinoctial. And suppose another circle on the earth's
surface passing from east to west through the poles. These two circles
will intersect in two places at right spherical angles and divide the
whole earth into four parts, one of which is our habitable region, namely,
that which is intercepted between the semicircle drawn from east to west
along
the equator and the semicircle carried
from east to west through the Arctic pole. Nor is that quarter entirely
habitable, since parts of it near the equator are uninhabitable because of
too great heat, and parts near the pole because of too great cold.
Suppose, then, a line parallel to the equator dividing the parts
uninhabitable on account of heat from those habitable parts toward the
north. And suppose another line equidistant at all points from the Arctic
pole dividing the parts which are uninhabitable for cold from the
habitable parts toward the equator. Between these two extreme lines
suppose six lines parallel to the equator, which, with the two former,
divide the whole habitable quarter into seven parts which are called the
"seven climes."
FIRST CLIME. -- The middle of the first clime is where the length of
the longest day is 13 hours and the pole is elevated above the horizon 16
degrees, and it is called the "clime of Meroe." It begins where the length
of the longest day is 12 3/4 hours and the pole is elevated above the
horizon 12 3/4 degrees. And its breadth extends to the place where the
length of the longest day is 13 1/4 hours and the pole is elevated above
the horizon 20 1/2 degrees, which distance is 440 miles.
SECOND CLIME. -- The middle of the second clime is where the longest
day is 13 1/2 hours and the elevation of the pole above the horizon is 24
1/4 degrees, and it is called the "clime of Syene." Its breadth from the
end of the first clime to a place where the longest day is 13 3/4 hours
and the pole is elevated 27 1/2 degrees, is a distance of 400 miles.
THIRD CLIME. -- The middle of the third clime is where the length of
the longest day is 14 hours, and the elevation of the pole above the
horizon is 3O 3/4 degrees, and it is called the "clime of Alexandria." Its
breadth is from the end of the second clime to where the longest day is 14
1/4 hours, and the altitude of the pole 33 2/3 degrees, which is a
distance of 350 miles.
FOURTH CLIME. -- The middle of the fourth clime is where the longest
day is 14 1/2 hours and the altitude of the axis is 36 2/5 degrees, and it
is called the "clime of Rhodes." Its breadth is from the end of the third
clime to where the longest day is 14 3/4 hours and the elevation of the
pole is 39 degrees, which distance is 300 miles.
FIFTH CLIME. -- The middle of the fifth clime is where the major day is
15 hours and the elevation of the pole is 41 1/3 degrees, and it is called
the "clime of Rome." Its breadth is from the end of the fourth clime to
where the longest day is 15 1/4 hours and the elevation of the axis is 43
1/2 degrees, which distance is 255 miles.
SIXTH CLIME. -- The middle of the sixth clime is where the longest day
is 15 1/2 hours and the pole is elevated above the horizon 45 2/5 degrees,
and it is called the "clime of
Boristhenes." Its breadth is from the end of the fifth clime to where the
length of the longest day is 15 3/4 hours and the elevation of the axis is
47 1/4 degrees, which distance is 212 miles.
SEVENTH CLIME. -- The middle of the seventh clime is where the longest
day is 16 hours and the elevation of the pole above the horizon is 48 2/3
degrees, and it is called the "clime of Ripheon." Its breadth is from the
end of the sixth clime to where the maximum day is 16 1/4 hours and the
pole is elevated above the horizon 50 1/2 degrees, which space of earth is
185 miles.
BEYOND IT. -- Beyond the end of this seventh clime there may be a
number of islands and human habitations, yet whatever there is, since
living conditions are bad, is not reckoned as a clime. Therefore, the
whole difference between the initial limit of the climes and their end is
3 1/2 hours, and of elevation of the pole above the horizon 38 degrees. So
then we have made clear the breadth of each clime from its beginning
toward the equator to its end toward the Arctic pole, and that the breadth
of the first clime is greater than the latitude of the second, and so on.
The length of a clime may be said to be the line drawn from east to west
parallel to the equator; wherefore the length of the first clime is
greater than the length of the second and so on, which happens because the
sphere narrows down.
MOVEMENT OF THE SUN. -- It should be noted that the sun has a single
circle in which it is moved in the plane of the ecliptic, and it is
eccentric. Any circle is called "eccentric" which, like that of the sun,
dividing the earth into equal parts, does not have the same center as the
earth but one outside it. Moreover, the point in the eccentric which
approaches closest to the firmament is called aux or augis,
meaning "elevation." The opposite point, which is farthest removed from
the firmament, is called the "opposition" of the aux.
Moreover, there are two movements of the sun from west to east, one of
which is its own in its eccentric, by which it is moved every day and
night about 60 minutes. The other is the slower movement of the sphere
itself on the poles of the axis of the circle of the signs, and it is
equal to the movement of the sphere of the fixed stars, namely, 1 degree
in a hundred years. From these two movements, then, is reckoned the sun's
course in the circle of the signs from west to east, by which it cleaves
the circle of the signs in 365 days and a fourth of one day, except for a
small fraction which is imperceptible.
OF THE OTHER PLANETS: EQUANT, DEFERENT, AND EPICYCLE. -- Every planet
except the sun has three circles, namely, equant, deferent, and epicycle.
The equant of the moon is a circle concentric with the earth and in the
plane of the ecliptic. Its deferent is an eccentric circle not in the
plane of the ecliptic -- nay, one half of it slants toward the north and
the other toward the south -- and the deferent intersects the equant in
two places, and the figure of that intersection is called the "dragon"
because it is wide in the middle and narrow toward the ends. That
intersection, then, through which the moon is moved from south to north is
called the "head of the dragon," while the other intersection through
which it is moved from north to south is called the "tail of the dragon."
Deferent and equant of each planet are equal, and know that both deferent
and equant of Saturn, Jupiter, Mars, Venus, and Mercury arc eccentric and
outside the plane of the ecliptic, and yet those two are in the same
plane. Also every planet except the sun has an epicycle. An epicycle is a
small circle on whose circumference is carried the body of the planet, and
the center of the epicycle is always carried along the circumference of
the deferent.
STATIONARY, DIRECT, AND RETROGRADE. -- If, then, two lines are drawn
from the center of the earth to include an epicycle, one on the east and
the other on the west, the point of contact on the east is called the
"first station," while the point of contact to the west is called the
"second station." And when a planet is in either of those stations it is
called "stationary." The upper arc of the epicycle intercepted between
those two stations is called "direction," and when the planet is there it
is called "direct." But the lower arc of the epicycle between the two
stations is called "retrogradation," and a planet existing there is called
"retrograde." But the moon is not stationary, direct, or retrograde
because of the swiftness of its motion in its epicycle.
CAUSE OF LUNAR ECLIPSE. -- Since the sun is larger than the earth, it
is necessary that half the sphere of earth be always illuminated by the
sun and that the shadow of the earth, extended into the air like a cone,
diminish in circumference until it ends in the plane of the circle of the
signs inseparable from the nadir of the sun. The nadir is a point in the
firmament directly opposite to the sun. Hence, when the moon, at full is
in the head or tail of the dragon beneath the nadir of the sun, then the
earth is interposed between sun and moon, and the cone of the earth's
shadow falls on the body of the moon. Wherefore, since the moon has no
light except from the sun, it actually is deprived of light and there is a
general eclipse, if it is in the head or tail of the dragon directly but
partial if it is almost within the bounds determined for eclipse. And it
always happens at full moon or
thereabouts. But, since in every opposition -- that is, at full moon --
the moon is not in the head or tail of the dragon or beneath the nadir of
the sun, it is not necessary that the moon suffer eclipse at every full
moon.
CAUSE OF SOLAR ECLIPSE. -- When the moon is in the head or tail of the
dragon or nearly within the limits and in conjunction with the sun, then
the body of the moon is interposed between our sight and the body of the
sun. Hence it will obscure the brightness of the sun for us, and so the
sun will suffer eclipse -- not that it ceases to shine but that it fails
us because of the interposition of the moon between our sight and the sun.
From these it is clear that a solar eclipse should always occur at the
time of conjunction or new moon. And it is to be noted that when there is
an eclipse of the moon, it is visible everywhere on earth. But when there
is an eclipse of the sun, that is by no means so. Nay, it may be visible
in one clime and not in another, which happens because of the different
point of view in different climes. Whence Virgil most aptly and concisely
expresses the nature of either eclipse:
Varied defects of the moon, and of the sun travails. [23]
ECLIPSE DURING THE PASSION MIRACULOUS. -- From the aforesaid it is also
evident that, when the sun was eclipsed during the Passion and the same
Passion occurred at full moon, that eclipse was not natural -- nay, it was
miraculous and contrary to nature, since a solar eclipse ought to occur at
new moon or thereabouts. On which account Dionysius the Areopagite is
reported to have said during the same Passion, "Either the God of nature
suffers, or the mechanism of the universe is dissolved."
NOTES:
[1]. The mediclinium, or "indicator," is
described in the first part, fourth chapter, of Messahala's treatise on
the astrolabe (English translation in R. G. Gunther, Early Science at
Oxford, V [1929], "Of Making an Allidada Which Is Called a Rule or
Mediclinium").
[2]. Georgics i. 242-43.
[3]. Georgics i. 233-34.
[4]. Metamorphoses i. 48.
[5]. Georgics i. 217-18.
[6]. Georgics i. 221, 223.
[7]. Ex Ponto viii, 28.
[8]. Pharsalia iv. 528.
[9]. Fasli ii. 457.
[10]. Georgics i. 222.
[11]. Georgics i. 218.
[12]. Lucan Pharsalia ix. 533-37.
[13]. That is, has risen; otherwise Sacrobosco is in
error.
[14]. Pharsalia ix. 531-32.
[15]. Pharsalia iii. 249-52.
[16]. Tristia i. 4. 1-2, or in some editions, i.
3. 103-4.
[17]. Georgics i. 242-43.
[18]. Pharsalia viii. 175. By "twin Arcton" is
meant Ursa Major and Ursa Minor.
[19]. Georgics i. 246.
[20]. Pharsalia iii. 247-48.
[21]. Pharsalia ii. 587.
[22]. Pharsalia iii. 253-55.
[23]. Georgics ii. 478. |
