Of the three indices which revolve from the left, the uppermost
completes its cycle within 12 hours, just as the hour index. The middle
one with two pointers on diametrically opposite sides, carries the marks
of conjunction and opposition of the luminous bodies, with a movement
equal to the course of the sun from lunar apogee or perigee. The lowest
index, fitted with a single pointer, indicates the motion of the moon
from its apogee or perigee. Under these three indices, there is situated
a common circle, divided into 12 parts, each of which are further
divided into 30 parts through its outer circumference. I have said a
common circle, for, with respect to the first index, the division
represents 12 hours, and the double subdivision representing the double
set of minutes of the hours serves for an excitator for anytime at all,
at will. For as often as the little index reaches the twelfth hour,
first being moved by hand wherever you prefer, a little hammer strikes
the little bell many times. But if you observe the second or the third
index, the first division provides the signs, and the subdivision of the
signs gives the individual degrees of the distance of the sun from the
lunar apogee, or of the moon from its apogee, respectively. To this is
added two other interior circles from the same center: to the larger is
inserted the equation of the center of the moon in its conjunctions and
oppositions; and on the smaller the equation of the same moon in its
quarters, astronomically-geometrically proportioned to the distance of
the moon from its apogee or perigee. In the first case, the equation is
to be subtracted from the mean longitude of the moon, descending from
apogee to perigee; in the second case, to be added to the mean longitude
of the moon ascending from perigee to apogee; and, in the third
semicircle of the index, as the rubric directs, common to both
equations, added around the center.
V
Perpendicularly under the center of the machine, two other indices are
carried about one and the same center. The one nearer to the
observer--bearing in one of two points diametrically opposite the small
disk of the sun, in the other the disk of the moon--runs a course equal
to the motion of the sun from the head or the tail of the dragon
(_Draco_). The other, of simple construction, marked with a small moon,
signifies in like manner the motion of the moon from the head or the
tail of the dragon.
Immediately below, there is a larger circle, common [referring] to both
these indices, which is divided into 12 parts. Each of these parts in
turn, in the outer periphery, is subdivided further into 30 parts, which
are the 12 signs of the zodiac and the individual degrees of the signs
of distance of the sun and the moon from the head of the dragon.
In the second circle is read the latitude of the moon, measured by
degrees, etc., on a trigonometric scale, by signs and degrees of
distance of the moon from its nodes, that is, from the head or tail of
the dragon. When the second index is descending from the head of the
dragon to the tail, the latitude will be to the north of the solar path;
that is, the ecliptic. On the other hand, it will be south of the
ecliptic when the same index is returning upward from the tail to the
head of the dragon as advised by the title inscribed on the third
circle.
Finally, on the fourth and last circle are seen more prime minutes of
the circle for reducing the orbit of the moon to the ecliptic. That the
true longitude of the moon may be obtained more accurately, these must
be subtracted from the longitude of the moon already calculated in the
first and third quadrant of the circle of the second index. On the other
hand, they are to be added to the same in the second and fourth
quadrant, as is noted in their respective places, according to the
theory of right ascensions.
Here, then, [you have] as finally completed, delineation of the great
index which was partially described before in this book.
From two points of that index which perpendicularly correspond to the
center of these circles, a pair of compasses, by an unvaried aperture up
to the circumference of the first larger circle, has marked off four
segments of a circle. The two larger segments, equal among themselves,
in one aperture refer to the sun, and the two smaller in the other,
likewise equal, refer to the moon. The one pointer is for determining
the solar eclipses; the other, for lunar. Both segments of each
division, like little wings of the index, stretch to the extent of the
degree of distance of the moon from its nodes, and to which that
determined latitude corresponds. On one side, that latitude precisely
equals the radii of the earth, the sun, and the moon, as the termini of
solar eclipses; and, on the other side, precisely equals the radii of
the earth's shadow and of the moon, as the confines of lunar eclipses.
The apexes of the last index, diametrically limited [opposite], indicate
the age of the moon, and its mean distance from the sun; one pointer,
upon which the sun sits, measuring the mean days and degrees from the
full moon; the other, on which the moon sits, measuring the mean days
and degrees from the new moon.