The Sphere of the World with Commentaries

by the rapid movement of the firmament describes a certain circle which is the last described by the sun from the side of the antarctic pole. Whence it is called the circle of the winter solstice or the winter tropic, because then the sun turns itself toward us. When, however, the zodiac declines from the equinoctial, the pole of the zodiac will also decline from the pole of the world. When, therefore, the eighth sphere moves, and the zodiac, which is a part of the eighth sphere, will move around the axis of the world, the pole of the zodiac will move around the pole of the world. This circle, therefore, which the pole of the zodiac describes around the arctic pole of the world, is called the arctic circle. That circle, however, which the other pole of the zodiac describes around the antarctic pole of the world is called the antarctic circle. Also, the maximum declination of the sun, namely from the equinoctial, is equal to the distance of the pole of the world to the pole of the zodiac, which is evident thus: Let the colure distinguishing the solstices be taken, which passes through the poles of the world and through the poles of the zodiac. Since, therefore, all quarters of one and the same circle are equal to each other, the quarter of this colure, which is from the equinoctial to the pole of the world, will be equal to the quarter of the same colure, which is from the first point of Cancer to the pole of the zodiac. Therefore, from those equal things, having removed the common arc which is 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 of the pole of the world to the pole of the zodiac. When, however, the arctic circle at every part of its length is equidistant from the pole of the world, it is evident that that part of the colure which is between the first point of Cancer and the arctic circle is nearly double the maximum declination of the sun, or the arc of the same colure which is intercepted between the arctic circle and the arctic pole of the world, which arc is also equal to the maximum declination of the sun. For when this colure, like other circles in the sphere, is 360 degrees, its quarter will be 90 degrees. Since, therefore, the maximum declination of the sun according to Ptolemy is 23 degrees and 51 minutes, and the arc which is between the arctic circle and the arctic pole of the world is the same number of degrees; if these two joined together, which nearly make 48 degrees, are subtracted from 90, the remainder will be 42 degrees, which is the amount of the arc of the colure which is between the first point of Cancer and the arctic circle. And thus it appears that that arc is nearly double the maximum declination of the sun. It is to be noted that the equinoctial with the four smaller circles are called five