equally distant from the inner surface of the horizon and meridian circles, that is, there should be a perfect adjustment of the enclosing rings and the enclosed ball. The surface of the sphere should be painted a dark color, as, for example, azure. He sets forth, with considerable detail, the proper method of procedure in locating the several principal circles, each of which should be graduated. The zodiac should be divided into twelve parts, and the constellations belonging to each of the several parts should be designated by name, beginning with Cancer, following this with Leo, Virgo, and so on, one after the other. In giving the globe a position which actually conforms to the world, the pole should be set to the north, and the movement of the sky can then be imitated by turning the globe to the left. Leontius, by way of summary and definition, at the conclusion of his treatise, speaks of a sphere as a solid having a surface, from all the points of which, if straight perpendicular lines of equal length be drawn, they will reach a point within called the center. This center in the great sphere of the universe is the earth. The poles of the sphere are the extremities of the axis on which it turns. The horizon cuts the sphere into two hemispheres, the one superior and the other inferior to the earth. The sky, which is continually turning, encircles all, one half of it being above, the other below the earth, which is as far removed from the superior part of the heavens as from the inferior.[48] NOTES [30] Cicero’s allusion to Thales, cited p. 16, is probably a reference to a tradition. [31] Wolf, R. Geschichte der Astronomie. München, 1877, p. 193; Gassendi, P. Opera Omnia. Leipzig, 1658. Vol. V, p. 375. See statement by Cicero, cited below, p. 17. [32] Aratus’ poem bore the title, “Phaenomena.” See, for an excellent edition of this poem, Prince, C. L. Phenomena. A literal translation of the astronomy and meteorology of Aratus. Lewes, 1895. In his “Bibliographical remarks,” the translator refers to one hundred and nineteen editions of this poem, dating from the first printed at Bonn in the year 1474. See also n. 19 (48), below. [33] Passeri, G. B. Atlas Farnesianus Marmoreus insigne vetustatis monumentum. (In: Gori, A. F. Thesaurus gemmarum antiquarum astriferarum. Firenze, 1750. Vol. III.); Denza, P. F. Globi celesti della Specola Vaticana. (In: Publicazioni della Specola Vaticana. Torino, 1894. pp. xx-xxiii.) [34] Cicero. De Republica. Bk. I, chap. xiv. The citation is from the translation by Hardingham, G. G. The Republic. London, 1884. [35] Lactantius. Institutiones divinae. Bk. II, chap. v. [36] Pappus. Collectionum mathematicarum. Edited by Commandino. Urbino, 1588. Bk. VII. See especially the introduction.