This is the more noteworthy because passages in the very same work show him to have accepted some of the theories which we have associated with magic. Thus he appears to believe in occult virtues and marvelous properties of things in nature, since he affirms that, while Africa in general abounds in serpents, no snake can live within the boundaries of the African city of Ismuc, and that this is a property of the soil of that locality which it retains when exported.[859] Vitruvius also mentions some marvelous waters. One breaks every metallic receptacle and can be retained only in a mule’s hoof. Some springs intoxicate; others take away the taste for wine. Others produce fine singing voices.[860] Vitruvius furthermore speaks of six and ten as perfect numbers and contends that the human body is symmetrical in the sense that the distances between the different parts are exact fractions of the whole.[861] He also tells how the Pythagoreans composed books on the analogy of the cube, allowing in any one treatise no more than three books of 216 lines each.[862] [Sidenote: Astrology.] Vitruvius also more than once implies his confidence in the art of astrology. In mapping out the ground-plan of his theater he advises inscribing four equilateral triangles within the circumference of a circle, “as the astrologers do in a figure of the twelve signs of the zodiac, when they are making computations from the musical harmony of the stars.”[863] I cannot make out that there is any astrological significance or magical virtue in this so far as the arrangement of the theater is concerned, but it shows that Vitruvius and his readers are familiar with the technique of astrology and the _trigona_ of the signs. In another passage, comparing the physical characteristics and temperaments of northern and southern races, which astrologers generally interpreted as evidence of the influence of the constellations upon mankind, Vitruvius patriotically contends that the inhabitants of Italy, and especially the Romans, represent a happy medium between north and south, combining the greater courage of the northerners with the keener intellects of the southerners, just as the planet Jupiter is a golden mean between the extreme influences of Mars and Saturn. So the Romans are fitted for world rule, overcoming barbarian valor by their superior intelligence and the devices of the southerners by their valor.[864] In a third passage Vitruvius says more expressly of the art of astrology: “As for the branch of astronomy which concerns the influences of the twelve signs, the five stars, the sun, and the moon upon human life, we must leave all this to the calculations of the Chaldeans, to whom belongs the art of casting nativities, which enables them to declare the past and the future by means of calculations based on the stars. These discoveries have been transmitted by men of genius and great acuteness who sprang directly from the nations of the Chaldeans; first of all, by Berosus,