De cometis

ssibility, could not be greater than six degrees by instruments suitably ordered for this. From this diversity of aspect, it necessarily follows that the body was distant from the surface of the earth at a ninefold distance to the semi-diameter of the earth, which is at least eight thousand and two hundred miles. It was, therefore, in the upper part of the supreme region of the air and not in the fire placed underneath, a reference to the Aristotelian elemental spheres where fire sits above air by a tenfold quantity of the measurement of the elements as the philosopher Aristotle determines in the second book De generatione On Generation and Corruption.

On the magnitude of the comet

Since the diameter of the head of the comet measured eleven minutes of a great circle, as the instruments indicated, the chord of which minutes is eleven minutes and almost a half, that chord, as has been said in the first part, should be multiplied by the distance of the comet from the earth, namely eight thousand and two hundred miles, and it produces ninety-four thousand and thirty. Let this be divided by the total sine, namely three thousand six hundred minutes, and the result will be twenty-six miles, which is the quantity of the diameter of the comet. The tails, however, extending around from the head of the comet, measured almost thirty-four minutes. The diameter of these was therefore almost eighty-one miles.

On the length of the comet

The tail, however, in its greater length, when the comet was around the stars of the Northern Fish and the tail extended almost to the Pleiades, distant from the head of the comet by thirty-five degrees, measured about thirty degrees. The length of these was therefore more than four thousand miles. The common length of them on the preceding days was two thousand and five hundred miles. For if it had not been distant from the earth by more than the quantity of the semi-diameter of the earth, the length of them would still have been four hundred and sixty miles. To bring forward the individual mathematical demonstrations of all these things would be prolix and very tedious.