Observatio & demonstratio cometae aetherei, qui anno 1577 et 1578 constitutus in sphaera veneris, apparvit, cum admirandis eius passionibus, varietate scilicet motus, loco, orbe, distantia à terrae centro, &c. adhibitis demonstrationibus geometricis & calculo arithmetico, cuiusmodi de alio quoquam cometa nunquam visa est

HALC and AIC, a sensible difference will be observed by the arc OP, just as, conversely, if the arc OP, or the difference of parallaxes, has escaped observations so that it cannot be perceived, it is not necessary that the distance of L and I from A be small, but rather such that AC does not become sensible compared to it. Therefore, there is no place for this demonstration except in the Moon and lunar books; other spheres are immune to this on account of their greater altitude. These things, demonstrated elsewhere, had to be recounted here, yet the demonstrations themselves, being known to beginners who have tasted the elements of Astronomy, are omitted.

If the stated observation of the 2nd of December is applied to these, the proposed goal will be easily manifest. For let Q be a star of Equiculus Equuleus, and let N be the true place of the Comet at the 6th hour. Then QN will be the visible distance of the Comet from the star. However, as the star descends by daily motion to R, the visible removal of the Comet from the star RO (if indeed it moves in the sphere of the Moon or any sublunary place) ought to appear greater than QN was before, by the quantity of the arc OP. But the observation overwhelms this with the clearly contrary: for in the later hour, the arc RO was not only not found greater, nor even equal, but smaller than QN, and that according to the proportion of the proper daily motion, as much as the straight line AIF has progressed in sequence. Wherefore it is most certain that the points M and N, and likewise FP and O, have almost coalesced into one, and that no difference of parallax of the Comet perceptible to the senses has arisen in the whole three-hour space, and so every parallax of it escapes the senses.

Since, therefore, universal experience, built upon the indubitable foundations of Geometry, proves that this Comet is devoid of those passions by which the Moon varies its positions hourly, and much more so any inferior second-magnitude star, it becomes most certain that it has flown far above the sublunary sphere and has sought a seat for itself in the superior ethereal world, to the altitude of which the Earth's semidiameter, as far as parallaxes are concerned, has no sensible proportion.

CHAPTER IV.

In the preceding chapter, it was demonstrated that this Comet is not to be affixed to the sublunary sphere. With this one proof, since I was intending to publish these my lucubrations in previous days (in which, however, I was held back by certain causes, especially by the shortness of time due to the approaching fairs), I wanted to be content, since