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

made more easterly, approaching the star as much as its own proper daily motion according to the order of the signs demanded. Hence it also happened that after an entire day had passed, it traversed that space of the stars, and on the 3rd of December it was higher, having cast aside the stars to the south, which on the 2nd were boreal northern to it. From this observation, as well as from many others, it is manifest that this Comet by no means moves in the sublunary sphere.

For let there be described by center A a great circle of the Earth BCD, around which let there be a circle of the ultimate sky BFG, concentric to the Earth, through our zenith C, which is marked at B. Let there also be HIK, in which the Comet moves, a vertical quadrant; let ACHB and ABKG be continued. It is demonstrated, however, in the elements of Astronomy that when a Comet, or any other star, is placed in the zenith H, the true and apparent place is found at B: for AHB and CHB do not differ. Now the true place of a star is that which a straight line drawn from the center of the Earth through the center of the star defines on the firmament or the ultimate sky: but its apparent place is that which a straight line thrown from our sight through the center of the star shows on the ultimate sky. These two places coincide at the zenith. But from there, as the star descends toward the horizon, the line of true and apparent motion soon separates, with this anomaly, however: the closer the star is to the zenith, the smaller the difference between the true and apparent place becomes, and it is greater the further away it is. For example: if a star is not far from the vertical line: with ALM and CLN drawn, the seen place will soon be at N, and the true at M, of which N is, however, perpetually closer to the horizon by the quantity of the arc MN, which the angle MLN or the vertical CLA determines. But if the star is closer to the horizon, as at I, with lines AIF and CIO drawn: it is demonstrated in the same place that the difference FO becomes much greater than MN was. With FP made equal to MN, OP remains, the excess of FO over MN. This MN or FO, the difference between the true and apparent place, is what is called parallax. If, therefore, the true place of the star M or F is known from elsewhere, and the apparent place N or O becomes known from observation: the distance of the star AL from the center of the Earth can be found by the demonstrations of Ptolemy. But if the true places M and F are not given, nevertheless, from the parallax difference OP, the altitude AL or AI can be computed according to the documents of Regiomontanus. However, the altitude of such a star cannot be so great that the Earth's semidiameter can hardly be compared to it. For if this were the case, no angle...

A geometric diagram shows the Earth (circle A, B, C, D) and the celestial sphere (arc B, F, G). Lines radiate from the center A and the surface point C to points on the celestial sphere (H, L, I, M, N, F, O) to illustrate the concept of parallax.

Demonstration.