Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/344

[as in Fig. 5.] and the Axis, as before AC, by which the plane of our Meridian would passe, in which plane should also be the Axis of the Suns revolution, with its Poles, one towards us, that is, in the apparent Hemisphere, which Pole we will represent by the point E, and the other shall fall in the occult Hemisphere, and I mark it I. Inclining therefore the Axis EI, with the superiour part E, towards us, the great circle described by the Suns conversion, shall be this BFDG, whose half by us seen, namely BFD, shall no longer seem unto us a right line, by reason the Poles EI are not in the circumference ABCD, but shall appear incurvated, and with its convexity towards the inferiour part C. And it is manifest, that the same will appear in all the lesser circles parallel to the same BFD. It is to be understood also, that when the Earth shall be diametrically opposite to this state, so that it seeth the other Hemisphere of the Sun, which now is hid, it shall of the said great circle behold the part DGB incurved, with its convexity towards the superiour part A; and the courses of the spots in these constitutions shall be first, by the arch BFD, and afterwards by the other DGB, and the first apparitions and ultimate occultations made about the points B and D, shall be equilibrated, and not those that are more or lesse elevated than these. But if we constitute the Earth in such a place of the Ecliptick, that neither the boundary ABCD, nor the Meridian AC, passeth by the Poles of the Axis EI, as I will shew you anon, drawing this other Figure [viz. Fig. 6.] wherein the apparent or visible Pole E falleth between the arch of the terminator AB, and the section of the Meridian AC; the diameter of the great circle shall be FOG, and the apparent semicircle FNG, and the occult semicircle GSF, the one incurvated with its convexity N towards the inferiour part, and the other also bending with its convexity S towards the upper part of the Sun. The ingressions and exitions of the spots, that is, the termes F and G shall not be librated, as the two others B and D; but F shall be lower, and G higher: but yet with lesser difference than in the first Figure. The arch also FNG shall be incurvated, but not so much as the precedent BFD; so that in this position the passages or motions of the spots shall be ascendent from the left side F, towards the right G, and shall be made by curved lines. And imagining the Earth to be constituted in the position diametrically opposite; so that the Hemisphere of the Sun, which was before the occult, may be the apparent, and terminated by the same boundary ABCD, it will be manifestly discerned, that the course of the spots shall be by the arch GSF, beginning from the upper point G, which shall then be likewise from the left hand of the beholder, and going to determine, des-cending