bed circle shall be in the line FG, which let be the point I; and because that of such lines as are drawn from the point G, which is not the centre, unto the circumference of the circumscribed circle, the biggest is that which passeth by the centre, GF shall be bigger than any other that is drawn from the point G, to the circumference of the said circle; and therefore that circumference will cut the line GH (which is equal to the line GF) and cutting GH, it will also cut AH. Let it cut it in L, and conjoyn the line LB. These two angles, therefore, AFB and ALB shall be equal, as being in the same portion of the circle circumscribed. But ALB external, is bigger than the internal H; therefore the angle F is bigger than the angle H. And by the same method we might demonstrate the angle H to be bigger than the angle E, because that of the circle described about the triangle AHB, the centre is in the perpendicular GF, to which the line GH is nearer than the line GE, and therefore the circumference of it cutteth GE, and also AE, whereupon the proposition is manifest. We will conclude from hence, that the difference of appearance, (which with the proper term of art, we might call the Parallax of the fixed stars) is greater, or lesse, according as the Stars observed are more or lesse adjacent to the Pole of the Ecliptick, so that, in conclusion of those Stars that are in the Ecliptick it self, the said diversity is reduced to nothing. In the next place,The Earth approacheth or recedeth from the fixed stars of the Ecliptick, the quantity of the Diameter of the Grand Orb. as to the Earths accession by that motion to, or recession from the Stars, it appeareth to, and recedeth from those that are in the Ecliptick, the quantity of the whole diameter of the grand Orb, as we did see even now, but that accession or recession to, or from the stars about the Pole of the Ecliptick, is almost nothing; and in going to and from others, this difference groweth greater, according as they are neerer to the Ecliptick. We may,The stars nearer to us make greater differences than the more remote. in the third place, know, that the said difference of Aspect groweth greater or lesser, according as the Star observed shall be neerer to us, or farther from us. For if we draw another Meridian, lesse distant from the Earth; as for example, this DFI [in Fig. 7.] a Star placed in F, and seen by the same ray AFE, the Earth being in A, would, in case it should be observed from the Earth in B, appear according to the ray BF, and would make the angle of difference, namely, BFA, bigger than the former AEB, being the exteriour angle of the triangle BFE.
Sagr.With great delight, and also benefit have I heard your discourse;The Epilogue of the Phænomena of the fixed stars caused by the annual motion of the Earth. and that I may be certain, whether I have rightly understood the same, I shall give you the summe of the Conclusions in a few words. As I take it, you have explained to us the different appearances, that by means of the Earths annual mo-tion
