Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/343

circle, either bigger or lesser, according as it is more or lesse remote from the said Poles, let us take the point F, equally distant from them, and draw the diameter FOG, which shall be perpendicular to the Axis EI, and shall be the diameter of the grand circle described about the Poles EI. Supposing not that the Earth, and we with her be in such a place of the Ecliptick, that the Hemisphere of the Sun to us apparent is determin'd or bounded by the circle ABCD, which passing (as it alwayes doth) by the Poles AC, passeth also by EI. It is manifest, that the grand circle, whose diameter is FG, shall be erect to the circle ABCD, to which the ray that from our eye falleth upon the centre O, is perpendicular; so that the said ray falleth upon the plane of the circle, whose diameter is FG, and therefore its circumference will appear to us a right line, and the self same with FG, whereupon if there should be in the point F, a spot, it comming afterwards to be carried about by the Solar conversion, would, upon the surface of the Sun, trace out the circumference of that circle, which seems to us a right line. Its course or passage will therefore seem straight. And straight also will the motion of the other spots appear, which in the said revolution shall describe lesser circles, as being all parallel to the greater, and to our eye placed at an immense distance from them. Now, if you do but consider, how that after the Earth shall in six moneths have run thorow half the grand Orb, and shall be situate opposite to that Hemisphere of the Sun, which is now occult unto us, so as that the boundary of the part that then shall be seen, may be the self same ABCD, which also shall passe by the Poles EI; you shall understand that the same will evene in the courses of the spots, as before, to wit, that all will appear to be made by right lines. But because that that accident takes not place, save onely when the teminator or boundary passeth by the Poles EI, and the said terminator from moment to moment, by meanes of the Earths annual motion, continually altereth, therefore its passage by the fixed Poles EI, shall be momentary, and consequently momentary shall be the time, in which the motions of those spots shall appear straight. From what hath been hitherto spoken one may comprehend also how that the apparition and beginning of the motion of the spots from the part F, proceeding towards G, their passages or courses are from the left hand, ascending towards the right; but the Earth being placed in the part diametrically opposite the appearance of the spots about G, shall still be to the left hand of the beholder, but the passage shall be descending towards the right hand F. Let us now describe the Earth to be situate one fourth part farther distant from its present state, and let us draw, as in the other figure, the terminator ABCD,[as