Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/375

on upon the Earths motion; for from the Earth in A it shall be seen according to the ray AE, with the elevation of the angle EAC; but from the Earth placed in B, it shall be seen according to the ray BE, with the elevation of the angle EBC, bigger than the other EAC, that being extern, and this intern and opposite in the triangle EAB, the distance therefore of the star E from the Ecliptick, shall appear changed; and likewise its altitude in the Meridian shall become greater in the position B, than in the place A, according as the angle EBC exceeds the angle EAC, which excesse is the quantity of the angle AEB: For in the triangle EAB, the side AB being continued to C, the exteriour angle EBC (as being equal to the two interiour and opposite E and A) exceedeth the said angle A, by the quantity of the angle E. And if we should take another star in the same Meridian, more remote from the Ecliptick, as for instance the star H, the diversity in it shall be greater by being observed from the two stations A and B, according as the angle AHB is greater than the other E; which angle shall encrease continually according as the observed star shall be farther and farther from the Ecliptick, till that at last the greatest mutation will appear in that star that should be placed in the very Pole of the Ecliptick. As for a full understanding thereof we thus demonstrate. Suppose the diameter of the Grand Orb to be AB, whose centre [in the same Figure] is G, and let it be supposed to be continued out as far as the Starry Sphere in the points D and C, and from the centre G let there be erected the Axis of the Ecliptick GF, prolonged till it arrive at the said Sphere, in which a Meridian DFC is supposed to be described, that shall be perpendicular to the Plane of the Ecliptick; and in the arch FC any points H and E, are imagined to be taken, as places of fixed stars: Let the lines FA, FB, AH, HG, HB, AE, GE, BE, be conjoyned. And let the angle of difference, or, if you will, the Parallax of the star placed in the Pole F, be AFB, and let that of the star placed in H, be the angle AHB, and let that of the star in E, be the angle AEB. I say, that the angle of difference of the Polar star F, is the greatest, and that of the rest, those that are nearer to the greatest are bigger than the more remote; that is to say, that the angle F is bigger than the angle H, and this bigger than the angle E. Now about the triangle FAB, let us suppose a circle to be described. And because the angle F is acute, (by reason that its base AB is lesse than the diameter DC, of the semicircle DFC) it shall be placed in the greater portion of the circumscribed circle cut by the base AB. And because the said AB is divided in the midst, and at right angles by FG, the centre of the circumscri-bed