Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/448

 be perpendicular to the same DE, by reason that the Colure is erect upon the grand Orb; and therefore the said DE, shall be the Tangent of the grand Orb in the point A. So that in this Position the motion of the Centre by the arch AE; that is, of one degree every day differeth very little; yea, is as if it were made by the Tangent DAE. And because by means of the diurnal motion the point D, carried about by G, unto E, encreaseth the motion of the Centre moved almost in the same line DE, as much as the whole diameter DE amounts unto; and on the other side diminisheth as much, moving about the other semicircle EFD. The additions and subductions in this place therefore, that is in the time of the solstice, shall be measured by the whole diameter DE.

Let us in the next place enquire, Whether they be of the same bigness in the times of the Equinoxes; and transporting the Centre of the Earth to the point I, distant a Quadrant of a Circle from the point A. Let us suppose the said Equinoctial to be GEFD, its common section with the grand Orb DE, the Axis with the same inclination CB; but the Tangent of the grand Orb in the point I shall be no longer DE, but another which shall cut that at right Angles; and let it be this marked HIL, according to which the motion of the Centre I, shall make its progress, proceeding along the circumference of this grand Orb. Now in this state the Additions and Substractions are no longer measured by the diameter DE, as before was done; because that diameter not distending it self according to the line of the annual motion HL, rather cutting it at right angles, those terms DE, do neither add nor substract any thing; but the Additions and Substractons are to be taken from that diameter that falleth in the plane that is errect upon the plane of the grand Orb, and that intersects it according to the line HL; which diameter in this case shall be this GF and the Adjective, if I may so say, shall be that made by the point G, about the semicircle GEF, and the Ablative shall be the rest made by the other semicircle FDG. Now this diameter, as not being in the same line HL of the annual motion, but rather cutting it, as we see in the point I, the term G being elevated above, and E depressed below the plane of the grand Orb, doth not determine the Additions and Substractions according to its whole length, but the quantity of those first ought to be taken from the part of the line HL, that is intercepted between the perpendiculars drawn upon it from the terms GF; namely, these two GS, and FV: So that the measure of the additions is the line SV lesser then GF, or then DE; which was the measure of the additions in the Solstice A. And so successively, according as the centre of the Earth shall be con-