Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

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            <p type="main">
              <s>
                <pb xlink:href="040/01/441.jpg" pagenum="419"/>
              be perpendicular to the ſame D E, by reaſon that the Colure is
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              erect upon the grand Orb; and therefore the ſaid D E,
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              ſhall be the Tangent of the grand Orb in the point A.
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              </s>
              <s>So that in this Poſition the motion of the Centre by the arch
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              A E; that is, of one degree every day differeth very little; yea,
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              is as if it were made by the Tangent D A E. </s>
              <s>And becauſe by
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              means of the diurnal motion the point D, carried about by G,
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              unto E, encreaſeth the motion of the Centre moved almoſt in the
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              ſame line D E, as much as the whole diameter D E amounts
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              unto; and on the other ſide diminiſheth as much, moving about
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              the other ſemicircle E F D. </s>
              <s>The additions and ſubductions
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              in this place therefore, that is in the time of the ſolſtice, ſhall be
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              meaſured by the whole diameter D E.</s>
            </p>
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              <s>Let us in the next place enquire, Whether they be of the ſame
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              bigneſs in the times of the
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              E
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              quinoxes; and tranſporting the
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              Centre of the Earth to the point I, diſtant a Quadrant of a
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              Circle from the point A. </s>
              <s>Let us ſuppoſe the ſaid Equinoctial
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              to be G E F D, its common ſection with the grand Orb D E, the
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              Axis with the ſame inclination C B; but the Tangent of the grand
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              Orb in the point I ſhall be no longer D E, but another which
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              ſhall cut that at right Angles; and let it be this marked H I L,
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              according to which the motion of the Centre I, ſhall make its
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              greſs, proceeding along the circumference of this grand Orb.
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              </s>
              <s>Now in this ſtate the Additions and Subſtractions are no longer
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              meaſured by the diameter D E, as before was done; becauſe that
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              diameter not diſtending it ſelf according to the line of the annual
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              motion H L, rather cutting it at right angles, thoſe terms D E, do
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              neither add nor ſubſtract any thing; but the Additions and
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              Subſtractons are to be taken from that diameter that falleth
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              in the plane that is errect upon the plane of the grand Orb, and
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              that interſects it according to the line H L; which diameter in this
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              caſe ſhall be this G F and the Adjective, if I may ſo ſay, ſhall
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              be that made by the point G, about the ſemicircle G E F, and the
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              Ablative ſhall be the reſt made by the other ſemicircle F D G.
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              </s>
              <s>Now this diameter, as not being in the ſame line H L of the
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              annual motion, but rather cutting it, as we ſee in the point I, the
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              term G being elevated above, and E depreſſed below the plane
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              of the grand Orb, doth not determine the Additions and
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              ſtractions according to its whole length, but the quantity of thoſe
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              firſt ought to be taken from the part of the line H L, that is
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              tercepted between the perpendiculars drawn upon it from the
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              terms G F; namely, theſe two G S, and F V: So that the
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              ſure of the additions is the line S V leſſer then G F, or then D E;
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              which was the meaſure of the additions in the Solſtice A. </s>
              <s>And
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              ſo ſucceſſively, according as the centre of the Earth ſhall be </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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