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

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            <p type="main">
              <s>
                <pb xlink:href="040/01/203.jpg" pagenum="185"/>
              ſame in concrete, as they are imagined to be in abſtract?</s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>This I do affirm.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>Then when ever in concrete you do apply a material Sphere </s>
            </p>
            <p type="main">
              <s>
                <arrow.to.target n="marg375"/>
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              to a material plane, youapply an imperfect Sphere to an imperfect
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              plane, & theſe you ſay do not touch only in one point. </s>
              <s>But I muſt
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              tell you, that even in abſtract an immaterial Sphere, that is, not a
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              perfect Sphere, may touch an immaterial plane, that is, not a
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              fect plane, not in one point, but with part of its ſuperficies, ſo that
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              hitherto that which falleth out in concrete, doth in like manner
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              hold true in abſtract. </s>
              <s>And it would be a new thing that the
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              putations and rates made in abſtract numbers, ſhould not
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              wards anſwer to the Coines of Gold and Silver, and to the
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              chandizes in concrete. </s>
              <s>But do you know
                <emph type="italics"/>
              Simplicius,
                <emph.end type="italics"/>
              how this
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              commeth to paſſe? </s>
              <s>Like as to make that the computations agree
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              with the Sugars, the Silks, the Wools, it is neceſſary that the
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              accomptant reckon his tares of cheſts, bags, and ſuch other things:
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              So when the
                <emph type="italics"/>
              Geometricall Philoſopher
                <emph.end type="italics"/>
              would obſerve in concrete
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              the effects demonſtrated in abſtract, he muſt defalke the
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              ments of the matter, and if he know how to do that, I do aſſure
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              you, the things ſhall jump no leſſe exactly, than
                <emph type="italics"/>
              Arithmstical
                <emph.end type="italics"/>
                <lb/>
              computations. </s>
              <s>The errours therefore lyeth neither in abſtract, nor
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              in concrete, nor in
                <emph type="italics"/>
              Geometry,
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              nor in
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              Phyſicks,
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              but in the
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              tor, that knoweth not how to adjuſt his accompts. </s>
              <s>Therefore if
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              you had a perfect Sphere and plane, though they were material,
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              you need not doubt but that they would touch onely in one point.
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              </s>
              <s>And if ſuch a Sphere was and is impoſſible to be procured, it was
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              much beſides the purpoſe to ſay,
                <emph type="italics"/>
              Quod Sphæra ænea non tangit in
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              puncto.
                <emph.end type="italics"/>
              Furthermore, if I grant you
                <emph type="italics"/>
              Simplicius,
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              that in matter a
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              figure cannot be procured that is perfectly ſpherical, or perfectly
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              level: Do you think there may be had two materiall bodies,
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              whoſe ſuperficies in ſome part, and in ſome ſort are incurvated as
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              irregularly as can be deſired?</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg375"/>
                <emph type="italics"/>
              Things are
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              actly the ſame in
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              abſtract as in
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              crete.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>Of theſe I believe that there is no want.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>If ſuch there be, then they alſo will touch in one ſole
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                <arrow.to.target n="marg376"/>
                <lb/>
              point; for this contact in but one point alone is not the ſole and
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              peculiar priviledge of the perfect Sphere and perfect plane. </s>
              <s>Nay, he
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              that ſhould proſecute this point with more ſubtil contemplations
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              would finde that it is much harder to procure two bodies that
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                <arrow.to.target n="marg377"/>
                <lb/>
              touch with part of their ſnperſicies, than with one point onely.
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              </s>
              <s>For if two ſuperficies be required to combine well together, it is
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              neceſſary either, that they be both exactly plane, or that if one be
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              convex, the other be concave; but in ſuch a manner concave,
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              that the concavity do exactly anſwer to the convexity of the other:
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              the which conditions are much harder to be found, in regard of
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              their too narrow determination, than thoſe others, which in their
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              caſuall latitude are infinite.</s>
            </p>
          </chap>
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