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

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            <p type="main">
              <s>
                <pb xlink:href="040/01/715.jpg" pagenum="23"/>
              meter C F, perpendicular to one of the two Lines A B, or D E
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              and immoveable; we ſuppoſe all this Figure to turn round about
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              that Perpendicular: It is manifeſt, that there will be deſcribed by
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              the Parallelogram A D E B, a Cylinder; by the Semi-circle A F B,
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              an Hemi-Sphære; and by the Triangle C D E a Cone. </s>
              <s>This pre­
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              ſuppoſed, I would have you imagine the Hemiſphære to be taken
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              away, leaving behind the Cone, and that which ſhall remain of
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              the Cylinder; which for the Figure, which it ſhall retain like to a
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              Diſh, we will hereafter call a Diſh: touching which, and the
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              Cone, we will ſirſt demonſtrate that they are equal; and next
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              a Plain being drawn parallel to the Circle, which is the foot or
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              Baſe of the Diſh, whoſe Diameter is the Line D E, and its Center
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              F; we will demonſtrate, that ſhould the ſaid Plain paſs,
                <emph type="italics"/>
              v. </s>
              <s>gr.
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              by
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              the Line G H, cutting the Diſh in the points G I, and O N; and
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              the Cone in the points H and L; it would cut the part of the
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              Cone C H L, equal alwaies to the part of the Diſh, whoſe Profile
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              is repreſented to us by the Triangles G A I, and B O N: and more­
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              over we will prove the Baſe alſo of the ſame Cone, (that is the
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              Circle, whoſe Diameter is H L) to be equal to that circular Su­
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              perficies, which is Baſe of the part of the Diſh; which is, as we
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              may ſay, a Rimme as broad as G I; (note here by the way what
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              Mathematical Definitions are: they be an impoſition of names, or,
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              we may ſay, abreviations of ſpeech, ordain'd and introduced to
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              prevent the trouble and pains, which you and I meet with, at pre­
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              ſent, in that we have not agreed together to call
                <emph type="italics"/>
              v. </s>
              <s>gr.
                <emph.end type="italics"/>
              this Super­
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              ficies a circular Rimme, and that very ſharp Solid of the Diſh a
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              round Razor:) now howſoever you pleaſe to call them, it ſufficeth
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              you to know, that the Plain produced to any diſtance at pleaſure,
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              ſo that it be parallel to the Baſe,
                <emph type="italics"/>
              viz.
                <emph.end type="italics"/>
              to the Circle whoſe Diame­
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              ter D E cuts alwaies the two Solids, namely, the part of the Cone
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              C H L, and the upper part of the Diſh equal to one another: and
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              likewiſe the two Superficies, Baſis of the ſaid Solids,
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              viz.
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              the ſaid
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              Rimme, and the Circle H L, equal alſo to one another. </s>
              <s>Whence
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              followeth the forementioned Wonder; namely, that if we ſhould
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              ſuppoſe the cutting-plain to be
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              ſucceſſively raiſed towards the
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                <figure id="id.040.01.715.1.jpg" xlink:href="040/01/715/1.jpg" number="57"/>
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              Line A B, the parts of the Solid
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              cut are alwaies equall, as alſo the
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              Superficies, that are their Baſes,
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              are evermore equal; and, in
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              fine, raiſing the ſaid Plain higher
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              and higher, the two Solids (ever
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              equal) as alſo their Baſes, (Su­
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              perficies ever equal) ſhall one couple of them terminate in a Cir­
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              cumference of a Circle, and the other couple in one ſole point; </s>
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