Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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          <p>
            <s xml:id="echoid-s8344" xml:space="preserve">
              <pb o="114" file="0300" n="300" rhead=""/>
            abſcindens A B F, cuius baſis ſit A E F, & </s>
            <s xml:id="echoid-s8345" xml:space="preserve">Canon rectus A B F. </s>
            <s xml:id="echoid-s8346" xml:space="preserve">Dico
              <lb/>
            hanc ſolidam portionem _MINIMAM_ eſſe earum, quæ à quocunque alio
              <lb/>
            plano per eandem A F ducto ex dato ſolido abſcindi poſſunt.</s>
            <s xml:id="echoid-s8347" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8348" xml:space="preserve">Diuidatur A F bifariam in G, & </s>
            <s xml:id="echoid-s8349" xml:space="preserve">per G in plano per axem A B C de-
              <lb/>
            ſcribatur in prima figura (exhibente Conum) Hyperbole G H I,
              <note symbol="a" position="left" xlink:label="note-0300-01" xlink:href="note-0300-01a" xml:space="preserve">4. ſec.
                <lb/>
              Conic.</note>
            aſymptoti ſint B A, B C; </s>
            <s xml:id="echoid-s8350" xml:space="preserve">in ſecunda verò (quodcunque aliorum ſolidorum
              <lb/>
            repræſentante) deſciibatur coni-ſectio G H I ſimilis, & </s>
            <s xml:id="echoid-s8351" xml:space="preserve">concentrica
              <note symbol="b" position="left" xlink:label="note-0300-02" xlink:href="note-0300-02a" xml:space="preserve">5. 6. 7.
                <lb/>
              primi h.</note>
            ctioni A B C, quæ in vtraque figura omnino continget rectam A F in G,
              <lb/>
            (nam ſi alia eſſet contingens per G ſectionem G H I, ipſa producta ad
              <lb/>
            vtranque partem exteriori ſectioni A B C occurreret, ac bifariam ſecare-
              <lb/>
            tur in G: </s>
            <s xml:id="echoid-s8352" xml:space="preserve">vnde duæ applicate per G in ſectione A B C ſe mutuò
              <note symbol="c" position="left" xlink:label="note-0300-03" xlink:href="note-0300-03a" xml:space="preserve">Coroll.
                <lb/>
              45. h.</note>
            ſecarent, quod eſſet contra 26. </s>
            <s xml:id="echoid-s8353" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s8354" xml:space="preserve">Conic.</s>
            <s xml:id="echoid-s8355" xml:space="preserve">, quæ vnicuique coni-ſectioni
              <lb/>
            inſeruit, licet de ſola Ellipſi, vel Circulo agat, ſed hoc idem, & </s>
            <s xml:id="echoid-s8356" xml:space="preserve">pro angulo
              <lb/>
            ſimul, aliter patet, ex primo Coroll. </s>
            <s xml:id="echoid-s8357" xml:space="preserve">68. </s>
            <s xml:id="echoid-s8358" xml:space="preserve">h.) </s>
            <s xml:id="echoid-s8359" xml:space="preserve">& </s>
            <s xml:id="echoid-s8360" xml:space="preserve">concipiatur circa commu-
              <lb/>
            nem axim B D H ſectio G H I in gyrum conuersá: </s>
            <s xml:id="echoid-s8361" xml:space="preserve">patet hanc deſcribere
              <lb/>
            ſolidum G H I ſimile, & </s>
            <s xml:id="echoid-s8362" xml:space="preserve">concentricum exteriori A B C; </s>
            <s xml:id="echoid-s8363" xml:space="preserve">& </s>
            <s xml:id="echoid-s8364" xml:space="preserve">cum recta A F
              <lb/>
            contingat ſectionem G H I in G, & </s>
            <s xml:id="echoid-s8365" xml:space="preserve">per A F ductum ſit planum A E F ipſi
              <lb/>
            plano per axem G H I perpendiculare, hoc ipſum continget
              <note symbol="d" position="left" xlink:label="note-0300-04" xlink:href="note-0300-04a" xml:space="preserve">55. h.</note>
            ſolidi ſuperficiem in puncto G.</s>
            <s xml:id="echoid-s8366" xml:space="preserve"/>
          </p>
          <figure number="243">
            <image file="0300-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0300-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s8367" xml:space="preserve">Ponatur primò punctum G eſſe extra axis verticem H, & </s>
            <s xml:id="echoid-s8368" xml:space="preserve">per G intelli-
              <lb/>
            gatur duci planum G L I ad axem erectum, quod in ſolido G H I circulum
              <lb/>
            efficiet centrum habentem in axe, vt in D, & </s>
            <s xml:id="echoid-s8369" xml:space="preserve">cuius communis ſectio
              <note symbol="e" position="left" xlink:label="note-0300-05" xlink:href="note-0300-05a" xml:space="preserve">4. primi
                <lb/>
              Conic. &
                <lb/>
              12. Arch.
                <lb/>
              de Co-
                <lb/>
              noid. &c.</note>
            plano per axem erit diameter G D I, cum alio autem plano A E F erit recta
              <lb/>
            E G, quæ cum ſit communis ſectio duorum planorum ad planum A B C
              <lb/>
            erectorum, erit ad idem planum recta, ac ideo cum diametro G D I
              <note symbol="f" position="left" xlink:label="note-0300-06" xlink:href="note-0300-06a" xml:space="preserve">19. vnd.
                <lb/>
              Elem.</note>
            ctum conſtituet angulum E G I, ſiue ipſa E G in puncto tantùm G circu-
              <lb/>
            lum continget.</s>
            <s xml:id="echoid-s8370" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8371" xml:space="preserve">Iam intelligatur per A F aliud planum duci ad planum per axem A B C
              <lb/>
            non erectum (ſed tale quod de exteriori ſolido aliam terminatam ſectionem
              <lb/>
            abſcindat) cuius communis ſectio cum circuli plano diuerſa erit à linea G E
              <lb/>
            (planum enim nunc ductum conuenit cum plano A E F per rectam tantùm
              <lb/>
            A F.) </s>
            <s xml:id="echoid-s8372" xml:space="preserve">Sit ipſa G L. </s>
            <s xml:id="echoid-s8373" xml:space="preserve">Et quoniam G E rectos facit angulos cum G I, ipſa.</s>
            <s xml:id="echoid-s8374" xml:space="preserve"/>
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