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

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          <pb o="95" file="0281" n="281" rhead=""/>
          <p>
            <s xml:id="echoid-s7849" xml:space="preserve">Iam ſi per verticem B ducatur in plano portionis E B G recta B L, ipſam
              <lb/>
              <note symbol="a" position="right" xlink:label="note-0281-01" xlink:href="note-0281-01a" xml:space="preserve">32. pri-
                <lb/>
              mi conic.</note>
            portionem contingens, hæc baſi E G æquidiſtabit: </s>
            <s xml:id="echoid-s7850" xml:space="preserve">& </s>
            <s xml:id="echoid-s7851" xml:space="preserve">ſi per B L concipia- tur planum duci, quod plano per axem E B G ſit erectum, id ſolidæ por-
              <lb/>
              <note symbol="b" position="right" xlink:label="note-0281-02" xlink:href="note-0281-02a" xml:space="preserve">55. h.</note>
            tionis ſuperficiem continget in B, atque baſi E H G I erit parallelum
              <note symbol="c" position="right" xlink:label="note-0281-03" xlink:href="note-0281-03a" xml:space="preserve">per Sch.
                <lb/>
              Clauijpoſt
                <lb/>
              18. vndec.
                <lb/>
              elem.</note>
            vtrunque planorum ſit eidem E B G rectum, & </s>
            <s xml:id="echoid-s7852" xml:space="preserve">communes ſectiones B L,
              <lb/>
            E G ſint parallelæ. </s>
            <s xml:id="echoid-s7853" xml:space="preserve">Quod ſecundò, &</s>
            <s xml:id="echoid-s7854" xml:space="preserve">c.</s>
            <s xml:id="echoid-s7855" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7856" xml:space="preserve">Siverò planum ſecans E H G I rectum non fuerit ad axem B D; </s>
            <s xml:id="echoid-s7857" xml:space="preserve">(& </s>
            <s xml:id="echoid-s7858" xml:space="preserve">tunc
              <lb/>
            ſectio erit Ellipſis) ſecetur denuò datum ſolidum quocunque alio plano
              <note symbol="d" position="right" xlink:label="note-0281-04" xlink:href="note-0281-04a" xml:space="preserve">13. 14.
                <lb/>
              15. Arch.
                <lb/>
              de Conoi.
                <lb/>
              &c.</note>
            H C I ad axem recto: </s>
            <s xml:id="echoid-s7859" xml:space="preserve">(quod tamen non tranſeat per interſectionem axis B
              <lb/>
            D cum plano E H G I, ſi hoc axem ſecuerit intra ſolidum) id in ſolido ſe-
              <lb/>
            ctionem faciet circulum, centrum habentem in axe B D, vti in D,
              <note symbol="e" position="right" xlink:label="note-0281-05" xlink:href="note-0281-05a" xml:space="preserve">12. Arch.
                <lb/>
              ib. à Co-
                <lb/>
              mãd. reſt.</note>
            autem ſecabit baſim E H G I per communem rectam H I tùm in Ellipſi, tùm
              <lb/>
            in circulo applicatam, cui ex D, circuli centro, ducta perpendiculari D M;
              <lb/>
            </s>
            <s xml:id="echoid-s7860" xml:space="preserve">per axem B D, ac rectam D M agatur planum in ſolido efficiens genitricem
              <lb/>
            ſectionem E A B G C, cuius communis ſectio cum circulo erit diameter A
              <lb/>
            C, & </s>
            <s xml:id="echoid-s7861" xml:space="preserve">cum Ellipſi erit recta E G.</s>
            <s xml:id="echoid-s7862" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7863" xml:space="preserve">Iam priùs oſtendam ſectio-
              <lb/>
              <figure xlink:label="fig-0281-01" xlink:href="fig-0281-01a" number="231">
                <image file="0281-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0281-01"/>
              </figure>
            nem hanc per B D axem du-
              <lb/>
            ctam ad ſecans planum E H
              <lb/>
            G I, ſiue ad baſim ſolidę por-
              <lb/>
            tionis E F G rectam eſſe.
              <lb/>
            </s>
            <s xml:id="echoid-s7864" xml:space="preserve">Quoniam cum planum circu-
              <lb/>
            li E H C I rectum ſit ad pla-
              <lb/>
            nũ per axem E A B C, cumq; </s>
            <s xml:id="echoid-s7865" xml:space="preserve">
              <lb/>
            linea I M in circulo perpen-
              <lb/>
            dicularis ſit ad A C horum
              <lb/>
            planorum communem ſectio-
              <lb/>
            nem, erit eadem linea I M
              <lb/>
            recta ad planum per
              <note symbol="f" position="right" xlink:label="note-0281-06" xlink:href="note-0281-06a" xml:space="preserve">4. def.
                <lb/>
              vnd. Ele.</note>
            E A B C: </s>
            <s xml:id="echoid-s7866" xml:space="preserve">quare omnia plana, quæ per ipſam ducentur ad idem planum E A
              <lb/>
            B C recta erunt, ſed E H G I baſis ſolidæ portionis tranſit per I M,
              <note symbol="g" position="right" xlink:label="note-0281-07" xlink:href="note-0281-07a" xml:space="preserve">18. vnd.
                <lb/>
              Elem.</note>
            baſis E H G I, ſiue planum ſecans rectum erit ad planum per axem E A B C,
              <lb/>
            ſiue id rectum ad planum ſecans, hoc eſt ad baſim ſolidæ portionis. </s>
            <s xml:id="echoid-s7867" xml:space="preserve">Quod
              <lb/>
            primò, &</s>
            <s xml:id="echoid-s7868" xml:space="preserve">c.</s>
            <s xml:id="echoid-s7869" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7870" xml:space="preserve">Cum ergo E G ſit communis ſectio planorum, eius ſcilicet, quod ſolidũ
              <lb/>
            ſecat, & </s>
            <s xml:id="echoid-s7871" xml:space="preserve">cius, quod per axem ducitur erectum ſuper planum ſecans, ipſa E
              <lb/>
            G erit axis Ellipſis E H G I, qua bifariam ſecta in N, erit N Ellipſis
              <note symbol="h" position="right" xlink:label="note-0281-08" xlink:href="note-0281-08a" xml:space="preserve">13. 14.
                <lb/>
              15. Arch.
                <lb/>
              de Conoi.
                <lb/>
              &c.</note>
            trum, ex quo, in plana portione E F G ſectionis per axem à recta E G ab-
              <lb/>
            ſciſſæ, & </s>
            <s xml:id="echoid-s7872" xml:space="preserve">ſuper baſim ſolidæ portionis erectæ, ducta diametro N F, & </s>
            <s xml:id="echoid-s7873" xml:space="preserve">per F
              <lb/>
            ſectionem contingente F O, per ipſam F O agatur planum, quod ad
              <note symbol="i" position="right" xlink:label="note-0281-09" xlink:href="note-0281-09a" xml:space="preserve">2. & 4.
                <lb/>
              pr. h.</note>
            planum per axem E B G rectum ſit, id ſolidæ portionis E F G ſuperficiem
              <lb/>
              <note symbol="l" position="right" xlink:label="note-0281-10" xlink:href="note-0281-10a" xml:space="preserve">55. h.</note>
            continget in F, & </s>
            <s xml:id="echoid-s7874" xml:space="preserve">baſi E H G I æquidiſtabit. </s>
            <s xml:id="echoid-s7875" xml:space="preserve"> Quod ſecundò, &</s>
            <s xml:id="echoid-s7876" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7877" xml:space="preserve">
              <note symbol="m" position="right" xlink:label="note-0281-11" xlink:href="note-0281-11a" xml:space="preserve">Schol.
                <lb/>
              Clauijpoſt
                <lb/>
              18. vndec.
                <lb/>
              Elem.</note>
            fuerit ergo Conoides quodcunque, vel Sphæra, &</s>
            <s xml:id="echoid-s7878" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7879" xml:space="preserve">poſſibile eſt, &</s>
            <s xml:id="echoid-s7880" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7881" xml:space="preserve">Quod
              <lb/>
            erat faciendum, ac demondrandum.</s>
            <s xml:id="echoid-s7882" xml:space="preserve"/>
          </p>
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