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

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            <s xml:id="echoid-s7818" xml:space="preserve">
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            vtcunque eleuatum, concipiaturque Acu-
              <lb/>
              <figure xlink:label="fig-0280-01" xlink:href="fig-0280-01a" number="230">
                <image file="0280-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0280-01"/>
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            minatum A B C moueri motu ſibi ipſi pa-
              <lb/>
            rallelo, ſed ita vt recta B D æquidiſtanter
              <lb/>
            incedat ſuper parallelogrammum B E, do-
              <lb/>
            nec congruat cum oppoſito latere E F.
              <lb/>
            </s>
            <s xml:id="echoid-s7819" xml:space="preserve">Huiuſmodi ſolidum occluſum à parallelis,
              <lb/>
            & </s>
            <s xml:id="echoid-s7820" xml:space="preserve">congruentibus Acuminatis A B C, G F
              <lb/>
            H, atque à ſuperficie, quæ à perimetro A
              <lb/>
            B C A in ſua latione deſcribitur, vocetur
              <lb/>
            CYLINDRICVS, Acuminatum verò A B C eius BASIS, & </s>
            <s xml:id="echoid-s7821" xml:space="preserve">parallelo-
              <lb/>
            grammum B E CANON DIAMETRALIS prædicti Cylindrici, cuius
              <lb/>
            altitudo metietur per rectam ad vtrunque oppoſitorum planorum perpen-
              <lb/>
            dicularem.</s>
            <s xml:id="echoid-s7822" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7823" xml:space="preserve">Itaque CYLINDRICVS dicetur omne ſolidum circa parallelogrãmum
              <lb/>
            quodcunque deſcriptum, & </s>
            <s xml:id="echoid-s7824" xml:space="preserve">cuius omnia plana baſi ſolidi æquidiſtantia, ac
              <lb/>
            per applicatas in parallelogrammo ducta, ſint plana Acuminata, eidem
              <lb/>
            baſi, ac inter ſe æqualia, & </s>
            <s xml:id="echoid-s7825" xml:space="preserve">ſimilia, & </s>
            <s xml:id="echoid-s7826" xml:space="preserve">ſimiliter poſita, & </s>
            <s xml:id="echoid-s7827" xml:space="preserve">quorum homologę
              <lb/>
            diametri ſint ipſæ applicatæ in prædicto parallelogrammo; </s>
            <s xml:id="echoid-s7828" xml:space="preserve">quod CANON
              <lb/>
            DIAMETRALIS Cylindrici vocabitur.</s>
            <s xml:id="echoid-s7829" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7830" xml:space="preserve">Omittimus vniuerſaliores Solidorum Acuminatorũ, ac Cylindricorum
              <lb/>
            definitiones, cum hoc loco de ijs ſermo minimè habendus ſit.</s>
            <s xml:id="echoid-s7831" xml:space="preserve"/>
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        <div xml:id="echoid-div807" type="section" level="1" n="319">
          <head xml:id="echoid-head328" xml:space="preserve">PROBL. XIV. PROP. LXIX.</head>
          <p>
            <s xml:id="echoid-s7832" xml:space="preserve">Si Conoides quodcunque, vel Sphæra, aut Sphæroides ob-
              <lb/>
            longum, vel prolatum plano ſecetur ex dato ſolido portionem
              <lb/>
            abſcindent: </s>
            <s xml:id="echoid-s7833" xml:space="preserve">poſſibile eſt per axem ſolidi, planum ducere, quod
              <lb/>
            ad baſim abſciſſæ portionis ſit erectum. </s>
            <s xml:id="echoid-s7834" xml:space="preserve">Item.</s>
            <s xml:id="echoid-s7835" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7836" xml:space="preserve">Poſſibile eſt baſi portionis aliud planum æquidiſtans ducere,
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            quod conuexam ſolidæ portionis ſnperficiem contingat.</s>
            <s xml:id="echoid-s7837" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7838" xml:space="preserve">ESto quodcunque ex prædictis ſolidis A B C, cuius axis reuolutionis ſit
              <lb/>
            B D, atque ex eo per planum E H G I ſit abſciſſa portio ſolida E F G,
              <lb/>
            cuius baſis E H G I (quæ, vel erit Ellipſis, vel circulus.) </s>
            <s xml:id="echoid-s7839" xml:space="preserve">Dico
              <note symbol="a" position="left" xlink:label="note-0280-01" xlink:href="note-0280-01a" xml:space="preserve">ex 13. 14
                <lb/>
              15. Arch.
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              de Conoi.
                <lb/>
              &c.</note>
            eſſe baſi E H G I planum ducere per ſolidi axem B D, quod ad baſim E H
              <lb/>
            G I rectum ſit. </s>
            <s xml:id="echoid-s7840" xml:space="preserve">Præterea poſſibile eſſe eidem baſi aliud planum æquidiſtans
              <lb/>
            ducere, quod ſolidæ portionis ſuperficiem contingat.</s>
            <s xml:id="echoid-s7841" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7842" xml:space="preserve">Si enim planum ſecans E I G fuerit ad axem B D erectum, hunc ſecans
              <lb/>
            in K, ſectio circulus erit, cuius centrum K; </s>
            <s xml:id="echoid-s7843" xml:space="preserve">& </s>
            <s xml:id="echoid-s7844" xml:space="preserve">ſi per axim B K
              <note symbol="b" position="left" xlink:label="note-0280-02" xlink:href="note-0280-02a" xml:space="preserve">12. Ar-
                <lb/>
              chim. ib.
                <lb/>
              à Comãd.
                <lb/>
              reſtit.</note>
            quodcunque planum E B G baſim portionis E H G I ſecans per rectam E
              <lb/>
            G, ſectionis portio plana E B G erit ea, quæ ſolidum genuit, cuius
              <note symbol="c" position="left" xlink:label="note-0280-03" xlink:href="note-0280-03a" xml:space="preserve">ibidem.</note>
            eadem E G, axis verò ipſe B K, & </s>
            <s xml:id="echoid-s7845" xml:space="preserve">ad baſim E H G I recta erit. </s>
            <s xml:id="echoid-s7846" xml:space="preserve">
              <note symbol="d" position="left" xlink:label="note-0280-04" xlink:href="note-0280-04a" xml:space="preserve">18. vnd.
                <lb/>
              Elem.</note>
            primò, &</s>
            <s xml:id="echoid-s7847" xml:space="preserve">c.</s>
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