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

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            <s xml:id="echoid-s7782" xml:space="preserve">
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            diſpoſitum, ſintque omnia plana G M H, I N L, &</s>
            <s xml:id="echoid-s7783" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7784" xml:space="preserve">quæ baſi A E C F
              <lb/>
            æquidiſtanter ducuntur per Acuminati A B C applicatas G H, I L, &</s>
            <s xml:id="echoid-s7785" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s7786" xml:space="preserve">ipſi baſi, ac inter ſe, ſimilia Acuminata, & </s>
            <s xml:id="echoid-s7787" xml:space="preserve">ſimiliter poſita, atque ipſæ
              <lb/>
            applicatæ G H, I L ſint eorundem Acuminatorum homologæ diametri: </s>
            <s xml:id="echoid-s7788" xml:space="preserve">
              <lb/>
            huiuſmodi figura SOLIDVM REGVLARE ACVMINATVM vocetur,
              <lb/>
            vel tantùm ACVMINATVM SOLIDVM; </s>
            <s xml:id="echoid-s7789" xml:space="preserve">A E C F verò BASIS ſoli-
              <lb/>
            di Acuminati; </s>
            <s xml:id="echoid-s7790" xml:space="preserve">ſed portionem A B C Acuminati plani intra Acuminatum
              <lb/>
            ſolidum interceptam (eò quod ipſa ſit tanquam Regula, vel Modulus,
              <lb/>
            aut Canon homologarum diametrorum ſimilium planorum ęquidiſtantium,
              <lb/>
            ac ſolidum procreantium) nuncupare liceat CANONEM ſolidi Acumina-
              <lb/>
            ti, qui ſi ad planum ba
              <unsure/>
            ſis A E C F rectus fuerit, dicatur CANON RECTVS
              <lb/>
            ſolidi Acuminati, & </s>
            <s xml:id="echoid-s7791" xml:space="preserve">B D diameter Canonis, nuncupetur quoque AXIS
              <lb/>
            ſolidi, & </s>
            <s xml:id="echoid-s7792" xml:space="preserve">eius VERTEX punctum B, in quod abit ſolidum, atque eiuſdem
              <lb/>
            ſolidi ALTITVDO dicatur recta B O, quæ à vertice B ſuper baſim A E C
              <lb/>
            F recta ducitur. </s>
            <s xml:id="echoid-s7793" xml:space="preserve">Plana verò A C, G H, I L, &</s>
            <s xml:id="echoid-s7794" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7795" xml:space="preserve">dicantur PLANA OR-
              <lb/>
            DINATIM DVCTA ad axim ſolidi Acuminati.</s>
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        <div xml:id="echoid-div803" type="section" level="1" n="317">
          <head xml:id="echoid-head326" xml:space="preserve">III.</head>
          <p>
            <s xml:id="echoid-s7797" xml:space="preserve">SOLIDA ACVMINATA PROPORTIONALIA dicantur illa, quo-
              <lb/>
            rum omnia plana ordinatim applicata per puncta, eorum axes proportio-
              <lb/>
            naliter diuidentia, ſint quoque inter ſe, & </s>
            <s xml:id="echoid-s7798" xml:space="preserve">baſibus proportionalia.</s>
            <s xml:id="echoid-s7799" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7800" xml:space="preserve">Videlicet ſi duo ſolida Acumi-
              <lb/>
              <figure xlink:label="fig-0279-01" xlink:href="fig-0279-01a" number="229">
                <image file="0279-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0279-01"/>
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            nata A B C, D E F, quorum baſes
              <lb/>
            ſint A G C I, L F H D axes verò
              <lb/>
            ſint B K, E O proportionaliter ſe-
              <lb/>
            cti in M, P; </s>
            <s xml:id="echoid-s7801" xml:space="preserve">& </s>
            <s xml:id="echoid-s7802" xml:space="preserve">in N, Q; </s>
            <s xml:id="echoid-s7803" xml:space="preserve">ita vt K
              <lb/>
            M, ad M B ſit vt O P, ad P E; </s>
            <s xml:id="echoid-s7804" xml:space="preserve">& </s>
            <s xml:id="echoid-s7805" xml:space="preserve">
              <lb/>
            K N ad N B, vt O Q ad Q E, &</s>
            <s xml:id="echoid-s7806" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s7807" xml:space="preserve">ſitque baſis A G C ad baſim L F H,
              <lb/>
            vt planum ordinatim applicatum
              <lb/>
            per M ad applicatum per P, & </s>
            <s xml:id="echoid-s7808" xml:space="preserve">vt
              <lb/>
            applicatum per N ad applicatum
              <lb/>
            per Q, &</s>
            <s xml:id="echoid-s7809" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7810" xml:space="preserve">talia ſolida, dicentur
              <lb/>
            SOLIDA ACVMINATA PROPORTIONALIA.</s>
            <s xml:id="echoid-s7811" xml:space="preserve"/>
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        <div xml:id="echoid-div805" type="section" level="1" n="318">
          <head xml:id="echoid-head327" xml:space="preserve">IIII.</head>
          <p>
            <s xml:id="echoid-s7812" xml:space="preserve">Si ſuper diametrum Acuminati plani deſcriptum ſit parallelogrammum
              <lb/>
            quodlibet ſuper ipſum planum quomodocunque eleuatum, idem que Acu-
              <lb/>
            minatum concipiatur ſibi ipſi æquidiſtanter moueri, ita vt eius diameter ſuo
              <lb/>
            motu parallelo prædictum parallelogrammum deſcribat: </s>
            <s xml:id="echoid-s7813" xml:space="preserve">ſolidum occluſum
              <lb/>
            à duobus oppoſitis Acuminatis congruentibus, ac parallelis, atque à ſuper-
              <lb/>
            ficie, quæ à perimetro figuræ motæ deſcribitur CYLINDRICVS vocetur.
              <lb/>
            </s>
            <s xml:id="echoid-s7814" xml:space="preserve">Acuminatum verò ſolidum procreans, dicatur BASIS, & </s>
            <s xml:id="echoid-s7815" xml:space="preserve">parallelogram-
              <lb/>
            mum, per quod fit æquidiſtans latio Acuminati plani Cylindricum pro-
              <lb/>
            creantis, CANON DIAMETRALIS nuncupetur.</s>
            <s xml:id="echoid-s7816" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7817" xml:space="preserve">Nimirum, ſit Acuminatum planum A B C, cuius diameter B D, cui in-
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            ſiſtat parallelogrammum quodcumq; </s>
            <s xml:id="echoid-s7818" xml:space="preserve">B D E F ſuper planum figuræ A B </s>
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