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

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          <head xml:id="echoid-head324" xml:space="preserve">DEFINITIONES.
            <lb/>
          I.</head>
          <p>
            <s xml:id="echoid-s7764" xml:space="preserve">PLANA ACVMINATA SIMILIA vocentur illa, quæ inter ſe ſint
              <lb/>
            proportionalia, & </s>
            <s xml:id="echoid-s7765" xml:space="preserve">quorum diametri ſuper baſes ſint æqualiter inclinatæ, ac
              <lb/>
            ijſdem baſibus proportionales.</s>
            <s xml:id="echoid-s7766" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7767" xml:space="preserve">Hoc eſt ſi ſint duo quælibet plana Acuminata proportionalia A B C, D
              <lb/>
            E F, quorum diametri B G, E H cum baſibus A C, D F æquales angulos
              <lb/>
            alterum alteri conſtituant, nempe A G B
              <lb/>
            ipſi D H E, & </s>
            <s xml:id="echoid-s7768" xml:space="preserve">qui ei eſt deinceps C G B
              <lb/>
              <figure xlink:label="fig-0278-01" xlink:href="fig-0278-01a" number="227">
                <image file="0278-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0278-01"/>
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            reliquo F H E ſit æqualis, ſitque diame-
              <lb/>
            ter B G ad baſim A C, vt diameter E H
              <lb/>
            ad baſim D F; </s>
            <s xml:id="echoid-s7769" xml:space="preserve">huiuſmodi plana inter ſe
              <lb/>
            vocentur SIMILIA ACVMINATA.
              <lb/>
            </s>
            <s xml:id="echoid-s7770" xml:space="preserve">Vnde, & </s>
            <s xml:id="echoid-s7771" xml:space="preserve">duæ ſimiles Ellipſes vocari pote-
              <lb/>
            runt ſimilia Acuminata, cum vtraque ex
              <lb/>
            duobus proportionalibus Acuminatis con-
              <lb/>
            ſtet, ſiue ex dua
              <unsure/>
            bus ſemi-Ellipſibus, per diametros æqualiter inclinatas diſ-
              <lb/>
            ſectis, quarum diametri ſunt baſibus proportionales, &</s>
            <s xml:id="echoid-s7772" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7773" xml:space="preserve">Idemque de duo-
              <lb/>
            bus circulis, &</s>
            <s xml:id="echoid-s7774" xml:space="preserve">c.</s>
            <s xml:id="echoid-s7775" xml:space="preserve"/>
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          <head xml:id="echoid-head325" xml:space="preserve">II.</head>
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            <s xml:id="echoid-s7776" xml:space="preserve">SOLIDVM ACVMINATVM REGVLARE, vel tantùm SOLIDVM
              <lb/>
            ACVMINATVM, voco omnem figuram ſolidam ad alteram partem defi-
              <lb/>
            cientem, circa planum Acuminatum deſcriptam, cuius omnia plana baſi ſo-
              <lb/>
            lidi æquidiſtantia per Acuminati applicatas ducta, ſint quoque plana Acu-
              <lb/>
            minata, eidem baſi, ac inter ſe ſimilia, & </s>
            <s xml:id="echoid-s7777" xml:space="preserve">ſimiliter poſita, & </s>
            <s xml:id="echoid-s7778" xml:space="preserve">quorum homo-
              <lb/>
            logæ diametri ſint ipſæ applicatæ prædicti Acuminati, &</s>
            <s xml:id="echoid-s7779" xml:space="preserve">c.</s>
            <s xml:id="echoid-s7780" xml:space="preserve"/>
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          <figure number="228">
            <image file="0278-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0278-02"/>
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          <p>
            <s xml:id="echoid-s7781" xml:space="preserve">Eſto planum quodcunque Acuminatum A B C, cuius baſis A C, dia-
              <lb/>
            meter B D, vertex B, & </s>
            <s xml:id="echoid-s7782" xml:space="preserve">ipſa A C, ſit vel diameter circuli, aut Ellipſis,
              <lb/>
            vel cuiuſcun que ipſarum figurarum portionis, aut diameter Parabolæ,
              <lb/>
            vel Hyperbolæ, vel cuiuslibet alij plani Acuminati A E C F, quod tan-
              <lb/>
            quam baſis, ad quemlibet inclinationis angulum cum plano A B C </s>
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