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

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        <div xml:id="echoid-div956" type="section" level="1" n="384">
          <pb o="145" file="0331" n="331" rhead=""/>
          <p>
            <s xml:id="echoid-s9173" xml:space="preserve">Duabus datis rectis lineis terminatis, non modò ad rectum, ſed
              <lb/>
            ad quemlibet angulum conſtitutis, & </s>
            <s xml:id="echoid-s9174" xml:space="preserve">per vnius ipſarum terminum
              <lb/>
            alia alteri ipſarum æquidiſtanter ducta, ad contrarias tamen par-
              <lb/>
            tes, & </s>
            <s xml:id="echoid-s9175" xml:space="preserve">in infinitum producta: </s>
            <s xml:id="echoid-s9176" xml:space="preserve">oportet per extremum terminum al-
              <lb/>
            terius, rectam ducere æquidiſtanti occurrentem, quæ cum bina
              <lb/>
            ſimilia triangula ad verticem conſtituat, ipſorum aggregatum ſit
              <lb/>
            MINIMA quantitas.</s>
            <s xml:id="echoid-s9177" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9178" xml:space="preserve">ſimulque noſtram Problematis enodationem his verbis enunciauimus;</s>
            <s xml:id="echoid-s9179" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9180" xml:space="preserve">Diuidatur ſecanda linea, ita vt ſegmentum ipſius propè termi-
              <lb/>
            natam parallelam, ad ſegmentum reliquum ſit in ratione diametri
              <lb/>
            cuiuslibet quadrati ad exceſſum diametri ſuper latus: </s>
            <s xml:id="echoid-s9181" xml:space="preserve">nam pũctum
              <lb/>
            interſectionis erit quæſitum.</s>
            <s xml:id="echoid-s9182" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9183" xml:space="preserve">ac demum de inuentione binorum æqualium ex triangulis aggregatorum,
              <lb/>
            tam ſupra, quàm infra punctum MINIMI aggregati eundem Cl. </s>
            <s xml:id="echoid-s9184" xml:space="preserve">Ado-
              <lb/>
            leſcentem commonefecimus. </s>
            <s xml:id="echoid-s9185" xml:space="preserve">Sed iam Appendicem aggrediamur.</s>
            <s xml:id="echoid-s9186" xml:space="preserve"/>
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        <div xml:id="echoid-div957" type="section" level="1" n="385">
          <head xml:id="echoid-head396" xml:space="preserve">LEMMA I. PROP. I.</head>
          <p>
            <s xml:id="echoid-s9187" xml:space="preserve">Si fuerint duo ordines quotcunque triangulorum æqualem al-
              <lb/>
            titudinem habentium; </s>
            <s xml:id="echoid-s9188" xml:space="preserve">erit aggregatum baſium triangulorum pri-
              <lb/>
            mi ordinis, ad aggregatum baſium triangulorum ſecundi, vt ag-
              <lb/>
            gregatum triangulorum primi, ad aggregatum triangulorum ſe-
              <lb/>
            cundi ordinis.</s>
            <s xml:id="echoid-s9189" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9190" xml:space="preserve">SIt vnus ordo triangulorum A B C, C D E, E F G, G H I, alter verò
              <lb/>
            triangulorum ordo L M N, N O P, P Q R, & </s>
            <s xml:id="echoid-s9191" xml:space="preserve">omnia ſint æqualis alti-
              <lb/>
            tudinis, vtriuſque autem ordinis triangula ſint ad eaſdem partes, & </s>
            <s xml:id="echoid-s9192" xml:space="preserve">ipſorum
              <lb/>
            baſes in directum diſponãtur, quarum baſium aggregatum, in primo ſit A I,
              <lb/>
            & </s>
            <s xml:id="echoid-s9193" xml:space="preserve">in ſecundo ſit L R. </s>
            <s xml:id="echoid-s9194" xml:space="preserve">Dico aggregatum A I, ad aggregatum L R eſſe vt
              <lb/>
            aggregatum triangulorum primi ordinis ad aggregatum tr iangulorũ ſecũdi.</s>
            <s xml:id="echoid-s9195" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9196" xml:space="preserve">Quoniam iunctis rectis A H,
              <lb/>
              <figure xlink:label="fig-0331-01" xlink:href="fig-0331-01a" number="262">
                <image file="0331-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0331-01"/>
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            C H, E H; </s>
            <s xml:id="echoid-s9197" xml:space="preserve">& </s>
            <s xml:id="echoid-s9198" xml:space="preserve">L Q, N Q: </s>
            <s xml:id="echoid-s9199" xml:space="preserve">erit
              <lb/>
            triangulum A B C ęquale trian-
              <lb/>
            gulo A H C, (cum ſint ſuper ea-
              <lb/>
            dembaſi A C, & </s>
            <s xml:id="echoid-s9200" xml:space="preserve">habeant ex hy-
              <lb/>
            potheſi eandem altitudinem) & </s>
            <s xml:id="echoid-s9201" xml:space="preserve">
              <lb/>
            C D E ęquale C H E, ac E F G
              <lb/>
            æquale E H G; </s>
            <s xml:id="echoid-s9202" xml:space="preserve">vnde communi
              <lb/>
            addito G H I, erunt omnia ſimul
              <lb/>
            primi ordinis æqualia vnico A
              <lb/>
            H I: </s>
            <s xml:id="echoid-s9203" xml:space="preserve">item oſtẽdetur omnia ſimul
              <lb/>
            ſecundi ordinis æqualia eſſe vni-
              <lb/>
            co L Q R; </s>
            <s xml:id="echoid-s9204" xml:space="preserve">ſed triangulum A H I ad L Q R eſt vt baſis A I ad L R, cum </s>
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