DelMonte, Guidubaldo, Mechanicorvm Liber

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        <body>
          <chap id="N1043F">
            <p id="id.2.1.11.1.0.0.0" type="main">
              <s id="id.2.1.11.1.1.3.0">
                <pb n="7" xlink:href="036/01/027.jpg"/>
              ſed ne minimum quidem eſſe, cum reperiri non poſsit, hoc mo­
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              do demonſtrare nituntur.
                <figure id="id.036.01.027.1.jpg" place="text" xlink:href="036/01/027/1.jpg" number="14"/>
              </s>
            </p>
            <p id="id.2.1.11.2.0.0.0" type="main">
              <s id="id.2.1.11.2.1.1.0">Exponantur eadem. </s>
              <s id="id.2.1.11.2.1.2.0">
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              à punctiſquè DE hori­
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              zonti
                <expan abbr="perpẽdiculares">perpendiculares</expan>
              du
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                <expan abbr="cãtur">cantur</expan>
              DHEK, atq; alius
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              ſit circulus LDM, cu­
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              ius
                <expan abbr="centrũ">centrum</expan>
              N, qui FDG
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              in puncto D contingat,
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              ipſiq; FDG ſit æqualis:
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              erit NC recta linea. </s>
              <s id="id.2.1.11.2.1.3.0">&
                <arrow.to.target n="note16"/>
                <lb/>
              quoniam angulus KEC
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              angulo HDN eſt æqua
                <arrow.to.target n="note17"/>
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              lis, angulusq; CEG an­
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              gulo NDM eſt etiam
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              æqualis; cum à ſemidiametris, æqualibusq; circumferentiis conti­
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              neatur; erit reliquus mixtuſquè angulus KEG reliquo mixtoquè
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              HDM æqualis. </s>
              <s id="id.2.1.11.2.1.4.0">& quia ſupponunt, quò minor eſt angulus linea
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              horizonti perpendiculari, & circumferentia contentus, eò pondus
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              in eo ſitu grauius eſſe. </s>
              <s id="id.2.1.11.2.1.5.0">vt quò minor eſt angulus HD, & circumfe
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              rentia DG contentus angulo KEG, hoc eſt angulo HDM; ita ſe
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              cundum hanc proportionem pondus in D grauius eſſe pondere in
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              E. </s>
              <s id="id.2.1.11.2.1.5.0.a">Proportio autem anguli MDH ad angulum HDG minor eſt
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              qualibet proportione, quæ ſit inter maiorem, & minorem quanti
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              tatem: ergo proportio ponderum DE omnium proportionum mi
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              nima erit. </s>
              <s id="id.2.1.11.2.1.6.0">immo neq; erit ferè proportio, cum ſit omnium pro
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              portionum minima. </s>
              <s id="id.2.1.11.2.1.7.0">quòd autem proportio MDH ad HDG ſit
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              omnium minima, ex hac neceſsitate oſtendunt; quia MDH exce
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              dit HDG angulo curuilineo MDG, qui quidem angulus omnium
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              angulorum rectilineorum minimus exiſtit: ergo cum non poſsit da
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              ri angulus minor MDG, erit proportio MDH ad HDG
                <expan abbr="omniũ">omnium</expan>
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              proportionum minima. </s>
              <s id="id.2.1.11.2.1.8.0">quæ ratio inutilis valde videtur eſſe; quia
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              quamquam angulus MDG ſit omnibus rectilineis angulis minor,
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              non idcirco ſequitur, abſolutè, ſimpliciterq; omnium eſſe
                <expan abbr="angulorũ">angulorum</expan>
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              minimum: nam ducatur à puncto D linea DO ipſi NC perpendicu
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              laris, hæc vtraſq; tanget circumferentias LDM FDG in puncto
                <arrow.to.target n="note18"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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