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

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          <p>
            <s xml:id="echoid-s9204" xml:space="preserve">
              <pb o="146" file="0332" n="332" rhead=""/>
            nantur æqualium altitudinum, quare aggregatum triangulorum primi, ad
              <lb/>
            aggregatum triangulorum ſecundi ordinis erit, vt A I ad L R, vel vt aggre-
              <lb/>
            gatum baſium primi ordinis ad aggregatum baſium ſecundi. </s>
            <s xml:id="echoid-s9205" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s9206" xml:space="preserve">c.</s>
            <s xml:id="echoid-s9207" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div959" type="section" level="1" n="386">
          <head xml:id="echoid-head397" xml:space="preserve">LEMMA II. PROP. II.</head>
          <p>
            <s xml:id="echoid-s9208" xml:space="preserve">In quocunque polygono regulari, aggregata perpendicularium
              <lb/>
            ex quibuſcunque punctis, (quæ tamen non ſint extra perimetrum
              <lb/>
            polygoni) ſuper omnia eius latera eductarum, inter ſe ſunt æqua-
              <lb/>
            lia. </s>
            <s xml:id="echoid-s9209" xml:space="preserve">Si verò alterum punctorum fuerit extra perimetrum, aggrega-
              <lb/>
            tum perpendicularium ex eo eductarum, maius ſemper erit quoli-
              <lb/>
            bet prædictorum aggregatorum ex puncto, quod non ſit extra.</s>
            <s xml:id="echoid-s9210" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9211" xml:space="preserve">ESto polygonum regulare A B C D E, & </s>
            <s xml:id="echoid-s9212" xml:space="preserve">duo quælibet puncta F, G, in
              <lb/>
            prima figura, vel intra, vel in ipſius perimetro, à quibus ſuper eius late-
              <lb/>
            ra eductæ ſint perpendiculares F N, F H, F I, F L, F M; </s>
            <s xml:id="echoid-s9213" xml:space="preserve">& </s>
            <s xml:id="echoid-s9214" xml:space="preserve">G O, G P, G
              <lb/>
            Q, G R, G S. </s>
            <s xml:id="echoid-s9215" xml:space="preserve">Dico talium perpendicularium aggregata inter ſe æqualia
              <lb/>
            eſſe. </s>
            <s xml:id="echoid-s9216" xml:space="preserve">Si verò alterum punctorum G, cadat extra, vt in ſecunda ſigura, dico
              <lb/>
            aggregatum perpendicularium ex G maius eſſe quolibet prædictorum ag-
              <lb/>
            gregatorum, vtputa perpendicularium ex F.</s>
            <s xml:id="echoid-s9217" xml:space="preserve"/>
          </p>
          <figure number="263">
            <image file="0332-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0332-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s9218" xml:space="preserve">Ductis enim rectis ex G, F ad omnes àngulos polygoni, vt in ſiguris:
              <lb/>
            </s>
            <s xml:id="echoid-s9219" xml:space="preserve">Patet ipſum polygonum vtrinque diuiſum eſſe in duos triangulorum ordines
              <lb/>
            æquales altitudineshabentium, quæ ſunt ipſa polygonilatera, ſuper quæ ca-
              <lb/>
            dunt perpendiculares, (ſinempe hæ accipiantur tanquam baſes) erit ergo
              <lb/>
            aggregatum baſiun triangulorum, quæ ſimul conueniunt in F, ad aggre-
              <lb/>
            gatum baſium triangulorum, quæ conueniunt in G, vt aggregatum
              <note symbol="*" position="left" xlink:label="note-0332-01" xlink:href="note-0332-01a" xml:space="preserve">per pri-
                <lb/>
              mam Ap-
                <lb/>
              pend.</note>
            gulorum, primiordinisex F, ad aggregatum triangulornm ſecundi ex G,
              <lb/>
            ſed hęc triangulorumaggregata in prima figura ſunt æqualia (namipſa idem
              <lb/>
            polygonum complent) ergo, & </s>
            <s xml:id="echoid-s9220" xml:space="preserve">aggregata baſium eorundem, hoc eſt ag-
              <lb/>
            gregata perpendicularium ex F, & </s>
            <s xml:id="echoid-s9221" xml:space="preserve">G, ſuper polygoni latera </s>
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