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

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          <p>
            <s xml:id="echoid-s6126" xml:space="preserve">
              <pb o="37" file="0219" n="219" rhead=""/>
            aut lux, & </s>
            <s xml:id="echoid-s6127" xml:space="preserve">calor, augebitur: </s>
            <s xml:id="echoid-s6128" xml:space="preserve">& </s>
            <s xml:id="echoid-s6129" xml:space="preserve">ſi à Solis corpore directè emanantes, ibi
              <lb/>
            fiet iccenſio
              <unsure/>
            , à qua punctum D foci nomen ademptum fuit.</s>
            <s xml:id="echoid-s6130" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6131" xml:space="preserve">Si autem incidentes radij axi paralleli R F, O A à quadam recta N P
              <lb/>
            axi ordinatim ducta ſecentur, erunt aggregata incidentium cum earum
              <lb/>
            reflexis, ſimul æqualia.</s>
            <s xml:id="echoid-s6132" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6133" xml:space="preserve">Nam cum A D, ex præcedenti Coroll. </s>
            <s xml:id="echoid-s6134" xml:space="preserve">2. </s>
            <s xml:id="echoid-s6135" xml:space="preserve">ſit æqualis aggregato H B,
              <lb/>
            cum B D, additis hinc inde æqualibus A O, H P, proueniet aggregatum
              <lb/>
            O A, A D, æquale aggregato P B cum B D, itemque aggregatum R F,
              <lb/>
            cum F D oſtendetur ęquale eidem aggregato P B cum B D, quare aggre-
              <lb/>
            gata O A D, R F D æqualia erunt: </s>
            <s xml:id="echoid-s6136" xml:space="preserve">quod acutiſſimè quidem à perſpica-
              <lb/>
            ciſſimo Caualerio, in eius Speculo Vſtorio animaduerſum fuit.</s>
            <s xml:id="echoid-s6137" xml:space="preserve"/>
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        <div xml:id="echoid-div636" type="section" level="1" n="253">
          <head xml:id="echoid-head261" xml:space="preserve">LEMMA VI. PROP. XXVII.</head>
          <p>
            <s xml:id="echoid-s6138" xml:space="preserve">Si in triangulo A B C, latus A C, ita ſectum fuerit in D, vt
              <lb/>
            rectangulum A C D ęquale ſit quadrato baſis B C. </s>
            <s xml:id="echoid-s6139" xml:space="preserve">Dico, iuncta
              <lb/>
            B D, angulum A B C ęqualem eſſe angulo B D C: </s>
            <s xml:id="echoid-s6140" xml:space="preserve">ſi verò A C D
              <lb/>
            rectangulum maius fuerit prædicto quadrato, & </s>
            <s xml:id="echoid-s6141" xml:space="preserve">angulus angulo
              <lb/>
            maior erit: </s>
            <s xml:id="echoid-s6142" xml:space="preserve">& </s>
            <s xml:id="echoid-s6143" xml:space="preserve">è contra.</s>
            <s xml:id="echoid-s6144" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6145" xml:space="preserve">NAm cum fuerit rectangulum A C D æquale quadrato C B, erit A C
              <lb/>
            ad C B, vt B C ad C D, quare triangula A B C, B D C, ad com-
              <lb/>
            munem angulum A conſtituta, ſimilia erunt, ob
              <lb/>
            idque angulus A B C æqualis angulo B D C.</s>
            <s xml:id="echoid-s6146" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6147" xml:space="preserve">At cum rectangulum A C D maius fuerit qua-
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                <image file="0219-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0219-01"/>
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            drato C B, facto rectangulo A C E æquali qua-
              <lb/>
            drato C B, erit C E minor C D, ergo iuncta B E,
              <lb/>
            erit angulus A B C, æqualis angulo B E C, ſed
              <lb/>
            B E C maior eſt angulo B D C, quare A B C om-
              <lb/>
            ninò maior erit angulo B D C.</s>
            <s xml:id="echoid-s6148" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6149" xml:space="preserve">Si tandem rectangulum A C D minus fuerit
              <lb/>
            quadrato C B, non abſimili modo oſtendetur
              <lb/>
            angulum A B C minorem eſſe angulo A D C.
              <lb/>
            </s>
            <s xml:id="echoid-s6150" xml:space="preserve">Quod vltimò erat, &</s>
            <s xml:id="echoid-s6151" xml:space="preserve">c.</s>
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          <head xml:id="echoid-head262" xml:space="preserve">LEMMA VII. PROP. XXVIII.</head>
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            <s xml:id="echoid-s6153" xml:space="preserve">Si duæ rectæ lineæ A B, C D proportionaliter ſectæ fuerint
              <lb/>
            in E, F, & </s>
            <s xml:id="echoid-s6154" xml:space="preserve">homologis ſegmentis A E, C F æqualia ſumantur
              <lb/>
            A G, C H, & </s>
            <s xml:id="echoid-s6155" xml:space="preserve">ſuper A B, C D deſcripta ſint ſimilia triangula
              <lb/>
            I A B, L C D. </s>
            <s xml:id="echoid-s6156" xml:space="preserve">Dico vt rectangulum G B E, ad quadratum B I,
              <lb/>
            ita eſſe rectangulum H D F ad quadratum D L.</s>
            <s xml:id="echoid-s6157" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6158" xml:space="preserve">CVm ſit enim A E ad E B, vt C F ad F D, erit conuertendo, & </s>
            <s xml:id="echoid-s6159" xml:space="preserve">com-
              <lb/>
            ponendo B A ad A E, vt D C ad C F, vel quadratum B A ad A </s>
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