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

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            <s xml:id="echoid-s5310" xml:space="preserve">
              <pb o="7" file="0189" n="189" rhead=""/>
            F Q H ſit obtuſus, eò quod alterno Q F B obtuſo ſit æqualis) ſed eſt F Q
              <lb/>
            maius F P, quare educta F H eò maior erit educta F P. </s>
            <s xml:id="echoid-s5311" xml:space="preserve">Ampliùs ducta
              <lb/>
            qualibet alia F R, adhuc maiorem angulum facient
              <unsure/>
            cum _MAXIMA_ F D,
              <lb/>
            agatur per R recta R S axi F E parallela, quæ cadet intra Ellipſim, (cum
              <lb/>
            ſit ad minorem axim H I ordinatim ducta) ſecabitque F P in S, ac in
              <lb/>
            triangulo F R S obtuſiangulo ad R, erit latus F S maius latere F R, & </s>
            <s xml:id="echoid-s5312" xml:space="preserve">
              <lb/>
            educta F P eò maior educta F R; </s>
            <s xml:id="echoid-s5313" xml:space="preserve">eademque ratione oſtendetur quamli-
              <lb/>
            bet eductarum ad peripheriam H A, vtputa F R, maiorem eſſe ſemi-ap-
              <lb/>
            plicata F A, ſi ex A ducatur A V parallela ad E F, &</s>
            <s xml:id="echoid-s5314" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5315" xml:space="preserve">quare eadem
              <lb/>
            ſemi-applicata F A omnium eductarum in portione maiori A D C erit
              <lb/>
            _MINIMA_. </s>
            <s xml:id="echoid-s5316" xml:space="preserve">Aliarum autem, quæ cum _MAXIMA_ F D maiorem angulum
              <lb/>
            conſtituit, maior eſt. </s>
            <s xml:id="echoid-s5317" xml:space="preserve">Quod omnino oſtendere opus fuerat.</s>
            <s xml:id="echoid-s5318" xml:space="preserve"/>
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        <div xml:id="echoid-div544" type="section" level="1" n="225">
          <head xml:id="echoid-head233" xml:space="preserve">LEMMA IV. PROP. VII.</head>
          <p>
            <s xml:id="echoid-s5319" xml:space="preserve">Si in triangulo A B C, cuius rectus angulus ſit ad B, fuerit
              <lb/>
            latus A B maius altero B C, ſitque de maiori B A abſciſſa pars
              <lb/>
              <note position="right" xlink:label="note-0189-01" xlink:href="note-0189-01a" xml:space="preserve">1.</note>
            B E, quæ non excedat dimidium ipſius B C, & </s>
            <s xml:id="echoid-s5320" xml:space="preserve">ex quolibet eius
              <lb/>
            puncto G ducta ſit G H parallela ad B C. </s>
            <s xml:id="echoid-s5321" xml:space="preserve">Dico primùm ipſam
              <lb/>
            G H ſemper maiorem eſſe aggregato B E cum E G.</s>
            <s xml:id="echoid-s5322" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5323" xml:space="preserve">DVcatur E F ęquidiſtans ad B C. </s>
            <s xml:id="echoid-s5324" xml:space="preserve">Et quoniam A B ponitur maior ip-
              <lb/>
            ſa B C; </s>
            <s xml:id="echoid-s5325" xml:space="preserve">B C verò dupla, vel plus quàm dupla ad B E, erit omni-
              <lb/>
            no A B plus quàm dupla ad B E, ſiue AE
              <lb/>
              <figure xlink:label="fig-0189-01" xlink:href="fig-0189-01a" number="149">
                <image file="0189-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0189-01"/>
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            plus quàm dimidium ipſius A B, quod
              <lb/>
            memento ſed, vt A E ad A B, ita E F
              <lb/>
            ad B C; </s>
            <s xml:id="echoid-s5326" xml:space="preserve">quare E F eſt maior dimidio
              <lb/>
            ipſius B C, hoc eſt maior ipſa B E. </s>
            <s xml:id="echoid-s5327" xml:space="preserve">Secta
              <lb/>
            igitur E S æquali ipſi B E, ducatur S K
              <lb/>
            D parallela ad B E, eritque B S paralle-
              <lb/>
            logrammum æquilaterum (cum E B,
              <lb/>
            E S ſint æquales) iungatur denique C S
              <lb/>
            rectam G H ſecans in T.</s>
            <s xml:id="echoid-s5328" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5329" xml:space="preserve">Itaque cum E B, ſiue B D poſita ſit
              <lb/>
            æqualis, vel minor dimidio ipſius B C,
              <lb/>
            erit C D æqualis, vel maior ipſa D B,
              <lb/>
            vel D S. </s>
            <s xml:id="echoid-s5330" xml:space="preserve">Cumque ſit, vt C D ad D S,
              <lb/>
            ita T K ad K S, erit quoque T K ęqua-
              <lb/>
            lis, vel maior ipſa K S, ſiue G E, qui-
              <lb/>
            bus T K, & </s>
            <s xml:id="echoid-s5331" xml:space="preserve">G E additis ęqualibus K G, E B, proueniet tota T G æqua-
              <lb/>
            lis, vel maior aggregato G E cum E B, ſed eſt H G maior ipſa T G: </s>
            <s xml:id="echoid-s5332" xml:space="preserve">qua-
              <lb/>
            re H G erit omnino maior aggregato B E cnm E G. </s>
            <s xml:id="echoid-s5333" xml:space="preserve">Quod, &</s>
            <s xml:id="echoid-s5334" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5335" xml:space="preserve"/>
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