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

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        <div xml:id="echoid-div489" type="section" level="1" n="198">
          <pb o="146" file="0170" n="170" rhead=""/>
          <p>
            <s xml:id="echoid-s4865" xml:space="preserve">Ducatur EF Ellipſim contingens, cui ex E perpendicularis erigatur ED,
              <lb/>
            maiori axi occurrens in L, minori verò in D: </s>
            <s xml:id="echoid-s4866" xml:space="preserve">quo facto centro, & </s>
            <s xml:id="echoid-s4867" xml:space="preserve">interual-
              <lb/>
            lo DE circulus deſcribatur EGHI. </s>
            <s xml:id="echoid-s4868" xml:space="preserve">Dico hunc eſſe quæſitum.</s>
            <s xml:id="echoid-s4869" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4870" xml:space="preserve">Nam eſſe circumſcriptum, pater ex ſecunda parte 92. </s>
            <s xml:id="echoid-s4871" xml:space="preserve">huius. </s>
            <s xml:id="echoid-s4872" xml:space="preserve">Sed eſt quoq;
              <lb/>
            </s>
            <s xml:id="echoid-s4873" xml:space="preserve">_MINIMVS_: </s>
            <s xml:id="echoid-s4874" xml:space="preserve">quoniam quilibet alius
              <lb/>
              <figure xlink:label="fig-0170-01" xlink:href="fig-0170-01a" number="136">
                <image file="0170-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0170-01"/>
              </figure>
            circulus, cuius radius, maior ſit ipſo
              <lb/>
            DE, eſt omnino maior circulo EG-
              <lb/>
            HI, & </s>
            <s xml:id="echoid-s4875" xml:space="preserve">cuius radius minor ſit D E,
              <lb/>
            eſt quidem minor, ſed vel totus ca-
              <lb/>
            dit intra Ellipſim, vel eius periphe-
              <lb/>
            riam neceſſariò ſecat. </s>
            <s xml:id="echoid-s4876" xml:space="preserve">Nam ſi cen-
              <lb/>
            trum fuerit in perpendiculari ED,
              <lb/>
            & </s>
            <s xml:id="echoid-s4877" xml:space="preserve">radius non maior diſtantia E L,
              <lb/>
            quæ cadit inter contactum E, &</s>
            <s xml:id="echoid-s4878" xml:space="preserve">
              <note symbol="a" position="left" xlink:label="note-0170-01" xlink:href="note-0170-01a" xml:space="preserve">92. h.</note>
            maiorem axim, circulus cadet totus
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            intra, & </s>
            <s xml:id="echoid-s4879" xml:space="preserve">ſi radius fuerit maior E L,
              <lb/>
            qualis eſt EP, tunc eius circulus ca-
              <lb/>
            det totus intra circulum EGHI, ſed
              <lb/>
            licet ipſius peripheria ad partes G,
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            B, ſtatim ac diſcedit ab E, cadat in-
              <lb/>
            ter peripheriam circuli AGH, & </s>
            <s xml:id="echoid-s4880" xml:space="preserve">perip heriam Ellipſis EBH, cum tamen in
              <lb/>
            ſe ipſum redeat, neceſſariò Ellipticam peripheriam EBH ſecabit, nam ſpa-
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            tium EGHB eſt vndique occluſum.</s>
            <s xml:id="echoid-s4881" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4882" xml:space="preserve">Si verò centrum fuerit extra perpendicularem ED, vt in Q: </s>
            <s xml:id="echoid-s4883" xml:space="preserve">iuncta QE
              <lb/>
            cum contingente SEF inæquales angulos efficiet, quorum alterum, videli-
              <lb/>
            cet SEQ obtuſus erit, quare ſi ipſi EQ erigatur perpendicularis ER, hæc
              <lb/>
            omninò ſecabit Ellipſim: </s>
            <s xml:id="echoid-s4884" xml:space="preserve">quare ſi cum centro Q, interuallo QE
              <note symbol="b" position="left" xlink:label="note-0170-02" xlink:href="note-0170-02a" xml:space="preserve">32. pri-
                <lb/>
              mi conic.</note>
            deſcribatur XEV, ipſæ ad partes ſecantis ER ſecabit omnino Ellipſis peri-
              <lb/>
            pheriam, vt per ſe patet. </s>
            <s xml:id="echoid-s4885" xml:space="preserve">Ergo circulus ex DE eſt _MINIMVS_ circumſcri-
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            ptus quæſitus. </s>
            <s xml:id="echoid-s4886" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s4887" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div492" type="section" level="1" n="199">
          <head xml:id="echoid-head204" xml:space="preserve">THEOR. XLVIII. PROP. XCVII.</head>
          <p>
            <s xml:id="echoid-s4888" xml:space="preserve">MAXIMI circuli angulo rectilineo inſcripti, & </s>
            <s xml:id="echoid-s4889" xml:space="preserve">ſucceſſiuè ſe
              <lb/>
            mutuò contingentes, ſunt inter ſe in continua, eademque ratione
              <lb/>
            geometrica, quæ progreditur iuxta quadrata tangentium, ex ver-
              <lb/>
            tice dati anguli ductarum.</s>
            <s xml:id="echoid-s4890" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4891" xml:space="preserve">ESto angulus ABC, cuius axis B D E F, in quo ſint centra D, E, F, &</s>
            <s xml:id="echoid-s4892" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s4893" xml:space="preserve">_MAXIMORVM_ circulorum dato angulo inſcriptorum, & </s>
            <s xml:id="echoid-s4894" xml:space="preserve">mutui ipſorum
              <lb/>
            contactus ſint G, H, &</s>
            <s xml:id="echoid-s4895" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4896" xml:space="preserve">ad latus verò anguli, contactus ſint L, M, C, &</s>
            <s xml:id="echoid-s4897" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4898" xml:space="preserve">
              <lb/>
            Dico hos circulos inter ſe eſſe in continua, eademque ratione geometrica,
              <lb/>
            ipſamque incedere iuxta quadrata contingentium BL, BM, BC, &</s>
            <s xml:id="echoid-s4899" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4900" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4901" xml:space="preserve">Iunctis enim DL, EM, FC, & </s>
            <s xml:id="echoid-s4902" xml:space="preserve">GL, IC. </s>
            <s xml:id="echoid-s4903" xml:space="preserve">Cum in triangulis BLD, BCF,
              <lb/>
            anguli BLD, BCF ſint recti, & </s>
            <s xml:id="echoid-s4904" xml:space="preserve">angulus ad B communis, erit reliquus </s>
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