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

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            reliquo BFC æqualis, qui ſunt anguli ad
              <lb/>
              <figure xlink:label="fig-0171-01" xlink:href="fig-0171-01a" number="137">
                <image file="0171-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0171-01"/>
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            centra D, F: </s>
            <s xml:id="echoid-s4905" xml:space="preserve">ergo ipſorum dimidia ad
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            circumferentias, hoc eſt anguli B G L,
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            B I C æquales erunt, vnde G L æquidi-
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            ſtabit I C: </s>
            <s xml:id="echoid-s4906" xml:space="preserve">quare, vt C B ad B L, ita I B,
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            ad BG, vel ſumpta communi altitudine
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            BH, ita rectangulum IBH, ſiue quadra-
              <lb/>
            tum B C, ad rectangulum H B G, vel ad
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            quadratum BM: </s>
            <s xml:id="echoid-s4907" xml:space="preserve">cum ergo ſit CB ad BL,
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            vt quadratum C B ad quadratum B M,
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            erunt tres contingentes BC, BM, BL,
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            in eadem ratione geometrica, ſed C B
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            ad B M, eſt vt C F ad M E, & </s>
            <s xml:id="echoid-s4908" xml:space="preserve">M B ad
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            B L, vt M E ad L D; </s>
            <s xml:id="echoid-s4909" xml:space="preserve">ergo C F, M E,
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            L D, vti etiam ipſarum quadrata, ſiue
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            _MAXIMI_ circuli ex FC, EM, DL erunt
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            in eadem ratione geometrica, quę pro-
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            cedit iuxta quadrata contingentium
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            B C, B M, B L. </s>
            <s xml:id="echoid-s4910" xml:space="preserve">Quod oſtendere pro-
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            ponebatur.</s>
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        <div xml:id="echoid-div494" type="section" level="1" n="200">
          <head xml:id="echoid-head205" xml:space="preserve">COROLL.</head>
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            <s xml:id="echoid-s4912" xml:space="preserve">HInc elicitur, quod ſi datus angulus fuerit angulus trianguli æquilateri,
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            ſiue duæ tertiæ vnius recti, prædicti _MAXIMI_ circuli erunt inter ſe
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            in continua progreſſione nonupla. </s>
            <s xml:id="echoid-s4913" xml:space="preserve">Tunc enim in triangulo ęquilatero BNO,
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            _MAXIMVS_ inſcriptus circulus ex DG ſingula latera ad puncta contactuum
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            bifariam ſecabit, quare BL æquabitur LN, ſiue NG, ſiue NM, (cum circu-
              <lb/>
            lum contingentes, ex eodem puncto ſint æquales) hoc eſt BM erit tripla
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            BL, & </s>
            <s xml:id="echoid-s4914" xml:space="preserve">quadratum BM nonuplum quadrati B L, vel circulus ex EM nonu-
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            plus circuli ex DL, itemque circulus ex F C nonuplus circuli ex E M, cum
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            ſint in eadem proportione geometrica, & </s>
            <s xml:id="echoid-s4915" xml:space="preserve">hoc ſemper, quotcunq; </s>
            <s xml:id="echoid-s4916" xml:space="preserve">ſint huiuſ-
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            modi circuli ſe mutuò, & </s>
            <s xml:id="echoid-s4917" xml:space="preserve">prædicti anguli latera contingentes.</s>
            <s xml:id="echoid-s4918" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4919" xml:space="preserve">Hic autem notandum eſt inter hos _MAXIMOS_ circulos non dari _MAXI-_
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            _MVM_, cum infra circulum FC alij infiniti in eadem progreſſione dato angu-
              <lb/>
            lo inſcribi poſſint, eò quod ipſe ad partes L ſit infinitæ extenſionis.</s>
            <s xml:id="echoid-s4920" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4921" xml:space="preserve">Item inter eoſdem _MAXIMOS_ circulos non dari _MINIMVM_; </s>
            <s xml:id="echoid-s4922" xml:space="preserve">quoniam
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            ad partes verticis B, ſupra circulum DL, reſiduo trilineo, licet terminato,
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            alij infiniti circuli perpetuò decreſcentes inſcribi poſſunt.</s>
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