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

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            ctionem M N, vt modò oſtendimus, ergo, & </s>
            <s xml:id="echoid-s8992" xml:space="preserve">ad rectam M B, quæ eſt in
              <lb/>
            eodem trianguli plano perpendicularis erit, ſiue B M perpendicularis ſuper
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            I M: </s>
            <s xml:id="echoid-s8993" xml:space="preserve">eodem modo oſtendetur B N perpendicularem eſſe ad L N.</s>
            <s xml:id="echoid-s8994" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s8995" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8996" xml:space="preserve">
              <emph style="sc">Iam</emph>
            perpendicularis B A maior eſt B C, cum B A ſit _MAXIMVM_ Coni
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            latus, & </s>
            <s xml:id="echoid-s8997" xml:space="preserve">B C _MINIMVM_, vt ſupra monuimus; </s>
            <s xml:id="echoid-s8998" xml:space="preserve">ob eandem rationem eſt
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            B A maior B I, ſed B I maior eſt B M, cum B M ſit perpendicularis ad I
              <lb/>
            M, ac ideo _MINIMA_ ad ipſam I M, ergo B A eò magis maior erit per-
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            pendiculari B M: </s>
            <s xml:id="echoid-s8999" xml:space="preserve">eodem modo demonſtrabitur B A maiorem eſſe perpen-
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            diculari B N, & </s>
            <s xml:id="echoid-s9000" xml:space="preserve">hoc ſemper, &</s>
            <s xml:id="echoid-s9001" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9002" xml:space="preserve">quare in ſingulis caſibus _MAXIMVM_
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            Conilatus B A eſt _MAXIMA_ prædictarum perpendicularium.</s>
            <s xml:id="echoid-s9003" xml:space="preserve"/>
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          <figure number="257">
            <image file="0323-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0323-01"/>
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          <p>
            <s xml:id="echoid-s9004" xml:space="preserve">2. </s>
            <s xml:id="echoid-s9005" xml:space="preserve">QVo autem ad _MINIMAM_ in prima figura. </s>
            <s xml:id="echoid-s9006" xml:space="preserve">Eſt B C minor B A, cum ea
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            ſit _MINIMVM_ Coni latus. </s>
            <s xml:id="echoid-s9007" xml:space="preserve">Ampliùs eſt perpendicularis E C
              <note symbol="a" position="right" xlink:label="note-0323-01" xlink:href="note-0323-01a" xml:space="preserve">97. h.</note>
            perpendiculari E M, vnde, & </s>
            <s xml:id="echoid-s9008" xml:space="preserve">quadratum E C minus eſt quadra-
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            to E M, & </s>
            <s xml:id="echoid-s9009" xml:space="preserve">communi addito quadrato E B, erunt duo ſimul quadrata C E,
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            E B, ſiue vnicum quadratum B C, minus duobus ſimul quadratis M E, E B,
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            ſiue vnico quadrato B M (ponitur enim B E recta ad baſim, ac ideo cum om-
              <lb/>
            nibus E C, E M, &</s>
            <s xml:id="echoid-s9010" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9011" xml:space="preserve">rectos efficit angulos) hoc eſt recta B C, quæ perpen-
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            dicularis eſt ad contingentem C H, minor erit recta B M, quæ eſt perpen-
              <lb/>
            dicularis ad contingentem I M; </s>
            <s xml:id="echoid-s9012" xml:space="preserve">eadem ratione oſtendetur B C minorem
              <lb/>
            eſſe perpendiculari B N, vel quacunque alia ex B ad quamlibet contingen-
              <lb/>
            tium ducta: </s>
            <s xml:id="echoid-s9013" xml:space="preserve">quare B C eſt ipſarum perpendicularium _MINIMA_.</s>
            <s xml:id="echoid-s9014" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s9015" xml:space="preserve">In ſecunda verò cum altitudo B E congruat cum perpendiculari B C ad
              <lb/>
            contingentem C H, cumque eadem B E ſit _MINIMA_ ad planum baſis
              <note symbol="b" position="right" xlink:label="note-0323-02" xlink:href="note-0323-02a" xml:space="preserve">52. h.</note>
            C, erit etiam perpendicularis B C _MINIMA_ ad idem planum, hoc eſt _MI-_
              <lb/>
            _NIMA_ quarumlibet perpendicularium. </s>
            <s xml:id="echoid-s9016" xml:space="preserve">In primo igitur, ac ſecundo caſu
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            recta B C, quæ eſt _MINIMVM_ Coni latus, perpendicularium ad prædi-
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            ctas contingentes eſt _MINIMA_.</s>
            <s xml:id="echoid-s9017" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s9018" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9019" xml:space="preserve">IN tertia denique, cum ſit recta B E ad planum baſis perpendicularis, ipſa
              <lb/>
            cum contingente E G rectos efficiet angulos, ſed ipſa B E eſt
              <note symbol="c" position="right" xlink:label="note-0323-03" xlink:href="note-0323-03a" xml:space="preserve">3. def. 11
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              Elem.</note>
              <note symbol="d" position="right" xlink:label="note-0323-04" xlink:href="note-0323-04a" xml:space="preserve">52. h.</note>
            _MA_ ad ipſum baſis planum, quare, & </s>
            <s xml:id="echoid-s9020" xml:space="preserve">_MINIMA_ quoque erit prædictarum
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            quarumlibet perpendicularium. </s>
            <s xml:id="echoid-s9021" xml:space="preserve">Quod vltimò oſtendere proponebatur.</s>
            <s xml:id="echoid-s9022" xml:space="preserve"/>
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