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

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            <s xml:id="echoid-s461" xml:space="preserve">
              <pb o="7" file="0027" n="27" rhead=""/>
            omnes Ellipſis affectiones circulo communes eſſe, ſed ferè omnes etiam Hy-
              <lb/>
            perbolæ, magnaque pars Parabolæ, præmittendo tamen nouas quaſdam ani-
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            maduerſiones, cautioneſque perutiles, nemini, quod ſciam, adhuc cognitæs,
              <lb/>
            præcipuèque vtendo methodo ab ipſo Apollonio ſatis diuerſa, certàque indu-
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            ſtria propoſitionum figuris characteres diſponendo, ad hoc vt eadem demon-
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            ſtratio cuin
              <unsure/>
            libet com-ſectioni ſimul inſeruiat, non abſimili modo ab eo, quo
              <lb/>
            in ſuperiori Theoremate vſi ſumus, ex quibus maximum doctrinæ conicæ
              <lb/>
            compendium oriretur; </s>
            <s xml:id="echoid-s462" xml:space="preserve">ſed quoniamid, plus laboris, ac temporis, quam in-
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            genij requireret, libenter opusrelinquo ijs, quibus multum ocij ſuppetit,& </s>
            <s xml:id="echoid-s463" xml:space="preserve">
              <lb/>
            quos magis iuuat in alienas lucubrationes commentaria ſcribere, quàm vel
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            ipſas latiùs promouere, vel nouas meditari, ac geometricè demonſtrare.</s>
            <s xml:id="echoid-s464" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s465" xml:space="preserve">Quod autem in Apollonij ſubcontraria ſectione tranſuerſum, rectumque
              <lb/>
            latus reperiatur eadem methodo, rationeque illorum rectangulorum qua vti-
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            mur in præcedenti, quodque hæc ipſa latera inter ſe ſint æqualia manifeſtum
              <lb/>
            fiet ex eo, quod mox demonſirabimus non tantum in prædicta ſectione ſub-
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            contraria, quæ recta eſt plano trianguli per axem recto plano baſis coni ſcale-
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            ni, ſed etiam ei quæ ſecat planum baſis com ſecundum rectam lineam perpen-
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            dicularem baſi cuiuſcunq; </s>
            <s xml:id="echoid-s466" xml:space="preserve">trianguli per axem non iſoſcelis, vel ei, quæ ipſi baſi
              <lb/>
            indirectum producitur, dummodò talis ſectio ex ipſomet triangulo, triangu-
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            lum auferat ſibi ſimile, ſed ſubcontr ariè poſitum.</s>
            <s xml:id="echoid-s467" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s468" xml:space="preserve">REpetitis igitur duabus vltimis præcedentibus figuris, intelligatur conũ
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            ABC ſcalenum eſſe, ſectumque plano per axem, quodcunque trian-
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              <figure xlink:label="fig-0027-01" xlink:href="fig-0027-01a" number="4">
                <image file="0027-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0027-01"/>
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            gulum efficiente ABC, dummodo non ſit æquicrure, (quod per doctrinam
              <lb/>
            lib. </s>
            <s xml:id="echoid-s469" xml:space="preserve">ſecundi Sereni, vnicum eſt) habent idcircò vnum latus altero </s>
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