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

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            ſtans. </s>
            <s xml:id="echoid-s902" xml:space="preserve">Dico ipſam cum ſectione conuenire, eamque omnino ſecare.</s>
            <s xml:id="echoid-s903" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s904" xml:space="preserve">Iungatur CS, quæ producta ſectioni occurret, per ſecundam partem 8.
              <lb/>
            </s>
            <s xml:id="echoid-s905" xml:space="preserve">huius, eritque ſectionis diameter: </s>
            <s xml:id="echoid-s906" xml:space="preserve">quare per Coroll. </s>
            <s xml:id="echoid-s907" xml:space="preserve">2. </s>
            <s xml:id="echoid-s908" xml:space="preserve">præcedentis, ipſa STX
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            ſectioni occurret, vt in X.</s>
            <s xml:id="echoid-s909" xml:space="preserve"/>
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            <s xml:id="echoid-s910" xml:space="preserve">Præterea, cum quæcunque contingenti æquidiſtans GI ſupra RX, inter
              <lb/>
            aſymptoton, & </s>
            <s xml:id="echoid-s911" xml:space="preserve">ſectionem intercepta, maior ſit ipſa RX, ſiue ipſa GZ, pun-
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            ctum Z cadet extra ſectionem, & </s>
            <s xml:id="echoid-s912" xml:space="preserve">ſic de quolibet alio puncto rectæ XTS. </s>
            <s xml:id="echoid-s913" xml:space="preserve">E
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            contra cum quælibet intercepta LY infra RX, parallela ad DB, minor ſit ip-
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            ſa RX, ſiue LF, punctum F cadet intra ſectionem, idemque de quolibet alio
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            puncto rectæ XF: </s>
            <s xml:id="echoid-s914" xml:space="preserve">vnde recta STX ab ipſo occurſu X cum ſectione, ad partes
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            verticis tota cadit extra, ad oppoſitas verò partes tota cadit intra ſectionem;
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            </s>
            <s xml:id="echoid-s915" xml:space="preserve">ideoque in vno tantum puncto X Hyperbolen ſecat. </s>
            <s xml:id="echoid-s916" xml:space="preserve">Quod erat propoſitum.</s>
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          <head xml:id="echoid-head47" xml:space="preserve">COROLL.</head>
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            <s xml:id="echoid-s918" xml:space="preserve">HInc eſt, lineam alteri aſymptoton æquidiſtantem per punctum, quod
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            ſit, vel in ipſa ſectione, vel intra, pariter in vno tantùm puncto ſe-
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            ctioni occurrere, eamque ſecare.</s>
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            <s xml:id="echoid-s920" xml:space="preserve">Nam recta XS ex puncto X, quod cſt in Hyperbola, vel recta FS ex pun-
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            cto F, quod eſt intra, æquidiſtanter ducta aſymptoto CD, ſi ad partes cen-
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            tri C producatur, alteri aſymptoto CE omnino occurrit, (quoniam EC, ſe-
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            cans DC vnam parallelarum ſecat quoque alteram CE) vnde aliqua pars,
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            ipſius rectæ XS, vel FS cadit in loco ab aſymptotis, & </s>
            <s xml:id="echoid-s921" xml:space="preserve">ſectione terminato,
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            ac ideo ex his, quæ ſuperius oſtendimus, ipſa linea in vno tantùm puncto ſe-
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            ctioni occurret, ac Hyperbolen ſecabit.</s>
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            <s xml:id="echoid-s923" xml:space="preserve">Qua propter, quælibet linea alteri aſymptoton æquidiſtans, dummodo ſit
              <lb/>
            ducta ex puncto, quod ſit in angulo ab aſymptotis facto, in vno tantùm pun-
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            cto Hyperbolæ occurrit, atque eam ſecat.</s>
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