Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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              <pb o="153" file="0177" n="177" rhead=""/>
            B Q ad B S, vt B S ad B D, quare cum B Q ſit 9, & </s>
            <s xml:id="echoid-s5056" xml:space="preserve">B S 12, erit B D
              <note symbol="a" position="right" xlink:label="note-0177-01" xlink:href="note-0177-01a" xml:space="preserve">1. Co-
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              roll. 13. h.</note>
            & </s>
            <s xml:id="echoid-s5057" xml:space="preserve">Q D 7, & </s>
            <s xml:id="echoid-s5058" xml:space="preserve">ſic vlteriùs demonſtrabuntur diametri huiuſmodi ſimilium El-
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            lipſium Parabolæ inſcriptarum, &</s>
            <s xml:id="echoid-s5059" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5060" xml:space="preserve">à vertice ſumptæ, augeri iuxta progreſ-
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            ſionem diſparium numerorum ab vnitate, nempe vt numeri 1. </s>
            <s xml:id="echoid-s5061" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5062" xml:space="preserve">5. </s>
            <s xml:id="echoid-s5063" xml:space="preserve">7. </s>
            <s xml:id="echoid-s5064" xml:space="preserve">9.
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            </s>
            <s xml:id="echoid-s5065" xml:space="preserve">11. </s>
            <s xml:id="echoid-s5066" xml:space="preserve">&</s>
            <s xml:id="echoid-s5067" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5068" xml:space="preserve">Sed Ellipſes ſimiles ſunt inter ſe, vt quadrata homologarum diame-
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            trorum: </s>
            <s xml:id="echoid-s5069" xml:space="preserve">quare eædem _MAXIMAE_ Ellipſes Parabolæ A B C inſcriptæ, & </s>
            <s xml:id="echoid-s5070" xml:space="preserve">
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            à vertice ſucceſſiuè ſe mutuò contingentes, ſunt in ratione quadratorum diſ-
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            parium numerorum ab vnitate. </s>
            <s xml:id="echoid-s5071" xml:space="preserve">Quod probandum erat.</s>
            <s xml:id="echoid-s5072" xml:space="preserve"/>
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        <div xml:id="echoid-div513" type="section" level="1" n="210">
          <head xml:id="echoid-head215" xml:space="preserve">COROLL.</head>
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            <s xml:id="echoid-s5073" xml:space="preserve">HInc iterum apparet veritas Prop. </s>
            <s xml:id="echoid-s5074" xml:space="preserve">77. </s>
            <s xml:id="echoid-s5075" xml:space="preserve">huius. </s>
            <s xml:id="echoid-s5076" xml:space="preserve">Nam ſi B D diameter da-
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            tæ Parabolæ A B C, fuerit axis; </s>
            <s xml:id="echoid-s5077" xml:space="preserve">& </s>
            <s xml:id="echoid-s5078" xml:space="preserve">prima Ellipſis circa ſegmentum
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            B F fuerit circulus, reliquæ Ellipſes infra hanc ſucceſſiuè inſcriptæ, erunt
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            pariter Circuli, & </s>
            <s xml:id="echoid-s5079" xml:space="preserve">demonſtratio, ac concluſio omnino erit eadem, ac in
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            ſuperiori.</s>
            <s xml:id="echoid-s5080" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div514" type="section" level="1" n="211">
          <head xml:id="echoid-head216" xml:space="preserve">Pag. 131. poſt Prop. 84.</head>
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            <s xml:id="echoid-s5081" xml:space="preserve">In hac, & </s>
            <s xml:id="echoid-s5082" xml:space="preserve">in proxima præcedenti 82. </s>
            <s xml:id="echoid-s5083" xml:space="preserve">propoſitione ex ipſamet conſtru-
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            ctione, ac demonſtratione elicitur, nos vtrobique aſſumpſiſſe datam appli-
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            catam A C ad diametrum datæ Ellipſis, nunquam per centrum tranſire: </s>
            <s xml:id="echoid-s5084" xml:space="preserve">in
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            hoc enim caſu vtriuſque Problematis ſolutio facillimè patebit, tunc nimirũ,
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            ſi hinc inde à centro ſuper diametrum ſumatur dimidium dati tranſuerſi la-
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            teris, atque circa ipſorum dimidiorum aggregatum, tanquam circa tranſ-
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            uerſum diametrum, & </s>
            <s xml:id="echoid-s5085" xml:space="preserve">per extrema ipſius applicatæ deſcribatur Ellipſis, quę
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            vel erit _MAXIMA_ inſcripta, vel _MINIMA_ datæ Ellipſi circumſcripta, cum eadem applicata A C ſit tanquam communis ſecunda diameter, vel
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              <note symbol="b" position="right" xlink:label="note-0177-02" xlink:href="note-0177-02a" xml:space="preserve">2. Co-
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              roll. 19. h.</note>
            prout commune tranſuerſum latus vtriuſque Ellipſis, &</s>
            <s xml:id="echoid-s5086" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5087" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div516" type="section" level="1" n="212">
          <head xml:id="echoid-head217" xml:space="preserve">Pag. 144. ad calcem Prop. 93.</head>
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            <s xml:id="echoid-s5088" xml:space="preserve">Lineæ, quæ ibi in figuris iungentes puncta C, D, manifeſtò indicant
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            in ipſa tranſcriptione omiſſum fuiſſe ſequens</s>
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        <div xml:id="echoid-div517" type="section" level="1" n="213">
          <head xml:id="echoid-head218" xml:space="preserve">SCHOLIVM.</head>
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            <s xml:id="echoid-s5089" xml:space="preserve">EX his aliàs manifeſtum fiet haud inutiliter animaduertiſſe in Parabola,
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            vel in Hyperbola, aut in quadrante Ellipſis circa maiorem axim, præ-
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            dictarum contingentibus perpendicularium ad eaſdem axis partes ductarũ,
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            quæ à contactu vertici remotiori ducitur occurrere axi infra occurſum ſupe-
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            rioris perpendicularis, ac ſimul vltra axim conuenire ad partes contactibus
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            oppoſitas: </s>
            <s xml:id="echoid-s5090" xml:space="preserve">ſed in quadrante Ellipſis circa minorem axim ſe mutuò ſecare in-
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            ter tangentium contactus, & </s>
            <s xml:id="echoid-s5091" xml:space="preserve">minorem axim in angulo quadrantis, qui dein-
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            ceps eſt ei, ad cuius peripheriam ductæ ſunt perpendiculares; </s>
            <s xml:id="echoid-s5092" xml:space="preserve">ac ideo oc-
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            curſum inferioris perpendicularis cum axe minori cadere ſupra occurſum
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            ſuperioris, quæ ducitur ex contactu vertici propiori.</s>
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