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

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          <head xml:id="echoid-head307" xml:space="preserve">THEOR. XXXVII. PROP. LVI.</head>
          <p>
            <s xml:id="echoid-s7109" xml:space="preserve">Si coni-ſectio, vel circulus coni-ſectionem, vel circulum intus,
              <lb/>
            vel extra, in vno, aut in duobus punctis contingat, & </s>
            <s xml:id="echoid-s7110" xml:space="preserve">harum ſectio-
              <lb/>
            num axes, vel ſibi mutuò congruant, vel æquidiſtent, vtraque au-
              <lb/>
            tem figura, altera immota, circa proprium axem conuertatur. </s>
            <s xml:id="echoid-s7111" xml:space="preserve">So-
              <lb/>
            lidum factum ab vna ſectionum nunquam ſecabit ſolidum ab altera
              <lb/>
            genitum, ſed omnino ſe mutuò contingent, velin vnico puncto, ſi
              <lb/>
            figurarum planarum contactus fuerit tantùm in puncto, ſiue axes
              <lb/>
            congruant, ſiue æquidiſtent; </s>
            <s xml:id="echoid-s7112" xml:space="preserve">vel in duobus tantùm, ſi ad duo pun-
              <lb/>
            cta ſe mutuò contingant, dum axes ſint paralleli; </s>
            <s xml:id="echoid-s7113" xml:space="preserve">vel denique ad
              <lb/>
            integram circuli peripheriam à contactibus genitam, ſi ad duo
              <lb/>
            puncta ſectiones ſimul occurrant, dum axes ſimul congruant.</s>
            <s xml:id="echoid-s7114" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7115" xml:space="preserve">SInt duæ coni-ſectiones A B C, D E F, quarum axes ſint B G, E H, & </s>
            <s xml:id="echoid-s7116" xml:space="preserve">
              <lb/>
            vel ſimul congruant, vt in prima, quinta, & </s>
            <s xml:id="echoid-s7117" xml:space="preserve">ſexta figura, vel inter ſe æ-
              <lb/>
            quidiſtent, vt in ſecunda, tertia, & </s>
            <s xml:id="echoid-s7118" xml:space="preserve">quarta, atque ſe mutuò contingant, vel
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            in vnico puncto I, vt in prima, ſecunda, & </s>
            <s xml:id="echoid-s7119" xml:space="preserve">tertia, vel in duobus tantùm I
              <lb/>
            L, vt in quarta, quinta, & </s>
            <s xml:id="echoid-s7120" xml:space="preserve">ſexta; </s>
            <s xml:id="echoid-s7121" xml:space="preserve">& </s>
            <s xml:id="echoid-s7122" xml:space="preserve">concipiatur modò figura A B C, ma-
              <lb/>
            nente alia D E F, circa axim B G conuerti; </s>
            <s xml:id="echoid-s7123" xml:space="preserve">modò figura D E F, manente
              <lb/>
            altera, ita vt ab ipſis ſolida conoidalia, ſphærica, aut ſphæroidalia deſcri-
              <lb/>
            bantur. </s>
            <s xml:id="echoid-s7124" xml:space="preserve">Dico talia ſolida nunquam ſimul ſecari, ſed vel in vnico puncto I,
              <lb/>
            in quo plana ſe contingunt, ſe quoque mutuò contingere in prima, ſecun-
              <lb/>
            da, & </s>
            <s xml:id="echoid-s7125" xml:space="preserve">tertia, vel in duobus tantùm I, L, in quarta vbi axes B G, E H </s>
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