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

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        <div xml:id="echoid-div694" type="section" level="1" n="277">
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        <div xml:id="echoid-div695" type="section" level="1" n="278">
          <head xml:id="echoid-head287" xml:space="preserve">THEOR. XXIV. PROP. XXXXIII.</head>
          <p>
            <s xml:id="echoid-s6654" xml:space="preserve">In congruentibus Parabolis per diuerſos vertices ſimul adſcri-
              <lb/>
            ptis, intercepta communium diametrorum ſegmenta inter ſe ſunt
              <lb/>
            æqualia, & </s>
            <s xml:id="echoid-s6655" xml:space="preserve">huiuſmodi Parabolæ dicantur ęquidiſtantes. </s>
            <s xml:id="echoid-s6656" xml:space="preserve">Contin-
              <lb/>
            gentes verò vtranq; </s>
            <s xml:id="echoid-s6657" xml:space="preserve">ſectionem ad terminos eiuſdem diametri inter
              <lb/>
            ſe æquidiſtant.</s>
            <s xml:id="echoid-s6658" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6659" xml:space="preserve">SInt duæ congruentes Parabolæ A B C, D E F per diuerſos vertices B, E
              <lb/>
            ſimul adſcriptæ circa communem diametrum B E H, & </s>
            <s xml:id="echoid-s6660" xml:space="preserve">inter ipſas du-
              <lb/>
            cta ſit quæcunque alia A D ipſi B E parallela, (quæ vtrique Parabolæ con-
              <lb/>
            ueniet in A, D eritque earum communis diameter) atque ex terminis
              <note symbol="a" position="left" xlink:label="note-0240-01" xlink:href="note-0240-01a" xml:space="preserve">26. primi
                <lb/>
              conic.</note>
              <note symbol="b" position="left" xlink:label="note-0240-02" xlink:href="note-0240-02a" xml:space="preserve">46. ibid.</note>
            D, agantur A I, D L Parabolas contingentes in A, D, & </s>
            <s xml:id="echoid-s6661" xml:space="preserve">communi diame-
              <lb/>
            tro B E occurrentes in I, L. </s>
            <s xml:id="echoid-s6662" xml:space="preserve">Dico diametrorum intercepta ſegmenta B
              <note symbol="c" position="left" xlink:label="note-0240-03" xlink:href="note-0240-03a" xml:space="preserve">24. ibid.</note>
            A D æqualia eſſe, & </s>
            <s xml:id="echoid-s6663" xml:space="preserve">contingentes A I, D L inter ſe æquidiſtare.</s>
            <s xml:id="echoid-s6664" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6665" xml:space="preserve">Nam primum patet ex primo Coroll. </s>
            <s xml:id="echoid-s6666" xml:space="preserve">42.
              <lb/>
            </s>
            <s xml:id="echoid-s6667" xml:space="preserve">
              <figure xlink:label="fig-0240-01" xlink:href="fig-0240-01a" number="198">
                <image file="0240-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0240-01"/>
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            primi huius: </s>
            <s xml:id="echoid-s6668" xml:space="preserve">cumq; </s>
            <s xml:id="echoid-s6669" xml:space="preserve">omnes interceptæ B E,
              <lb/>
            A D, &</s>
            <s xml:id="echoid-s6670" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6671" xml:space="preserve">ſint æquales vocentur, huiuſmodi
              <lb/>
            Parabolæ inter ſe ęquidiſtantes. </s>
            <s xml:id="echoid-s6672" xml:space="preserve">Secundum
              <lb/>
            verò, ita oſtenditur.</s>
            <s xml:id="echoid-s6673" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6674" xml:space="preserve">Applicentur ex A, D ad diametrum B H
              <lb/>
            rectæ A G, D H; </s>
            <s xml:id="echoid-s6675" xml:space="preserve">erit A H parallelogram-
              <lb/>
            mum, ex quo G H æqualis erit A D, ſiue
              <lb/>
            ipſi B E, quare dempta, vel addita, vti opus
              <lb/>
            fuerit, communi G E, proueniet B G ęqua-
              <lb/>
            lis H E, & </s>
            <s xml:id="echoid-s6676" xml:space="preserve">dupla I G duplæ L H
              <note symbol="d" position="left" xlink:label="note-0240-04" xlink:href="note-0240-04a" xml:space="preserve">35. ibid.</note>
            erit, & </s>
            <s xml:id="echoid-s6677" xml:space="preserve">eſt G A æqualis H D, & </s>
            <s xml:id="echoid-s6678" xml:space="preserve">angulus
              <lb/>
            I G A angulo L H D æqualis, ergo angu-
              <lb/>
            lus quoque G I A angulo H L D æqualis erit. </s>
            <s xml:id="echoid-s6679" xml:space="preserve">Quare contingentes A I, D
              <lb/>
            L inter ſe æquidiſtant. </s>
            <s xml:id="echoid-s6680" xml:space="preserve">Quod, &</s>
            <s xml:id="echoid-s6681" xml:space="preserve">c.</s>
            <s xml:id="echoid-s6682" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div699" type="section" level="1" n="279">
          <head xml:id="echoid-head288" xml:space="preserve">THEOR. XXV. PROP. XXXXIV.</head>
          <p>
            <s xml:id="echoid-s6683" xml:space="preserve">In Hyperbolis, aut Ellipſibus ſimilibus, & </s>
            <s xml:id="echoid-s6684" xml:space="preserve">concentricis, per
              <lb/>
            diuerſos vertices ſimul adſcriptis, intercepta communium dia-
              <lb/>
            metrorum ſegmenta ad proprias ſemi-diametros vnam eandem-
              <lb/>
            que habent rationem, & </s>
            <s xml:id="echoid-s6685" xml:space="preserve">quæ ſectiones contingunt ad terminos
              <lb/>
            eiuſdem diametri inter ſe æquidiſtant.</s>
            <s xml:id="echoid-s6686" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6687" xml:space="preserve">SInt duæ Hyperbolæ ſimiles in prima figura, vel duæ ſimiles Ellipſes in ſe-
              <lb/>
            cunda, quarum commune centrum ſit G, & </s>
            <s xml:id="echoid-s6688" xml:space="preserve">communis ſemi- diameter
              <lb/>
            G B E, ſitque ducta quæcumque alia G A D, (quæ tamen in Ellipſi cadat in-
              <lb/>
            ter coniugatas ſemi-diametros G E, G N) eritque G A D, item
              <note symbol="e" position="left" xlink:label="note-0240-05" xlink:href="note-0240-05a" xml:space="preserve">47. ibid.</note>
            nis ſectionum ſemi-diameter, ducãturque A L, D M ad terminos A, D </s>
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