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

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              <pb o="26" file="0208" n="208" rhead=""/>
            in F, G (nam Parabole A B C eſt _MINIMA_ Ellipſi F B G
              <note symbol="a" position="left" xlink:label="note-0208-01" xlink:href="note-0208-01a" xml:space="preserve">ibidem.</note>
            ptibilium) è quorum altero F ducta ſit ordinata F H I communem axem
              <lb/>
              <note symbol="b" position="left" xlink:label="note-0208-02" xlink:href="note-0208-02a" xml:space="preserve">2. primi
                <lb/>
              huius.</note>
            in H, regulam verò ſecante
              <unsure/>
            in I; </s>
            <s xml:id="echoid-s5787" xml:space="preserve">ſitque F L Parabolen contingens ad F, axemque ſecans in L.</s>
            <s xml:id="echoid-s5788" xml:space="preserve"/>
          </p>
          <note symbol="c" position="left" xml:space="preserve">24. pri-
            <lb/>
          mi conic.</note>
          <figure number="169">
            <image file="0208-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0208-01"/>
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          <p>
            <s xml:id="echoid-s5789" xml:space="preserve">Iam, in triangulo E B D cum ſit E B dupla B D, erit I H dupla H D,
              <lb/>
            ſed eſt quoque L H dupla H B, quare vt L H ad H B, ita I H ad H D:
              <lb/>
            </s>
            <s xml:id="echoid-s5790" xml:space="preserve">rectangulum ergo L H D æquale eſt rectangulo B H I, ſiue quadrato
              <note symbol="d" position="left" xlink:label="note-0208-04" xlink:href="note-0208-04a" xml:space="preserve">Coroll.
                <lb/>
              primæ 1.
                <lb/>
              huius.</note>
            H, eſtque F H ipſi L D perpendicularis, quare angulus D F L rectus & </s>
            <s xml:id="echoid-s5791" xml:space="preserve">F L Parabolen contingit in F: </s>
            <s xml:id="echoid-s5792" xml:space="preserve">vnde D F eſt _MINIMA_ ducibilium
              <note symbol="e" position="left" xlink:label="note-0208-05" xlink:href="note-0208-05a" xml:space="preserve">203. Se-
                <lb/>
              pt. Pappi.</note>
            dato puncto D ad peripheriam Parabolæ F B G. </s>
            <s xml:id="echoid-s5793" xml:space="preserve">Conſimili ratione oſten-
              <lb/>
            detur, quamlibet aliam inſcriptam P B R Ellipſis peripheriam B F G D
              <lb/>
              <note symbol="f" position="left" xlink:label="note-0208-06" xlink:href="note-0208-06a" xml:space="preserve">11. huius
                <lb/>
              ad nu. 1.</note>
            ſecare, vt in P, R, & </s>
            <s xml:id="echoid-s5794" xml:space="preserve">iunctam D P, vel D R eſſe _MINIMAM_, &</s>
            <s xml:id="echoid-s5795" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5796" xml:space="preserve">Qua-
              <lb/>
            re ſemita _MINIMARV M_ ex D ad huiuſmodi Parabolarum peripherias, eſt
              <lb/>
            prædictæ Ellipſis perimeter. </s>
            <s xml:id="echoid-s5797" xml:space="preserve">Quod oſtendere propoſitum fuit.</s>
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          <head xml:id="echoid-head251" xml:space="preserve">PROBL. II. PROP. XXII.</head>
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            <s xml:id="echoid-s5799" xml:space="preserve">A dato puncto, ad datę Hyperbolæ peripheriam, MINI-
              <lb/>
            MAM rectam lineam ducere.</s>
            <s xml:id="echoid-s5800" xml:space="preserve"/>
          </p>
          <figure number="170">
            <image file="0208-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0208-02"/>
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          <p>
            <s xml:id="echoid-s5801" xml:space="preserve">SIt data Hyperbole A B C,
              <lb/>
            cuius axis B D, rectum B E
              <lb/>
            tranſuerfum verò B G, centrum
              <lb/>
            H, & </s>
            <s xml:id="echoid-s5802" xml:space="preserve">datum vbicunque ſit pun-
              <lb/>
            ctum F. </s>
            <s xml:id="echoid-s5803" xml:space="preserve">Oportet ex F ad Hyper-
              <lb/>
            bolæ peripheriam A B C _MINI-_
              <lb/>
            _MAM_ rectam lineam ducere.</s>
            <s xml:id="echoid-s5804" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5805" xml:space="preserve">Si primò datum punctum F,
              <lb/>
            in prima figura fuerit in axe pro-
              <lb/>
            ducto, extra Hyperbolen, ipſa
              <lb/>
            F B erit _MINIMA_.</s>
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          <note symbol="g" position="left" xml:space="preserve">10. h.</note>
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