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

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          <p>
            <s xml:id="echoid-s5862" xml:space="preserve">
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            tranſuerſum latus ad rectum, per conſtructionem, vel vt
              <note symbol="a" position="right" xlink:label="note-0211-01" xlink:href="note-0211-01a" xml:space="preserve">37. primi
                <lb/>
              conic.</note>
            H P Q ad quadratum P A; </s>
            <s xml:id="echoid-s5863" xml:space="preserve">ſed eadem H P ad P R (ſumpta communi al-
              <lb/>
            titudine P Q) eſt vt idem rectangulum H P Q ad rectangulum R P Q,
              <lb/>
            quare quadratum P A æquabitur rectangulo R P Q, eſtque A P ipſi R Q
              <lb/>
            perpendicularis, vnde angulus R A Q, & </s>
            <s xml:id="echoid-s5864" xml:space="preserve">in quarta, & </s>
            <s xml:id="echoid-s5865" xml:space="preserve">quinta figura, qui
              <lb/>
            ei deinceps Q A F rectus erit, ſed A Q ſectionem contingit, quare
              <note symbol="b" position="right" xlink:label="note-0211-02" xlink:href="note-0211-02a" xml:space="preserve">203. Se-
                <lb/>
              pt. Pappi.</note>
            pendicularis F A erit _MINIMA_ quæſita.</s>
            <s xml:id="echoid-s5866" xml:space="preserve"/>
          </p>
          <note symbol="c" position="right" xml:space="preserve">10. et 11.
            <lb/>
          huius ad
            <lb/>
          num. 1.</note>
          <p>
            <s xml:id="echoid-s5867" xml:space="preserve">Si denique datum punctum F ſit extra Hyperbolen, ſed ſupra axem
              <lb/>
            coniugatum H S, vt in octaua, & </s>
            <s xml:id="echoid-s5868" xml:space="preserve">nona figura. </s>
            <s xml:id="echoid-s5869" xml:space="preserve">A centro H date Hyper-
              <lb/>
            bolæ ad datum punctum F ducatur H F, quæ ita ſecetur in I, ita vt H I
              <lb/>
            ad I F, ſit vt tranſuerſum latus G B ad rectum B E, ſumptaque H L ęqua-
              <lb/>
            li ipſi I F, per I agatur I O N ordinatim ductis æquidiſtans, & </s>
            <s xml:id="echoid-s5870" xml:space="preserve">per L re-
              <lb/>
            cta L O M axi H B D parallela, & </s>
            <s xml:id="echoid-s5871" xml:space="preserve">in angulo N O M per datum punctum
              <lb/>
            H (quod eſt centrum Hyperbolæ) deſcribatur alia Hyperbole H A,
              <note symbol="d" position="right" xlink:label="note-0211-04" xlink:href="note-0211-04a" xml:space="preserve">4. ſecun-
                <lb/>
              diconic.</note>
            alteram A B C in vno tantùm puncto A ſecabit. </s>
            <s xml:id="echoid-s5872" xml:space="preserve">Dico iunctam F A
              <note symbol="e" position="right" xlink:label="note-0211-05" xlink:href="note-0211-05a" xml:space="preserve">12. h.</note>
            _MINIMAM_ quæſitam.</s>
            <s xml:id="echoid-s5873" xml:space="preserve"/>
          </p>
          <figure number="174">
            <image file="0211-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0211-01"/>
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          <p>
            <s xml:id="echoid-s5874" xml:space="preserve">Sit A P axi ordinatim applicata, & </s>
            <s xml:id="echoid-s5875" xml:space="preserve">A Q ex A ſectionem
              <note symbol="f" position="right" xlink:label="note-0211-06" xlink:href="note-0211-06a" xml:space="preserve">2. pr. h.</note>
            axemque ſecans in Q, iungaturque IP. </s>
            <s xml:id="echoid-s5876" xml:space="preserve">Iam in Hyperbola A H,
              <note symbol="g" position="right" xlink:label="note-0211-07" xlink:href="note-0211-07a" xml:space="preserve">24. primi
                <lb/>
              conic.</note>
            aſymptoti O N, O M, ſumptum eſt punctum P, à quo ductæ ſunt P A,
              <lb/>
            P H aſymptotis æquidiſtantes, & </s>
            <s xml:id="echoid-s5877" xml:space="preserve">Hyperbolæ occurrentes in A, H, & </s>
            <s xml:id="echoid-s5878" xml:space="preserve">ab
              <lb/>
            eorum altero H ducta eſt H L I vtranque aſymptoton ſecans in I, L, eſt-
              <lb/>
            que I F in directum, & </s>
            <s xml:id="echoid-s5879" xml:space="preserve">æqualis poſita ipſi H L, rectaque F A coniungit
              <lb/>
            extremum F cum altero datorum A; </s>
            <s xml:id="echoid-s5880" xml:space="preserve">ipſa F A æquidiſtabit iungenti
              <note symbol="h" position="right" xlink:label="note-0211-08" xlink:href="note-0211-08a" xml:space="preserve">15. h.</note>
            P; </s>
            <s xml:id="echoid-s5881" xml:space="preserve">ſed H P ſecat I P quare producta ſecabit quoque alteram parallela-
              <lb/>
            rum F A, ſi hæc vltra F A producatur. </s>
            <s xml:id="echoid-s5882" xml:space="preserve">Sit ergo harum occurſus R. </s>
            <s xml:id="echoid-s5883" xml:space="preserve">Erit
              <lb/>
            in triangulo F H R recta H P ad P R, vt H I ad I F, vel vt latus tranſuer-
              <lb/>
            ſum ad rectum, ex conſtructione, vel vt rectangulum H P Q ad
              <note symbol="i" position="right" xlink:label="note-0211-09" xlink:href="note-0211-09a" xml:space="preserve">37. primi
                <lb/>
              conic.</note>
            tum P A, ſed eadem H P ad P R (ſumpta communi altitudine P Q) eſt
              <lb/>
            vt idem rectangulum H P Q ad rectangulum R P Q: </s>
            <s xml:id="echoid-s5884" xml:space="preserve">quare </s>
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