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

Table of Notes

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          <p>
            <s xml:id="echoid-s5807" xml:space="preserve">Si datum punctum F ſit in axe intra ſectionem, vt in ſecunda figura,
              <lb/>
            quod tamen diſtet à vertice per interuallum non maius dimidio recti B E:
              <lb/>
            </s>
            <s xml:id="echoid-s5808" xml:space="preserve">item F B erit _MINIMA_.</s>
            <s xml:id="echoid-s5809" xml:space="preserve"/>
          </p>
          <note symbol="a" position="right" xml:space="preserve">9. huius
            <lb/>
          ad nu. 1.</note>
          <p>
            <s xml:id="echoid-s5810" xml:space="preserve">Cum verò, in eadem figura,
              <lb/>
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                <image file="0209-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0209-01"/>
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            ſegmentũ F B excedet prædictum
              <lb/>
            recti dimidium: </s>
            <s xml:id="echoid-s5811" xml:space="preserve">dematur B I ęqua-
              <lb/>
            lis ſemi-recto B E, & </s>
            <s xml:id="echoid-s5812" xml:space="preserve">tunc habe-
              <lb/>
            bit H B ad B I maiorem rationem
              <lb/>
            quàm ad B F: </s>
            <s xml:id="echoid-s5813" xml:space="preserve">ſi ergo H F ſecetur
              <lb/>
            in L, ita vt H L ad L F, ſit vt H B
              <lb/>
            ad B I, punctum L omnino cadet
              <lb/>
            inter B & </s>
            <s xml:id="echoid-s5814" xml:space="preserve">F; </s>
            <s xml:id="echoid-s5815" xml:space="preserve">itaque ducta A L C
              <lb/>
            ordinatim axi applicata, iunctaq;
              <lb/>
            </s>
            <s xml:id="echoid-s5816" xml:space="preserve">F A. </s>
            <s xml:id="echoid-s5817" xml:space="preserve">Dico ipſam F A eſſe _MINI-_
              <lb/>
            _MAM_ quæſitam.</s>
            <s xml:id="echoid-s5818" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5819" xml:space="preserve">Ducta enim ex A
              <note symbol="b" position="right" xlink:label="note-0209-02" xlink:href="note-0209-02a" xml:space="preserve">2. pr. h.</note>
            A M, quæ axi occurret in M. </s>
            <s xml:id="echoid-s5820" xml:space="preserve">Erit rectangulum H L M ad
              <note symbol="c" position="right" xlink:label="note-0209-03" xlink:href="note-0209-03a" xml:space="preserve">24. pri-
                <lb/>
              mi conic.</note>
            L A, vt tranſuerſum latus ad rectum, vel vt G B ad B E; </s>
            <s xml:id="echoid-s5821" xml:space="preserve">vel ſumptis ſubduplis, vt H B ad B I; </s>
            <s xml:id="echoid-s5822" xml:space="preserve">vel, ob conſtructionem, vt H L ad L F; </s>
            <s xml:id="echoid-s5823" xml:space="preserve">vel,
              <lb/>
              <note symbol="d" position="right" xlink:label="note-0209-04" xlink:href="note-0209-04a" xml:space="preserve">37. ibid.</note>
            ſumpta communi altitudine L M, vt idem rectangulum H L M ad rectan-
              <lb/>
            gulum F L M: </s>
            <s xml:id="echoid-s5824" xml:space="preserve">ergo quadratum L A æquabitur rectangulo F L M, ſed eſt
              <lb/>
            A L ipſi F M perpendicularis: </s>
            <s xml:id="echoid-s5825" xml:space="preserve">quare angulus F A M rectus erit, ſed A
              <note symbol="e" position="right" xlink:label="note-0209-05" xlink:href="note-0209-05a" xml:space="preserve">203. Se-
                <lb/>
              pt. Pappi.</note>
            ſectionem contingit in A: </s>
            <s xml:id="echoid-s5826" xml:space="preserve">ergo F A eſt _MINIMA_ ducibilium ex F ad
              <lb/>
            Hyperbolæ peripheriam A B C, eſt autem F C ęqualis F A: </s>
            <s xml:id="echoid-s5827" xml:space="preserve">vnde
              <note symbol="f" position="right" xlink:label="note-0209-06" xlink:href="note-0209-06a" xml:space="preserve">11. h. ad
                <lb/>
              num. 1.</note>
            hoc caſu duę erunt _MINIMAE_, &</s>
            <s xml:id="echoid-s5828" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5829" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s5830" xml:space="preserve">At ſi datum punctum F fuerit in axe coniugato H F, vt in tertia figu-
              <lb/>
            ra. </s>
            <s xml:id="echoid-s5831" xml:space="preserve">Diuidatur F H in I, ita vt F I ad I H ſit vt tranſuerſum G B ad rectũ
              <lb/>
            B E, & </s>
            <s xml:id="echoid-s5832" xml:space="preserve">per I agatur I A axi æquidiſtans, quæ in vno tantùm puncto A
              <lb/>
            Hyperbolæ occurret. </s>
            <s xml:id="echoid-s5833" xml:space="preserve">Dico iunctam F A eſſe _MINIMAM_ quæſitam.</s>
            <s xml:id="echoid-s5834" xml:space="preserve"/>
          </p>
          <note symbol="g" position="right" xml:space="preserve">26. pri-
            <lb/>
          mi conic.</note>
          <p>
            <s xml:id="echoid-s5835" xml:space="preserve">Producatur F A axi occurrens
              <lb/>
              <figure xlink:label="fig-0209-02" xlink:href="fig-0209-02a" number="172">
                <image file="0209-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0209-02"/>
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            in L, cui applicetur A M, duca-
              <lb/>
              <note symbol="h" position="right" xlink:label="note-0209-08" xlink:href="note-0209-08a" xml:space="preserve">2. pr. h.</note>
            turque ex A contingens A N,
              <note symbol="i" position="right" xlink:label="note-0209-09" xlink:href="note-0209-09a" xml:space="preserve">24. primi
                <lb/>
              conic.</note>
            axi occurret in Q. </s>
            <s xml:id="echoid-s5836" xml:space="preserve">Erit in trian- gulo F L H, ob parallelas, H M ad
              <lb/>
            ad M L, vt F A ad A L, vel vt F I
              <lb/>
            ad I H; </s>
            <s xml:id="echoid-s5837" xml:space="preserve">vel vt tranſuerſum ad re-
              <lb/>
            ctum per conſtructionem; </s>
            <s xml:id="echoid-s5838" xml:space="preserve">vel vt re-
              <lb/>
              <note symbol="l" position="right" xlink:label="note-0209-10" xlink:href="note-0209-10a" xml:space="preserve">37. ibid.</note>
            ctangulum H M N ad quadratum M A, ſed eadem H M ad M L, (ſum-
              <lb/>
            pta communi altitudine M N) eſt
              <lb/>
            vt idem rectangulum H M N ad re-
              <lb/>
            ctangulum L M N; </s>
            <s xml:id="echoid-s5839" xml:space="preserve">vnde quadratum
              <lb/>
            M A, æquabitur rectangulo N M L, & </s>
            <s xml:id="echoid-s5840" xml:space="preserve">eſt A M ipſi L N perpendicularis:
              <lb/>
            </s>
            <s xml:id="echoid-s5841" xml:space="preserve">quare angulus L A N, & </s>
            <s xml:id="echoid-s5842" xml:space="preserve">qui ei deinceps eſt F A N rectus erit, ſed A
              <note symbol="m" position="right" xlink:label="note-0209-11" xlink:href="note-0209-11a" xml:space="preserve">203. Se-
                <lb/>
              pt. Pappi.</note>
            ſectionem contingit, ergo F A eſt _MINIMA_ quæſita.</s>
            <s xml:id="echoid-s5843" xml:space="preserve"/>
          </p>
          <note symbol="n" position="right" xml:space="preserve">10. h.</note>
          <p>
            <s xml:id="echoid-s5844" xml:space="preserve">Si autem datum punctum F ſit extra Hyperbolen inter axem coniuga-
              <lb/>
            tum S H T, & </s>
            <s xml:id="echoid-s5845" xml:space="preserve">ſectionis peripheriam, vt in quarta, & </s>
            <s xml:id="echoid-s5846" xml:space="preserve">quinta figura, </s>
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