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

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            <s xml:id="echoid-s1654" xml:space="preserve">
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            recto BI, quod excedat BL, eſt
              <note symbol="a" position="left" xlink:label="note-0072-01" xlink:href="note-0072-01a" xml:space="preserve">ibidem.</note>
              <figure xlink:label="fig-0072-01" xlink:href="fig-0072-01a" number="42">
                <image file="0072-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0072-01"/>
              </figure>
            dem maior ipſa HBI, ſed vel ſecat Hy-
              <lb/>
              <note symbol="b" position="left" xlink:label="note-0072-02" xlink:href="note-0072-02a" xml:space="preserve">1. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            perbolen ABC, quod accidit ſi iun- cta regula GL, ac infra contingentem
              <lb/>
            BL producta, ſecet productam regu-
              <lb/>
            lam DE; </s>
            <s xml:id="echoid-s1655" xml:space="preserve">vel cadit extra eandẽ ABC,
              <lb/>
            quando iuncta regula GL, cum
              <note symbol="c" position="left" xlink:label="note-0072-03" xlink:href="note-0072-03a" xml:space="preserve">ibidem.</note>
            gula DE infra eandem contingentem
              <lb/>
            nunquam conueniat. </s>
            <s xml:id="echoid-s1656" xml:space="preserve">Quare huiuſmo-
              <lb/>
            di Hyperbole HBI erit _MAXIMA_
              <lb/>
            quæſita.</s>
            <s xml:id="echoid-s1657" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1658" xml:space="preserve">Si deniq; </s>
            <s xml:id="echoid-s1659" xml:space="preserve">datũ trã ſuerſum latus BM
              <lb/>
            ſit minus tranfuerſo BD, ducatur MF
              <lb/>
            ipſi BE parallela, & </s>
            <s xml:id="echoid-s1660" xml:space="preserve">cũ tranſuerſo BM,
              <lb/>
            ac recto BF, per vcrticem B, Hyper-
              <lb/>
            bolæ ABC adſcribatur
              <note symbol="d" position="left" xlink:label="note-0072-04" xlink:href="note-0072-04a" xml:space="preserve">6. huius.</note>
            HBI, quæ ipſi ABC ſimilis erit, cum
              <lb/>
            ſit tranſuerſum DB ad rectum BE, vt
              <lb/>
            tranſuerſum MB ad rectum BF, eritq;
              <lb/>
            </s>
            <s xml:id="echoid-s1661" xml:space="preserve">inſcripta Hyperbolæ ABC, cum ſit minorum laterum. </s>
            <s xml:id="echoid-s1662" xml:space="preserve">Dico hanc
              <note symbol="e" position="left" xlink:label="note-0072-05" xlink:href="note-0072-05a" xml:space="preserve">5. prop.
                <lb/>
              19. huius.</note>
            _MAXIMAM_ quæſitam.</s>
            <s xml:id="echoid-s1663" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1664" xml:space="preserve">Quoniã quælibet alia, quæ cum recto minore ipſo BF adſcribitur, ſemper
              <lb/>
              <note symbol="f" position="left" xlink:label="note-0072-06" xlink:href="note-0072-06a" xml:space="preserve">2. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            eſt minor HBI, quæ verò cum recto, quod excedat BF, eſt quidem maior ipſa HBI, ſed vel ſecat Hyperbolen ABC, quod ſit cum rectum cadit inter
              <lb/>
            F, & </s>
            <s xml:id="echoid-s1665" xml:space="preserve">E, vt in N, nam iuncta regula MN, & </s>
            <s xml:id="echoid-s1666" xml:space="preserve">producta, ſecat regulam
              <note symbol="g" position="left" xlink:label="note-0072-07" xlink:href="note-0072-07a" xml:space="preserve">ibidem.</note>
            infra contingentem BE; </s>
            <s xml:id="echoid-s1667" xml:space="preserve">vel cadit tota extra ABC, quod euenit cũ
              <note symbol="h" position="left" xlink:label="note-0072-08" xlink:href="note-0072-08a" xml:space="preserve">1. Co-
                <lb/>
              rol. prop.
                <lb/>
              19. huius.</note>
            velidem fuerit cum recto BE, vel maius ipſo BE, quale eſt BL; </s>
            <s xml:id="echoid-s1668" xml:space="preserve">tunc enim
              <lb/>
            iuncta regula ML infra contingentem BE, diſiunctim procederet à regula
              <lb/>
              <note symbol="i" position="left" xlink:label="note-0072-09" xlink:href="note-0072-09a" xml:space="preserve">3. 1. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            DE, cum eam ſecaret priſu4;</s>
            <s xml:id="echoid-s1669" xml:space="preserve">s ſupra BE. </s>
            <s xml:id="echoid-s1670" xml:space="preserve">Eſt igitur talis Hy perbole HBI _MA_-
              <lb/>
            _XIMA_ quæſita. </s>
            <s xml:id="echoid-s1671" xml:space="preserve">Quod primò, &</s>
            <s xml:id="echoid-s1672" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1673" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1674" xml:space="preserve">Amplius, ſit data Hyperbole HBI, cuius tranſuerſum latus ſit BD, rectum
              <lb/>
            BE, & </s>
            <s xml:id="echoid-s1675" xml:space="preserve">regula DE, & </s>
            <s xml:id="echoid-s1676" xml:space="preserve">ipſi oporteat per verticem B _MINIMAM_ Hyperbolen
              <lb/>
            circumſcribere, cum dato quolibet tranſuerſo latere.</s>
            <s xml:id="echoid-s1677" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1678" xml:space="preserve">Si datum tranſuerſum circumſcribendæ Hyperbolæ fuerit minus ipſo BD,
              <lb/>
            quale eſt BM: </s>
            <s xml:id="echoid-s1679" xml:space="preserve">adſcribatur datæ HBI, per verticem B Hyperbole
              <note symbol="l" position="left" xlink:label="note-0072-10" xlink:href="note-0072-10a" xml:space="preserve">6. prop.
                <lb/>
              huius.</note>
            cuius tranſuerſum ſit BM, rectum verò ſit idem BE: </s>
            <s xml:id="echoid-s1680" xml:space="preserve">Nam ipſa erit
              <note symbol="m" position="left" xlink:label="note-0072-11" xlink:href="note-0072-11a" xml:space="preserve">3. Co-
                <lb/>
              rol prop.
                <lb/>
              19. huius.</note>
            ſcripta, eritque _MINIMA_ quæſita; </s>
            <s xml:id="echoid-s1681" xml:space="preserve">quoniam quælibet alia adſcripta cum
              <lb/>
            tranſuerſo BM, ſed cum recto quod excedat BE, quale eſſet BL, eſt maior ipſa ABC; </s>
            <s xml:id="echoid-s1682" xml:space="preserve">quælibet verò adſcripta, cum eodem tranſuerſo BM, & </s>
            <s xml:id="echoid-s1683" xml:space="preserve">cum re-
              <lb/>
              <note symbol="n" position="left" xlink:label="note-0072-12" xlink:href="note-0072-12a" xml:space="preserve">2. corol.
                <lb/>
              prop. 19.
                <lb/>
              huius.</note>
            cto quod minus ſit BE, eſt quidem minor ipſa ABC, ſed vel ſecat Hyper- bolen HBI, tum cum earum regulæ infra contingentem BE ſe mutuò ſecant,
              <lb/>
              <note symbol="o" position="left" xlink:label="note-0072-13" xlink:href="note-0072-13a" xml:space="preserve">ibidem.</note>
            vel cadit intra HBI, quando earundem regulæ infra prædictam
              <note symbol="p" position="left" xlink:label="note-0072-14" xlink:href="note-0072-14a" xml:space="preserve">2. Co-
                <lb/>
              roll prop.
                <lb/>
              19. huius.</note>
            tem nunquam ſimul conueniant. </s>
            <s xml:id="echoid-s1684" xml:space="preserve">Quare ipſa ABC erit _MINIMA_ quæſita.</s>
            <s xml:id="echoid-s1685" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1686" xml:space="preserve">Si autem datum tranſuerſum latus fuerit maius ipſo BD quale eſt BG; </s>
            <s xml:id="echoid-s1687" xml:space="preserve">du-
              <lb/>
              <note symbol="q" position="left" xlink:label="note-0072-15" xlink:href="note-0072-15a" xml:space="preserve">ibidem.</note>
            catur GL parallela ad DE, & </s>
            <s xml:id="echoid-s1688" xml:space="preserve">datæ Hyperbolæ HBI cum tranſuerſo BG, re-
              <lb/>
            ctoque BL adſcribatur per B Hyperbole ABC, quæ datæ HBI erit
              <note symbol="r" position="left" xlink:label="note-0072-16" xlink:href="note-0072-16a" xml:space="preserve">6. huius.</note>
            cum ipſarum latera ſint proportionalia, eritque circumſcripta, cum ſit </s>
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