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

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          <pb o="47" file="0071" n="71" rhead=""/>
          <p>
            <s xml:id="echoid-s1620" xml:space="preserve">Quoniam, quæcunque ſectio ſimilis ſectioni DBE adſcripta per B ſectioni
              <lb/>
            ABC, cumrecto BM, quod minus ſit recto BF, minor eſt ſectione
              <note symbol="a" position="right" xlink:label="note-0071-01" xlink:href="note-0071-01a" xml:space="preserve">5. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            quælibet verò adſcripta cum recto BO; </s>
            <s xml:id="echoid-s1621" xml:space="preserve">quod maius ſit recto BF eſt quidem maior ipſa DBE, ſed datam ABC omnino ſecat; </s>
            <s xml:id="echoid-s1622" xml:space="preserve"> quoniam ipſius
              <note symbol="b" position="right" xlink:label="note-0071-02" xlink:href="note-0071-02a" xml:space="preserve">ibidem.</note>
            ON, quæ æquidiſtat regulæ FH, ſecat infra contingentem BF
              <note symbol="c" position="right" xlink:label="note-0071-03" xlink:href="note-0071-03a" xml:space="preserve">1. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            FIG, nam altera parallelarum FH ab eadem FIG ſecatur in F: </s>
            <s xml:id="echoid-s1623" xml:space="preserve">vnde ipſa
              <lb/>
            DBE eſt _MINIMA_ ſibi ſimilium, &</s>
            <s xml:id="echoid-s1624" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1625" xml:space="preserve">Quod erat primò, &</s>
            <s xml:id="echoid-s1626" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1627" xml:space="preserve"/>
          </p>
          <note symbol="d" position="right" xml:space="preserve">5. prop.
            <lb/>
          19. huius.</note>
          <p>
            <s xml:id="echoid-s1628" xml:space="preserve">Nunc verò ſit coni-ſectio DBE, cuius rectum BF, & </s>
            <s xml:id="echoid-s1629" xml:space="preserve">regula FH, ipſique
              <lb/>
            circumſcripta ſit cum eodem recto BF, per verticem B coni-ſectio ABC, quæ
              <lb/>
            erit _MINIMA_ circumſcripta, per iam demonſtrata, eiuſque regula ſit GFI.
              <lb/>
            </s>
            <s xml:id="echoid-s1630" xml:space="preserve">Dico hanc _MINIMAM_ ſectionem ABC eſſe quoque _MINIMAM_ ſibi ſimi-
              <lb/>
            lium, eidem ſectioni DBE per verticem circumſcriptarum.</s>
            <s xml:id="echoid-s1631" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1632" xml:space="preserve">Nam quælibet coni-ſectio ſimilis ABC, adſcripta per B datæ ſectioni DB
              <lb/>
            E, cum recto BO, quod maius ſit recto BF maior eſt ſectione ABC,
              <note symbol="e" position="right" xlink:label="note-0071-05" xlink:href="note-0071-05a" xml:space="preserve">5. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            libet verò adſcripta cum recto BM, quod minus ſit recto BF eſt quidem
              <lb/>
            minor ipſa ABC, ſed datam ſecat DBE, quoniam ipſius regula QM, quę re-
              <lb/>
            gulæ GFI æquidiſtat, ſecat regulam FH, nam altera parallelarum GFI ſecat
              <lb/>
            infra BF ipſam FH in F. </s>
            <s xml:id="echoid-s1633" xml:space="preserve">Quare ipſa ABC eſt _MINIMA_ ſibi ſimilium, &</s>
            <s xml:id="echoid-s1634" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s1635" xml:space="preserve">Quod erat ſecundò, &</s>
            <s xml:id="echoid-s1636" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1637" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div142" type="section" level="1" n="81">
          <head xml:id="echoid-head86" xml:space="preserve">PROBL. VIII. PROP. XXIII.</head>
          <p>
            <s xml:id="echoid-s1638" xml:space="preserve">Datæ Hyperbolæ, cum dato quocunque tranſuerſo latere, per
              <lb/>
            ipſius verticem MAXIMAM Hyperbolen inſcribere: </s>
            <s xml:id="echoid-s1639" xml:space="preserve">& </s>
            <s xml:id="echoid-s1640" xml:space="preserve">è contra.</s>
            <s xml:id="echoid-s1641" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1642" xml:space="preserve">Datæ Hyperbolæ cum dato quolibet tranſuerſo latere per eius
              <lb/>
            verticem MINIMAM Hyperbolen circumſcribere.</s>
            <s xml:id="echoid-s1643" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1644" xml:space="preserve">SIt data Hyperbole ABC, cuius
              <lb/>
              <figure xlink:label="fig-0071-01" xlink:href="fig-0071-01a" number="41">
                <image file="0071-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0071-01"/>
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            vertex B, tranſuerſum latus BD,
              <lb/>
            rectum BE, & </s>
            <s xml:id="echoid-s1645" xml:space="preserve">regula DE: </s>
            <s xml:id="echoid-s1646" xml:space="preserve">oportet pri-
              <lb/>
            mò cum dato quocunque alio tranſ-
              <lb/>
            uerſo latere, per verticem B, _MAXI_-
              <lb/>
            _MAM_ Hyperbolen inſcribere.</s>
            <s xml:id="echoid-s1647" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1648" xml:space="preserve">Iam, vel datum tranſuerſum latus
              <lb/>
            exceditranſuerſum BD, datę Hyper-
              <lb/>
            bolæ, vel eodem minus eſt. </s>
            <s xml:id="echoid-s1649" xml:space="preserve">Si pri-
              <lb/>
            mùm quale eſt BG; </s>
            <s xml:id="echoid-s1650" xml:space="preserve"> adſcribatur Hy- perbolę ABC per verticem B, cum
              <lb/>
              <note symbol="a" position="right" xlink:label="note-0071-06" xlink:href="note-0071-06a" xml:space="preserve">6. huius.</note>
            dato tranſuerſo BG, & </s>
            <s xml:id="echoid-s1651" xml:space="preserve">cum eodem
              <lb/>
            recto BE Hyperbole HBI. </s>
            <s xml:id="echoid-s1652" xml:space="preserve">Patet ip-
              <lb/>
            ſam HBI datæ ABC eſſe inſcriptam;</s>
            <s xml:id="echoid-s1653" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-0071-07" xlink:href="note-0071-07a" xml:space="preserve">3. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            quàm dico eſſe _MAXIMAM_: </s>
            <s xml:id="echoid-s1654" xml:space="preserve">quoniam
              <lb/>
            quælibet alia ipſi HBI adſcripta cum
              <lb/>
            eodem tranſuerſo BG, ſed cumrecto,
              <lb/>
            quod ſit minus BE, ſemper minor
              <note symbol="c" position="right" xlink:label="note-0071-08" xlink:href="note-0071-08a" xml:space="preserve">2. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            ipſa HBI, quelibet vero adſcripta </s>
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