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

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        <div xml:id="echoid-div320" type="section" level="1" n="137">
          <head xml:id="echoid-head142" xml:space="preserve">COROLL. I.</head>
          <p>
            <s xml:id="echoid-s3385" xml:space="preserve">EX quinque proximè præcedentibus problematibus ſatis conſtat, _MAXI-_
              <lb/>
            _MAM_, vel _MINIMAM_ Hyperbolen, inſcriptam, vel circumſcriptam
              <lb/>
            cuilibet datæ per punctum intra, vel extra Hyperbolen datũ in locis poſſibili-
              <lb/>
            bus, ad eandem regulam, aut concentricè adſcriptam, vel cuius centrum pro
              <lb/>
            inſcripta cadat infra centrum datæ, & </s>
            <s xml:id="echoid-s3386" xml:space="preserve">pro circumſcripta cadat vltra, ſemper
              <lb/>
            eidem datæ Hyperbolæ ſimilem eſſe.</s>
            <s xml:id="echoid-s3387" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div321" type="section" level="1" n="138">
          <head xml:id="echoid-head143" xml:space="preserve">COROLL. II.</head>
          <p>
            <s xml:id="echoid-s3388" xml:space="preserve">PAtet quoque, _MAXIMAM_ Hyperbolarum datæ Hyperbolæ ſimilium,
              <lb/>
            per datum intra ipſam punctum inſcriptarum, eſſe concentricam, cum
              <lb/>
            hæc, inter ſimiles, ſit _MAXIMORVM_ laterum. </s>
            <s xml:id="echoid-s3389" xml:space="preserve">Item _MINIMAM_ Hyperbola-
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            rum datæ Hyperbolæ ſimilium per datum extra ipſam punctum in angulo
              <lb/>
            aſymptotali, circumſcriptarum, eſſe pariter concentricam, cum eadem, in-
              <lb/>
            ter ſimiles, ſit _MINIMORV M_ laterum.</s>
            <s xml:id="echoid-s3390" xml:space="preserve"/>
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        <div xml:id="echoid-div322" type="section" level="1" n="139">
          <head xml:id="echoid-head144" xml:space="preserve">PROBL. XXIII. PROP. LVII.</head>
          <p>
            <s xml:id="echoid-s3391" xml:space="preserve">Datis magnitudine, & </s>
            <s xml:id="echoid-s3392" xml:space="preserve">poſitione cuiuslibet coni- ſectionis dia-
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            metri ſegmento, & </s>
            <s xml:id="echoid-s3393" xml:space="preserve">vna applicatarum, & </s>
            <s xml:id="echoid-s3394" xml:space="preserve">pro Hyperbola, & </s>
            <s xml:id="echoid-s3395" xml:space="preserve">Ellipſi
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            dato etiam tranſuerſo latere; </s>
            <s xml:id="echoid-s3396" xml:space="preserve">imperatam coni-ſectionem deſcri-
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            bere.</s>
            <s xml:id="echoid-s3397" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3398" xml:space="preserve">SIt in qualibet ſigura, pro quacunque coni-ſectione, datum magnitudine,
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            & </s>
            <s xml:id="echoid-s3399" xml:space="preserve">poſitione diametri ſegmentum AB, & </s>
            <s xml:id="echoid-s3400" xml:space="preserve">vna applicatarum CD, & </s>
            <s xml:id="echoid-s3401" xml:space="preserve">pro
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            Hyperbola, & </s>
            <s xml:id="echoid-s3402" xml:space="preserve">Ellipſi in ſecunda, & </s>
            <s xml:id="echoid-s3403" xml:space="preserve">tertia, datum ſit quoque rectum latus
              <lb/>
            AF, quod pro Hyperbola in ſecunda vltra BA ipſi in directum ponatur, & </s>
            <s xml:id="echoid-s3404" xml:space="preserve">in
              <lb/>
            tertia, ex A ad partes B: </s>
            <s xml:id="echoid-s3405" xml:space="preserve">oportet circa diametrum AB, ſuper applicatam
              <lb/>
            CD, quæſitam coni-ſectionem deſcribere.</s>
            <s xml:id="echoid-s3406" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3407" xml:space="preserve">Fiat in ſingulis figuris, vt
              <lb/>
              <figure xlink:label="fig-0125-01" xlink:href="fig-0125-01a" number="90">
                <image file="0125-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0125-01"/>
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            AB ad BC, ita BC ad BE
              <lb/>
            ipſi BC in directum poſitã,
              <lb/>
            & </s>
            <s xml:id="echoid-s3408" xml:space="preserve">per E, in prima figura,
              <lb/>
            ducta EG parallela ad BA,
              <lb/>
            vel in ſecunda, & </s>
            <s xml:id="echoid-s3409" xml:space="preserve">tertia iun-
              <lb/>
            cta FE, occurrat AG, (quæ
              <lb/>
            ipſi CD æquidiſtet) in G, & </s>
            <s xml:id="echoid-s3410" xml:space="preserve">
              <lb/>
            per verticem A cum data
              <lb/>
            diametro AB, datiſque la-
              <lb/>
            teribus AF, A G deſcriba-
              <lb/>
            tur quæſiti nominis
              <note symbol="a" position="right" xlink:label="note-0125-01" xlink:href="note-0125-01a" xml:space="preserve">5. 6. 7.
                <lb/>
              huius.</note>
            CAD, cuius ordinatim du-
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            ctæ ad angulum ABD </s>
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