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

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          <pb o="40" file="0222" n="222" rhead=""/>
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        <div xml:id="echoid-div647" type="section" level="1" n="257">
          <head xml:id="echoid-head265" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s6211" xml:space="preserve">CVm fuerit axis E B minor ſuo recto B F, ijſdem rationibus oſtende-
              <lb/>
            tur rectangulum D M H minus eſſe quadrato M A, & </s>
            <s xml:id="echoid-s6212" xml:space="preserve">angulum D A
              <lb/>
            M, ſiue D L I minorem eſſe angulo A H M, ſiue angulo I B L, ac propte-
              <lb/>
            rea latus I L maius eſſe latere I B, ideoque rectangulum G I A ad quadra-
              <lb/>
            tum I L, ſiue tranſuerſum axem E B ad rectum B F, minorem habere ratio-
              <lb/>
            nem, quàm idem rectangulum G I A ad quadratum I B, vel quàm tranſuer-
              <lb/>
            fa G A ad rectum A K.</s>
            <s xml:id="echoid-s6213" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div648" type="section" level="1" n="258">
          <head xml:id="echoid-head266" xml:space="preserve">COROLL.</head>
          <p>
            <s xml:id="echoid-s6214" xml:space="preserve">EX his patet, in Hyperbola, cuius axis tranſuerſus ſit maior recto, maio-
              <lb/>
            rem eſſe rationem axis ad propriumrectum, quàm cuiuslibet aliæ trãſ-
              <lb/>
            uerſæ diametri ad proprium rectum.</s>
            <s xml:id="echoid-s6215" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6216" xml:space="preserve">Et ſi axis, ſuo recto æqualis fuerit, axem ad proprium rectum eandem ra-
              <lb/>
            tionem habere, quàm quęlibet alia tranſuerſa ad proprium rectum, ob ęqua-
              <lb/>
            litatem.</s>
            <s xml:id="echoid-s6217" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6218" xml:space="preserve">Si denique axis ſuo recto fuerit minor, minorem eſſe rationem inter axem,
              <lb/>
            ac proprium rectum, quàm inter quamcunque aliam diametrum propriumq;
              <lb/>
            </s>
            <s xml:id="echoid-s6219" xml:space="preserve">rectum. </s>
            <s xml:id="echoid-s6220" xml:space="preserve">Sed hæc ſunt præter inſtitutum noſtrum, & </s>
            <s xml:id="echoid-s6221" xml:space="preserve">fuſim à præclariſſimo
              <lb/>
            Mydorgio pertractata.</s>
            <s xml:id="echoid-s6222" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6223" xml:space="preserve">Hinc, humanum eſſe errare deprehenditur, cum propoſitio 70. </s>
            <s xml:id="echoid-s6224" xml:space="preserve">de Hy-
              <lb/>
            perbola Gregorij à Sancto Vincentio, contrarium his falsò concludat cx
              <lb/>
            præcedenti 69. </s>
            <s xml:id="echoid-s6225" xml:space="preserve">in qua (pace tanti Viri dictum ſit) neſcio quo fato halluci-
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            natus eſt.</s>
            <s xml:id="echoid-s6226" xml:space="preserve"/>
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        <div xml:id="echoid-div649" type="section" level="1" n="259">
          <head xml:id="echoid-head267" xml:space="preserve">LEMMA IX. PROP. XXXI.</head>
          <p>
            <s xml:id="echoid-s6227" xml:space="preserve">Si quatuor magnitudinum, prima A ad ſecundam B minorem
              <lb/>
            habuerit rationem, quàm tertia C D ad quartam E, ſitque prima
              <lb/>
            maior ſecunda, erit tertia maior quarta.</s>
            <s xml:id="echoid-s6228" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6229" xml:space="preserve">FIat enim vt A ad B, ita C F ad E; </s>
            <s xml:id="echoid-s6230" xml:space="preserve">cum
              <lb/>
              <figure xlink:label="fig-0222-01" xlink:href="fig-0222-01a" number="184">
                <image file="0222-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0222-01"/>
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            ergo A ad B minorem habeat ratio-
              <lb/>
            nem quàm C D ad E, habebit quoque C F
              <lb/>
            ad E, minorem quàm C D ad E; </s>
            <s xml:id="echoid-s6231" xml:space="preserve">quare C
              <lb/>
            F erit minor C D. </s>
            <s xml:id="echoid-s6232" xml:space="preserve">Et cum ſit A ad B vt C F
              <lb/>
            ad E, dataque ſit A, maior B, erit C F
              <lb/>
            maior E, & </s>
            <s xml:id="echoid-s6233" xml:space="preserve">eò magis C D maior eadem
              <lb/>
            E. </s>
            <s xml:id="echoid-s6234" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s6235" xml:space="preserve">c.</s>
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