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

Table of Notes

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        <div xml:id="echoid-div95" type="section" level="1" n="56">
          <head xml:id="echoid-head61" xml:space="preserve">THEOR. IX. PROP. XVII.</head>
          <p>
            <s xml:id="echoid-s1250" xml:space="preserve">Parabole ſeſquitertia eſt trianguli eandem ipſi baſim, & </s>
            <s xml:id="echoid-s1251" xml:space="preserve">ean-
              <lb/>
            dem altitudinem habentis.</s>
            <s xml:id="echoid-s1252" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1253" xml:space="preserve">REpetito præcedenti diagrammate, dico Parabolen AB8 ſeſquitertiam
              <lb/>
            eſſe inſcripti trianguli AB8.</s>
            <s xml:id="echoid-s1254" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1255" xml:space="preserve">Nam ducta G9 parallela ad AC deſcribatur ſemi Parabole 9, 8, cuius dia-
              <lb/>
            meter ſit 9C, & </s>
            <s xml:id="echoid-s1256" xml:space="preserve">ſemi-applicata ſit C8, æqualis baſi AC Parabolæ
              <lb/>
            AGC. </s>
            <s xml:id="echoid-s1257" xml:space="preserve">Et cum ſit ſemi-Parabole ABC æqualis ſemi-Parabolæ CB8, &</s>
            <s xml:id="echoid-s1258" xml:space="preserve">
              <note symbol="a" position="right" xlink:label="note-0055-01" xlink:href="note-0055-01a" xml:space="preserve">Coroll.
                <lb/>
              prop. 14. h.</note>
            Parabole AGC æqualis ſemi-Parabolæ C98, ſitque C98 dimidium
              <note symbol="b" position="right" xlink:label="note-0055-02" xlink:href="note-0055-02a" xml:space="preserve">Coroll.
                <lb/>
              prop. 14. h.</note>
            (nam eſt C9 dimidium CB &</s>
            <s xml:id="echoid-s1259" xml:space="preserve">c.) </s>
            <s xml:id="echoid-s1260" xml:space="preserve">erit Parabole AGC dimidium ſemi-Parabo-
              <lb/>
              <note symbol="c" position="right" xlink:label="note-0055-03" xlink:href="note-0055-03a" xml:space="preserve">15. h.</note>
            læ ABC, ſiue æqualis trilineo AHBCGA, ac etiam trilineo AEBH; </s>
            <s xml:id="echoid-s1261" xml:space="preserve">
              <note symbol="d" position="right" xlink:label="note-0055-04" xlink:href="note-0055-04a" xml:space="preserve">16. h.</note>
            totum triangulum AEC ſeſqui alterum erit ſemi-Parabolæ ABC, ſiuc erit
              <lb/>
            vt 6 ad 4, ſed ad triangulum ABC eſt vt 6 ad 3, cum ſit EC dupla CB, vnde
              <lb/>
            ſemi-Parabole ABC ad triangulum ABC, hoc eſt dupla ad duplum, nempe
              <lb/>
            Parabole AB8 ad inſcriptum triangulum AB8, erit vt 4 ad 3. </s>
            <s xml:id="echoid-s1262" xml:space="preserve">Quod demon-
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            ſtrare oportebat.</s>
            <s xml:id="echoid-s1263" xml:space="preserve"/>
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        <div xml:id="echoid-div97" type="section" level="1" n="57">
          <head xml:id="echoid-head62" xml:space="preserve">MONITVM.</head>
          <p style="it">
            <s xml:id="echoid-s1264" xml:space="preserve">VT hoc loco, ex aduerſo indirectæ Antiquorum viæ per duplicem
              <lb/>
            poſitionem, luce clarius pateat quantum facilitatis, breuitatis,
              <lb/>
            atquæ euidentiæ naſciſcatur è noua, directaque methodo (rectè
              <lb/>
            tamen cautèque vſurpata) acutiſsimi Geometræ Caualerij,
              <lb/>
            per indiuiſibilium doctrinam, nobis amiciſsimam, ex hac alteram accipe
              <lb/>
            eiuſdem theorematis demonſtr ationem, conſimili arte cōp@catam, ac in præ-
              <lb/>
            cedenti.</s>
            <s xml:id="echoid-s1265" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div98" type="section" level="1" n="58">
          <head xml:id="echoid-head63" xml:space="preserve">THEOR. X. PROP. XVIII.</head>
          <p>
            <s xml:id="echoid-s1266" xml:space="preserve">Parabole ſeſquitertia eſt trianguli eandem ipſi baſim, & </s>
            <s xml:id="echoid-s1267" xml:space="preserve">ean-
              <lb/>
            dem altitudinem habentis.</s>
            <s xml:id="echoid-s1268" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1269" xml:space="preserve">SIt Parabole ABC, cuius diameter BD, baſis AC: </s>
            <s xml:id="echoid-s1270" xml:space="preserve">dico ipſam ſeſquiter-
              <lb/>
            tiam eſſe inſcripti trianguli ABC.</s>
            <s xml:id="echoid-s1271" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1272" xml:space="preserve">Bifariam enim ſecta AD in G, per quod ducta GF parallela ad DB, & </s>
            <s xml:id="echoid-s1273" xml:space="preserve">per
              <lb/>
            F, FH parallela ad AD, ac deſcriptis, vt in præcedenti figura Parabola
              <lb/>
            AED, & </s>
            <s xml:id="echoid-s1274" xml:space="preserve">portione Parabolæ HCD, cuius diameter ſit HD, & </s>
            <s xml:id="echoid-s1275" xml:space="preserve">ſemi-applica-
              <lb/>
            ta ſit DC ducatur in tota ABC quælibet applicata NI. </s>
            <s xml:id="echoid-s1276" xml:space="preserve">diametrum ſecans in
              <lb/>
            M, eritque NM æqualis ML, & </s>
            <s xml:id="echoid-s1277" xml:space="preserve">ſic de quibuslibet alijs applicatis ipſi AC æ-
              <lb/>
            quidiſtantibus, quare omnes ſimul in portione ABD, omnibus ſimul in por-
              <lb/>
            tione DBC æquales erunt, ſiue portio ABD æqualis DBC, nempè vtraque
              <lb/>
            erit ſemi-Parabole, & </s>
            <s xml:id="echoid-s1278" xml:space="preserve">eadem ratione oſtendetur DHC ſemi-Parabolen eſſe.</s>
            <s xml:id="echoid-s1279" xml:space="preserve"/>
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