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

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        <div xml:id="echoid-div781" type="section" level="1" n="308">
          <p>
            <s xml:id="echoid-s7634" xml:space="preserve">
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            & </s>
            <s xml:id="echoid-s7635" xml:space="preserve">in reliquis, erunt proprijs ſemi- diametris proportionalia, hoc eſt ipſæ
              <lb/>
            portiones æquales erunt. </s>
            <s xml:id="echoid-s7636" xml:space="preserve">De portionibus tandem eiuſdem anguli,
              <note symbol="a" position="right" xlink:label="note-0273-01" xlink:href="note-0273-01a" xml:space="preserve">40. h.</note>
            ſunt triangula, iam notum eſt, quandò baſes ipſorum altitudinibus ſint reci-
              <lb/>
            procè proportionales, ipſa triangula eſſe æqualia. </s>
            <s xml:id="echoid-s7637" xml:space="preserve">Quare, &</s>
            <s xml:id="echoid-s7638" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7639" xml:space="preserve">quod ſecun-
              <lb/>
            dò probandum erat.</s>
            <s xml:id="echoid-s7640" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7641" xml:space="preserve">Haud incongruum, neque inutile duximus hic adnotaſſe Theorema
              <lb/>
            huiuſmodi.</s>
            <s xml:id="echoid-s7642" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div785" type="section" level="1" n="309">
          <head xml:id="echoid-head318" xml:space="preserve">THEOR. XLI. PROP. LXVI.</head>
          <p>
            <s xml:id="echoid-s7643" xml:space="preserve">Æquales portiones eiuſdem coni-ſectionis, vel circuli (quæ
              <lb/>
            tamen in Ellipſi ſint, vel vnà æquales, vel vnà maiores, vel vnà
              <lb/>
            minores ſemi- Ellipſi) ad inſcripta ſibi triangula, (nempè ad ea,
              <lb/>
            quorum baſes eædem ſunt, ac portionum, eædemque altitudi-
              <lb/>
            nes, ſiuè ijdem vertices) vel ad circumſcripta parallelogram-
              <lb/>
            ma, ſunt inter ſe in vnà eademque ratione.</s>
            <s xml:id="echoid-s7644" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7645" xml:space="preserve">NAm cum baſes æqualium portionum eiuſdem coni- ſectionis, vel cir-
              <lb/>
            culi earum altitudinibus ſint reciprocæ, baſes quoque
              <note symbol="b" position="right" xlink:label="note-0273-02" xlink:href="note-0273-02a" xml:space="preserve">65. h. ad
                <lb/>
              num. 1.</note>
            triangulorum, eorum altitudinibus reciprocabuntur, cum vtrobique altitu-
              <lb/>
            dines, & </s>
            <s xml:id="echoid-s7646" xml:space="preserve">baſes ponantur eædem; </s>
            <s xml:id="echoid-s7647" xml:space="preserve">ac propterea ipſa triangula æqualia erunt.
              <lb/>
            </s>
            <s xml:id="echoid-s7648" xml:space="preserve">Quare, vt portio ad portionem, ita triangulum ad triangulum, ob æquali-
              <lb/>
            tatem tùm portionum, tùm triangulorum; </s>
            <s xml:id="echoid-s7649" xml:space="preserve">& </s>
            <s xml:id="echoid-s7650" xml:space="preserve">permutando, portio ad ſibi in-
              <lb/>
            ſcriptum triangulum, vt altera æqualis portio de eadem coni- ſectione, vel
              <lb/>
            circulo ad ſibi inſcriptum triangulum. </s>
            <s xml:id="echoid-s7651" xml:space="preserve">Et ſumptis conſequentium duplis,
              <lb/>
            portio ad circumſcriptum parallelogrammum, erit vt altera portio ad cir-
              <lb/>
            cumſcriptum parallelogrammum. </s>
            <s xml:id="echoid-s7652" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s7653" xml:space="preserve">c.</s>
            <s xml:id="echoid-s7654" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7655" xml:space="preserve">Hoc de ſolis Parabolæ portionibus, etiam ſi inæqualibus, nec de
              <lb/>
            eadem Parabola, manifeſtum iam erat ex Archimede (omnis
              <lb/>
            enim Parabolæ portio ad ſibi inſcriptum triangulum ha-
              <lb/>
            bet rationem ſeſquitertiam.) </s>
            <s xml:id="echoid-s7656" xml:space="preserve">De reliquarum
              <note symbol="c" position="right" xlink:label="note-0273-03" xlink:href="note-0273-03a" xml:space="preserve">17. pr. h.</note>
            coni- ſectionum æqualibus portionibus,
              <lb/>
            non dum.</s>
            <s xml:id="echoid-s7657" xml:space="preserve"/>
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