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

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        <div xml:id="echoid-div630" type="section" level="1" n="249">
          <pb o="36" file="0218" n="218" rhead=""/>
          <p>
            <s xml:id="echoid-s6103" xml:space="preserve">Erigatur ex A contingenti A G perpendicularis A L, quæ axi
              <note symbol="a" position="left" xlink:label="note-0218-01" xlink:href="note-0218-01a" xml:space="preserve">88. pri-
                <lb/>
              mi huius.</note>
            ret in L, cui applicata A H, erit intercepta L H æqualis dimidio
              <note symbol="b" position="left" xlink:label="note-0218-02" xlink:href="note-0218-02a" xml:space="preserve">90. pri-
                <lb/>
              mi huius.</note>
            B I, hoc eſt dupla interuallo D B, (cum punctum D diſtet à vertice B
              <lb/>
            per quartam recti lateris partem ex hypoteſi) & </s>
            <s xml:id="echoid-s6104" xml:space="preserve">H G dupla eſt quoq;</s>
            <s xml:id="echoid-s6105" xml:space="preserve">
              <note symbol="c" position="left" xlink:label="note-0218-03" xlink:href="note-0218-03a" xml:space="preserve">35. pri-
                <lb/>
              mi conic.</note>
            G B, quare, & </s>
            <s xml:id="echoid-s6106" xml:space="preserve">tota L G dupla eſt tota G D, ſiue L D æqualis D G, eſt-
              <lb/>
            que angulus L A G rectus, quare ſi
              <lb/>
            cum centro D, interuallo G, vel L
              <lb/>
              <figure xlink:label="fig-0218-01" xlink:href="fig-0218-01a" number="179">
                <image file="0218-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0218-01"/>
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            circulus deſcribatur, ipſe omnino
              <lb/>
            tranſibit per A; </s>
            <s xml:id="echoid-s6107" xml:space="preserve">vnde D A item æ-
              <lb/>
            qualis erit ipſis D G, D L, ſiue L G
              <lb/>
            erit dupla D A. </s>
            <s xml:id="echoid-s6108" xml:space="preserve">Et cum rectum axis
              <lb/>
            B D, ad rectum diametri A E, ſit vt
              <lb/>
            quadratum A H ad A G, vel
              <note symbol="d" position="left" xlink:label="note-0218-04" xlink:href="note-0218-04a" xml:space="preserve">Coroll.
                <lb/>
              24. huius.</note>
            triangulorum ſimilitudinem, vt qua-
              <lb/>
            dratum A L ad L G, vel vt recta
              <lb/>
            H L ad rectam L G (cum L A ſit
              <lb/>
            media proportionalis inter G L, L H)
              <lb/>
            ſumptis harum ſubduplis, erit rectũ
              <lb/>
            axis ad rectum diametri A E, vt D
              <lb/>
            B dimidium H L ad D A dimidium L G. </s>
            <s xml:id="echoid-s6109" xml:space="preserve">Quod erat demonſtrandum.
              <lb/>
            </s>
            <s xml:id="echoid-s6110" xml:space="preserve">Vocatur autem punctum D, focus Parabolæ.</s>
            <s xml:id="echoid-s6111" xml:space="preserve"/>
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        <div xml:id="echoid-div632" type="section" level="1" n="250">
          <head xml:id="echoid-head258" xml:space="preserve">COROLL. I.</head>
          <p>
            <s xml:id="echoid-s6112" xml:space="preserve">HInc cõſtat, omnes eductas à foco ad Parabolę peripheriam, ęqua-
              <lb/>
            ri quartæ parti rectorum, earum diametrorum, quarum vertices
              <lb/>
            ſint termini, quibus ipſæ eductæ ſectioni occurrunt: </s>
            <s xml:id="echoid-s6113" xml:space="preserve">rectum enim axis
              <lb/>
            B D ad rectum diametri A E, eſt vt D B ad D A, eſtque D B quarta pars
              <lb/>
            recti B I, quare, & </s>
            <s xml:id="echoid-s6114" xml:space="preserve">D A erit quarta pars recti lateris diametri A E, & </s>
            <s xml:id="echoid-s6115" xml:space="preserve">D F
              <lb/>
            quadrans recti, diametri F R. </s>
            <s xml:id="echoid-s6116" xml:space="preserve">Vnde quò diametri ab axe remotiores
              <lb/>
            fuerint, eò ipſarum recta maiora erunt. </s>
            <s xml:id="echoid-s6117" xml:space="preserve">nam eſt D F maior D A, &</s>
            <s xml:id="echoid-s6118" xml:space="preserve">c.</s>
            <s xml:id="echoid-s6119" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div633" type="section" level="1" n="251">
          <head xml:id="echoid-head259" xml:space="preserve">COROLL. II.</head>
          <p>
            <s xml:id="echoid-s6120" xml:space="preserve">PAtet etiam, quamlibet eductam ex foco, ęquari aggregato ex inter-
              <lb/>
            uallo foci ab axis vertice, & </s>
            <s xml:id="echoid-s6121" xml:space="preserve">ſegmento axis inter verticem, & </s>
            <s xml:id="echoid-s6122" xml:space="preserve">ap-
              <lb/>
            plicatam ex occurſu eductæ cum ſectione. </s>
            <s xml:id="echoid-s6123" xml:space="preserve">Oſtenſa eſt enim D A æqua-
              <lb/>
            lis D G, quæ æqualis eſt aggregato G B, cum B D, vel H B cum B D.</s>
            <s xml:id="echoid-s6124" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div634" type="section" level="1" n="252">
          <head xml:id="echoid-head260" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s6125" xml:space="preserve">CVm demonſtratum ſit D G æqualem eſſe D A, erit angulus D G A,
              <lb/>
            vel parallelarum externus E A M, æqualis angulo D A G, ſed M
              <lb/>
            A G Parabolen contingit in A, quare ex Opticæ legibus, ſi E A fuerit
              <lb/>
            radius incidens ad concauam peripheriam A B C, ipſe A D erit
              <note symbol="e" position="left" xlink:label="note-0218-05" xlink:href="note-0218-05a" xml:space="preserve">Breuiùs,
                <lb/>
              & clariùs
                <lb/>
              quàm à
                <lb/>
              Vitellione
                <lb/>
              in 41. 9.</note>
            xus, atque omnes radij axi Parabolę æquidiſtantes in punctum D coi-
              <lb/>
            bunt; </s>
            <s xml:id="echoid-s6126" xml:space="preserve">vnde ſi ipſi fuerint ſonori, aut lucidi, ſimulque calidi, ibi </s>
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