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

Table of Notes

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          <head xml:id="echoid-head284" xml:space="preserve">PROBL. VI. PROP. XXXXI.</head>
          <p>
            <s xml:id="echoid-s6610" xml:space="preserve">Per datum punctum in angulo rectilineo, rectam applicare,
              <lb/>
            quæ de angulo abſcindat triangulum MINIMVM.</s>
            <s xml:id="echoid-s6611" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6612" xml:space="preserve">ESto angulus rectilineus A B C, in quo datum ſit punctum D. </s>
            <s xml:id="echoid-s6613" xml:space="preserve">Oportet ex
              <lb/>
            D rectam applicare, quæ ab angulo auferat triangulum _MINIMVM_.</s>
            <s xml:id="echoid-s6614" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6615" xml:space="preserve">Iungatur diameter B D, ad quàm applicetur per D recta A D C, quæ in
              <lb/>
            dato puncto D bifariam ſecetur. </s>
            <s xml:id="echoid-s6616" xml:space="preserve">Dico hanc ipſam quæſitum ſoluere,
              <note symbol="a" position="left" xlink:label="note-0238-01" xlink:href="note-0238-01a" xml:space="preserve">ex 66. 1.
                <lb/>
              huius.</note>
            eſt triangulum A B C eſſe _MINIMVM_.</s>
            <s xml:id="echoid-s6617" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6618" xml:space="preserve">Ducatur quælibet alia E D F, & </s>
            <s xml:id="echoid-s6619" xml:space="preserve">ab extremo
              <lb/>
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            applicatæ A C, quod cadit ſupra E F, ſiue ex
              <lb/>
            puncto C agatur C G ipſi E A ęquidiſtans. </s>
            <s xml:id="echoid-s6620" xml:space="preserve">Et
              <lb/>
            cum ſit A D æqualis D C, ob conſtructionem,
              <lb/>
            erit quoque E D ęqualis D G, & </s>
            <s xml:id="echoid-s6621" xml:space="preserve">angulus A D E
              <lb/>
            ęquatur angulo C D G, ergo triangulum A D E,
              <lb/>
            triangulo C D G ęquale erit, ac ideò A D E mi-
              <lb/>
            nus triangulo C D F; </s>
            <s xml:id="echoid-s6622" xml:space="preserve">ſi ergo addatur commune
              <lb/>
            trapetium B E D C, erit triangulum A B C mi-
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            nus triangulo E B F, & </s>
            <s xml:id="echoid-s6623" xml:space="preserve">hoc ſemper: </s>
            <s xml:id="echoid-s6624" xml:space="preserve">quare trian-
              <lb/>
            gulum A B C eſt _MINIMVM_. </s>
            <s xml:id="echoid-s6625" xml:space="preserve">Quod reperien-
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            dum erat.</s>
            <s xml:id="echoid-s6626" xml:space="preserve"/>
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          <head xml:id="echoid-head285" xml:space="preserve">PROBL. VII. PROP. XXXXII.</head>
          <p>
            <s xml:id="echoid-s6627" xml:space="preserve">Per datum punctum intra coni-ſectionem, vel circulum rectam
              <lb/>
            applicare, quæ de ipſa auferat portionem MINIMAM.</s>
            <s xml:id="echoid-s6628" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6629" xml:space="preserve">ESto A B C data Parabole, vt in prima figura, vel Hyperbole, vt in ſe-
              <lb/>
            cunda, aut Ellipſis, vel circulus, vt in tertia, quarum centrum H, & </s>
            <s xml:id="echoid-s6630" xml:space="preserve">
              <lb/>
            punctum intra datum ſit D. </s>
            <s xml:id="echoid-s6631" xml:space="preserve">Oportet per D rectam applicare, quæ de ſe-
              <lb/>
            ctione abſcindat portionem _MINIMAM_.</s>
            <s xml:id="echoid-s6632" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6633" xml:space="preserve">Ducatur H B D ſectionis diameter tranſiens per datum punctum D, per
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            quod ei ordinatim applicetur recta A D C. </s>
            <s xml:id="echoid-s6634" xml:space="preserve">Dico portionem A B C eſſe _MI-_
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            _NIMAM_ quæſitam.</s>
            <s xml:id="echoid-s6635" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6636" xml:space="preserve">Nam applicata per D in ſectione qualibet alia E D F, cum ipſa E F alte-
              <lb/>
            ram applicatam A C in ſectione bifariam ſecet in D, ipſæ ſe mutuò bifariam
              <lb/>
            non ſecabunt, per 6. </s>
            <s xml:id="echoid-s6637" xml:space="preserve">ſecundi conicorum, quæ licet de ſola Ellipſi, vel circu-
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            lo agat, verificatur quoque de quacunque data coni-ſectione. </s>
            <s xml:id="echoid-s6638" xml:space="preserve">Secetur er-
              <lb/>
            go E F bifariam in G, per quod ducatur eius diameter G I H ſectioni oc-
              <lb/>
            currens in I, per quod agatur ſectionem contingens IL, quæ ipſi E G F æ-
              <lb/>
            quidiſtabit, quare ſi iungatur I B, cum ipſa tota cadat intra ſectionem, &</s>
            <s xml:id="echoid-s6639" xml:space="preserve">
              <note symbol="b" position="left" xlink:label="note-0238-02" xlink:href="note-0238-02a" xml:space="preserve">5. ſecun-
                <lb/>
              di conic.</note>
              <note symbol="c" position="left" xlink:label="note-0238-03" xlink:href="note-0238-03a" xml:space="preserve">10. primi
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              conic.</note>
            alteram parallelarum L I ſecet in I, producta ad partes B, conueniet cum
              <lb/>
            reliqua producta F D E ad partes E, ac ideò D M, quæ ex D ducitur ipſi
              <lb/>
            B I æquidiſtans cadet ſupra D F, ſecabitque diametrum I G, vt in M, </s>
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