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

Table of handwritten notes

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            hoc eſt portiones A B C, S O R eſſe æqualium baſium, ſed H O I maior eſt
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            S O R, totum parte, ergo, & </s>
            <s xml:id="echoid-s6906" xml:space="preserve">A B C, quæ ipſi H O I eſt æqualis, erit
              <note symbol="a" position="left" xlink:label="note-0250-01" xlink:href="note-0250-01a" xml:space="preserve">45. h.</note>
            eadem S O R, & </s>
            <s xml:id="echoid-s6907" xml:space="preserve">hoc ſemper, &</s>
            <s xml:id="echoid-s6908" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6909" xml:space="preserve">vnde portio A B C eſt _MAXIMA_ portio-
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            num æqualium baſium. </s>
            <s xml:id="echoid-s6910" xml:space="preserve">Quod primò erat, &</s>
            <s xml:id="echoid-s6911" xml:space="preserve">c.</s>
            <s xml:id="echoid-s6912" xml:space="preserve"/>
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          <figure number="206">
            <image file="0250-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0250-01"/>
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            <s xml:id="echoid-s6913" xml:space="preserve">Pręterea, cũ in tertia figura, quæ ex K ducitur interiorem Ellipſim F D G
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            contingens ſit _MAXIMA_ eandem Ellipſim contingentium, ipſa erit
              <note symbol="b" position="left" xlink:label="note-0250-02" xlink:href="note-0250-02a" xml:space="preserve">47. h.</note>
            no maior A C; </s>
            <s xml:id="echoid-s6914" xml:space="preserve">quare eidem axi applicata, quæ ipſi A C ſit æqualis, mino-
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            rem axim ſecabit inter L, & </s>
            <s xml:id="echoid-s6915" xml:space="preserve">K, & </s>
            <s xml:id="echoid-s6916" xml:space="preserve">ſit ea T V X. </s>
            <s xml:id="echoid-s6917" xml:space="preserve">Si ergo concipiatur per V
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            deſcripta Ellipſis, datis A B C, F D G ſimilis, & </s>
            <s xml:id="echoid-s6918" xml:space="preserve">concentrica, recta T V X
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            hanc Ellipſim continget, eritque _MAXIMA_ eandem Ellipſim
              <note symbol="c" position="left" xlink:label="note-0250-03" xlink:href="note-0250-03a" xml:space="preserve">ibidem.</note>
            tium, quapropter portiones, quarum baſes ſint æquales baſi T V X, hanc
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            mediam Ellipſim omnino ſecabunt, ac ideo maiores erunt portione T L X,
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            cum portiones ab ijſdem contingentibus abſciſſæ ſint omnes portioni
              <note symbol="d" position="left" xlink:label="note-0250-04" xlink:href="note-0250-04a" xml:space="preserve">45. h.</note>
            æquales. </s>
            <s xml:id="echoid-s6919" xml:space="preserve">Quare portio T L X eſt _MINIMA_ portionum æqualium baſium,
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            ex eadem Ellipſi A B C abſciſſarum. </s>
            <s xml:id="echoid-s6920" xml:space="preserve">Quod erat vltimò demonſtrandum.</s>
            <s xml:id="echoid-s6921" xml:space="preserve"/>
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        <div xml:id="echoid-div726" type="section" level="1" n="290">
          <head xml:id="echoid-head299" xml:space="preserve">COROLL.</head>
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            <s xml:id="echoid-s6922" xml:space="preserve">EX his conſtat _MINIMAM_ portionum ſemi-Ellipſi maiorum, quarum
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            baſes ſint ęquales eam eſſe, cuius diameter ſit ſegmentum maioris axis,
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            _MAXIMAM_ verò, cuius diameter ſit ſegmentum minoris.</s>
            <s xml:id="echoid-s6923" xml:space="preserve"/>
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            <s xml:id="echoid-s6924" xml:space="preserve">Nam in tertia figura, cum portionum A B C, S O R, T L X, &</s>
            <s xml:id="echoid-s6925" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6926" xml:space="preserve">ſemi-El-
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            lipſi minorum, & </s>
            <s xml:id="echoid-s6927" xml:space="preserve">ſuper æqualibus baſibus, ipſa A B C ſit _MAXIMA_, & </s>
            <s xml:id="echoid-s6928" xml:space="preserve">TLX
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            _MINIMA_, ac ipſæ ſint portiones eiuſdem terminatæ magnitudinis, ſiue Elli-
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            pſis eiuſdem A B C N, patet reliquarum portionum ſemi-Ellipſi maiorum
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            A N C, S N R, X M T, &</s>
            <s xml:id="echoid-s6929" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6930" xml:space="preserve">quæ item ſunt ſuper æquales baſes A C, S R,
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            T X, portionem A N C eſſe _MAXIMAM_, & </s>
            <s xml:id="echoid-s6931" xml:space="preserve">X M T _MINIMAM_.</s>
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