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

Table of handwritten notes

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          <p>
            <s xml:id="echoid-s7146" xml:space="preserve">
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            ter ſit I N; </s>
            <s xml:id="echoid-s7147" xml:space="preserve">patet tales circulos in ipſo puncto I ſe mutuò contingere, ideo-
              <lb/>
            que, & </s>
            <s xml:id="echoid-s7148" xml:space="preserve">ſolida in eodem contactus puncto I ſe tantùm contingere, & </s>
            <s xml:id="echoid-s7149" xml:space="preserve">ob ean-
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            demrationẽ in quarta figura in altero contactus puncto L ſe contingent, &</s>
            <s xml:id="echoid-s7150" xml:space="preserve">c.
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            </s>
            <s xml:id="echoid-s7151" xml:space="preserve">At in quinta, & </s>
            <s xml:id="echoid-s7152" xml:space="preserve">ſexta, in quibus ſectiones ſunt circa communem axim B G,
              <lb/>
            & </s>
            <s xml:id="echoid-s7153" xml:space="preserve">in duobus punctis I, L ſe contingunt, ſi ex contactu I ducatur communis
              <lb/>
            applicata I M, & </s>
            <s xml:id="echoid-s7154" xml:space="preserve">producatur, ipſa ad alterum contactus punctum L omni-
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            no pertinget; </s>
            <s xml:id="echoid-s7155" xml:space="preserve">quoniam producta I M vtranque ſectionem ſecan@ in O, P, eſt
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            ſemi- applicata I M, in ſectione A B C, æqualis ſemi- applicatæ I M, in
              <lb/>
            ſectione D E F, ſed eſt M O in ſectione A B C æqualis I M, & </s>
            <s xml:id="echoid-s7156" xml:space="preserve">M P in ſe-
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            ctione D E F æqualis eidem I M, ergo M O, M P ſunt æquales, hoc eſt
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            puncta O, P vnum, ac idem ſunt; </s>
            <s xml:id="echoid-s7157" xml:space="preserve">quare ſectiones in puncto P ſimul con-
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            ueniunt, ſed conueniunt quoque in I, & </s>
            <s xml:id="echoid-s7158" xml:space="preserve">in duobus tantùm punctis I, & </s>
            <s xml:id="echoid-s7159" xml:space="preserve">L
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            poſitum fuit eas ſimul occurrere, ergo punctum P idem eſt, ac punctum
              <lb/>
            contactus L: </s>
            <s xml:id="echoid-s7160" xml:space="preserve">quare I M L eſt communis ſectionum applicata, per quam ſi
              <lb/>
            ducatur planum ad axem erectum, efficiet in vtroque ſolido circulum, cuius
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            diameter erit eadem I L; </s>
            <s xml:id="echoid-s7161" xml:space="preserve">itaque per huius circuli peripheriam à puncto
              <note symbol="a" position="right" xlink:label="note-0259-01" xlink:href="note-0259-01a" xml:space="preserve">ex Com
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              mand. cõ-
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              ment. in
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              lib. Arch.
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              de Co-
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              noid.</note>
            ex ſectionum reuolutione deſcriptam, huiuſmodiſolida ſe cõtingent. </s>
            <s xml:id="echoid-s7162" xml:space="preserve">Quod
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            erat vltimò demonſtrandum.</s>
            <s xml:id="echoid-s7163" xml:space="preserve"/>
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        <div xml:id="echoid-div752" type="section" level="1" n="299">
          <head xml:id="echoid-head308" xml:space="preserve">PROBL. VIII. PROP. LVII.</head>
          <p>
            <s xml:id="echoid-s7164" xml:space="preserve">A puncto extra conum rectum dato ad eius conuexam ſuperfi-
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            ciem, MINIMAM rectam lineam ducere.</s>
            <s xml:id="echoid-s7165" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7166" xml:space="preserve">ESto conus rectus, cuius axis A B. </s>
            <s xml:id="echoid-s7167" xml:space="preserve">Oportet per punctum G datum extra
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            conum ad eius conuexam ſuperficiem _MINIMAM_ rectam lineam du-
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            cere.</s>
            <s xml:id="echoid-s7168" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7169" xml:space="preserve">Secetur conus, in
              <lb/>
              <figure xlink:label="fig-0259-01" xlink:href="fig-0259-01a" number="215">
                <image file="0259-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0259-01"/>
              </figure>
            vtraque figura, plano
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            per axem A B, ac per
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            datum punctum G
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            tranſeunte, quod ef-
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            ficiat in ſuperficie
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            triangulum C A D:
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            </s>
            <s xml:id="echoid-s7170" xml:space="preserve">producatur axis B A
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            in K; </s>
            <s xml:id="echoid-s7171" xml:space="preserve">& </s>
            <s xml:id="echoid-s7172" xml:space="preserve">cum anguli
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            C A B, D A B ſint ę-
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            quales, & </s>
            <s xml:id="echoid-s7173" xml:space="preserve">acuti, qui
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            ipſis deinceps ſunt C
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            A K, D A K erunt ę-
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            quales, & </s>
            <s xml:id="echoid-s7174" xml:space="preserve">obtuſi. </s>
            <s xml:id="echoid-s7175" xml:space="preserve">Fiant igitur ex vertice A anguli C A E, D A F recti, & </s>
            <s xml:id="echoid-s7176" xml:space="preserve">
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            primò ſit datum punctum G in prima figura in altero rectorum angulorum,
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            vt puta in ipſo C A E, demittaturque ex G recta G H perpendicularis late-
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            ri A C (quæ, vt patet _MINIMA_ eſt ad anguli latera, &</s>
            <s xml:id="echoid-s7177" xml:space="preserve">c.) </s>
            <s xml:id="echoid-s7178" xml:space="preserve">Dico ipſam G
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            H eſſe _MINIMAM_ quæſitam.</s>
            <s xml:id="echoid-s7179" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7180" xml:space="preserve">Concipiatur enim per rectam A C duci planum N I L M, quod rectum
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            ſit ad planum per axem D A C, in quo eſt recta G H.</s>
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