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

Table of Notes

< >
[Note]
Page: 80
[Note]
Page: 80
[Note]
Page: 81
[Note]
Page: 81
[Note]
Page: 81
[Note]
Page: 81
[Note]
Page: 81
[Note]
Page: 81
[Note]
Page: 81
[Note]
Page: 81
[Note]
Page: 81
[Note]
Page: 81
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 83
[Note]
Page: 83
[Note]
Page: 83
[Note]
Page: 83
[Note]
Page: 83
< >
page |< < (76) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div752" type="section" level="1" n="299">
          <pb o="76" file="0260" n="260" rhead=""/>
          <p>
            <s xml:id="echoid-s7182" xml:space="preserve">Iam cum planum N L rectum ſit ad planum D A C, cumque in plano N
              <lb/>
            L ſit G H communi planorum ſectioni A C perpendicularis, erit ipſa G H
              <lb/>
            ad idem planum N L recta hoc eſt _MINIMA_ ducibilium à puncto G
              <note symbol="a" position="left" xlink:label="note-0260-01" xlink:href="note-0260-01a" xml:space="preserve">4. def.
                <lb/>
              11. Elem.</note>
              <note symbol="b" position="left" xlink:label="note-0260-02" xlink:href="note-0260-02a" xml:space="preserve">52. h.</note>
            quodcunque aliud punctum eiuſdem plani N L, ſed conuexa coni ſuperfi-
              <lb/>
            cies tota eſt infra planum N L, ipſum tantùm contingens per rectam A
              <note symbol="c" position="left" xlink:label="note-0260-03" xlink:href="note-0260-03a" xml:space="preserve">53. h.</note>
            quare eadem G H eò ampliùs _MINIMA_ erit ad conuexam dati conirecti
              <lb/>
            C A B ſuperficiem.</s>
            <s xml:id="echoid-s7183" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7184" xml:space="preserve">Si autem datum
              <lb/>
              <figure xlink:label="fig-0260-01" xlink:href="fig-0260-01a" number="216">
                <image file="0260-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0260-01"/>
              </figure>
            punctum fuerit in ip-
              <lb/>
            ſa perpendiculari E
              <lb/>
            A, vt in E, eodem
              <lb/>
            modo demonſtrabi-
              <lb/>
            tur E A rectam eſſe
              <lb/>
            ad planũ N L, ideo-
              <lb/>
            que ad ipſum _MINI_-
              <lb/>
            _MAM_, & </s>
            <s xml:id="echoid-s7185" xml:space="preserve">eò magis
              <lb/>
            ad coni ſuperficiem.</s>
            <s xml:id="echoid-s7186" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7187" xml:space="preserve">Si denique datum
              <lb/>
            punctum G fuerit in-
              <lb/>
            tra angulum E A F,
              <lb/>
            vt in ſecunda figura. </s>
            <s xml:id="echoid-s7188" xml:space="preserve">Iungatur G A, & </s>
            <s xml:id="echoid-s7189" xml:space="preserve">hæc erit _MINIMA_ quæſita.</s>
            <s xml:id="echoid-s7190" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7191" xml:space="preserve">Nam cũ angulus C A G ſit maior recto, in plano per axem D A C, in quo
              <lb/>
            eſt A G, fiat rectus angulus O A G, & </s>
            <s xml:id="echoid-s7192" xml:space="preserve">linea O A producatur ad P: </s>
            <s xml:id="echoid-s7193" xml:space="preserve">patet A P
              <lb/>
            cadere inter A G, & </s>
            <s xml:id="echoid-s7194" xml:space="preserve">A D cum angulus G A P ſit rectus, & </s>
            <s xml:id="echoid-s7195" xml:space="preserve">duo ſimul G A F,
              <lb/>
            F A D recto ſint maiores: </s>
            <s xml:id="echoid-s7196" xml:space="preserve">(eſt. </s>
            <s xml:id="echoid-s7197" xml:space="preserve">n. </s>
            <s xml:id="echoid-s7198" xml:space="preserve">vnicus D A F rectus, ex conſtructione) ita-
              <lb/>
            que ſi per rectam O P concipiatur planum Q R, quod rectum ſit ad planum
              <lb/>
            D A C, in quo eſt A G, ob rationem ſuperiùs allatam, ipſa G A recta erit
              <lb/>
            ad planum Q R, hoc eſt _MINIMA_, ſed planum Q R in ipſo tantùm
              <note symbol="d" position="left" xlink:label="note-0260-04" xlink:href="note-0260-04a" xml:space="preserve">52. h.</note>
            ce A coni ſuperficiem contingit, quæ tota cadit ad inferiorem partem
              <note symbol="e" position="left" xlink:label="note-0260-05" xlink:href="note-0260-05a" xml:space="preserve">54. h,</note>
            ni Q R, quare eadem G A erit _MINIMA_ ducibilium ex G ad conuexam
              <lb/>
            coni ſuperficiem. </s>
            <s xml:id="echoid-s7199" xml:space="preserve">Ducta eſt ergo à puncto G extra conum rectum dato, &</s>
            <s xml:id="echoid-s7200" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s7201" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s7202" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div757" type="section" level="1" n="300">
          <head xml:id="echoid-head309" xml:space="preserve">PROBL. IX. PROP. LVIII.</head>
          <p>
            <s xml:id="echoid-s7203" xml:space="preserve">A puncto extra Conoides Parabolicum, aut Hyperbolicum,
              <lb/>
            vel Sphæram, aut Sphæroides dato, ad eius conuexam ſuperficiem
              <lb/>
            MINIMAM rectam lineam ducere.</s>
            <s xml:id="echoid-s7204" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7205" xml:space="preserve">ESto Conoides Parabolicũ, aut Hyperbolicũ, in 1. </s>
            <s xml:id="echoid-s7206" xml:space="preserve">figura, vel Sphęra, aut
              <lb/>
            Sphęroides in ſecunda, cuius axis A B, & </s>
            <s xml:id="echoid-s7207" xml:space="preserve">oporteat per pũctum C extra
              <lb/>
            datum ad conuexam ſolidi ſuperficiem _MINIMAM_ rectam lineam ducere.</s>
            <s xml:id="echoid-s7208" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7209" xml:space="preserve">Secetur datum ſolidum plano per axem A B, ac per datum punctum C,
              <lb/>
            efficiente in ſuperficie genitricem ſolidi ſectionem D A E, ad cuius peri-
              <lb/>
            pheriam ex puncto C ducatur _MINIMA_ linea C F. </s>
            <s xml:id="echoid-s7210" xml:space="preserve">Dico hanc
              <note symbol="f" position="left" xlink:label="note-0260-06" xlink:href="note-0260-06a" xml:space="preserve">20. 22.
                <lb/>
              23. h.</note>
            eſſe _MINIMAM_ ad conuexam dati ſolidi ſuperficiem.</s>
            <s xml:id="echoid-s7211" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum