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

Table of Notes

< >
[Note]
Page: 85
[Note]
Page: 85
[Note]
Page: 87
[Note]
Page: 87
[Note]
Page: 88
[Note]
Page: 88
[Note]
Page: 88
[Note]
Page: 88
[Note]
Page: 88
[Note]
Page: 89
[Note]
Page: 89
[Note]
Page: 89
[Note]
Page: 90
[Note]
Page: 90
[Note]
Page: 90
[Note]
Page: 90
[Note]
Page: 90
[Note]
Page: 91
[Note]
Page: 91
[Note]
Page: 93
[Note]
Page: 94
[Note]
Page: 94
[Note]
Page: 94
[Note]
Page: 94
[Note]
Page: 94
[Note]
Page: 95
[Note]
Page: 95
[Note]
Page: 95
[Note]
Page: 95
[Note]
Page: 96
< >
page |< < (135) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div930" type="section" level="1" n="372">
          <pb o="135" file="0321" n="321" rhead=""/>
          <p>
            <s xml:id="echoid-s8936" xml:space="preserve">Ex centro C ad punctum contactus F ducatur radius C F; </s>
            <s xml:id="echoid-s8937" xml:space="preserve">patet ipſum
              <lb/>
            cum contingente F H rectum angulum efficere, ſed angulus quoque D H F,
              <lb/>
            rectus eſt ex hypotheſi, quare D H ipſi C F eſt parallela, vnde perpendi-
              <lb/>
            cularis D H, occurrit tangenti extra punctum contactus F. </s>
            <s xml:id="echoid-s8938" xml:space="preserve">Iungatur de-
              <lb/>
            nique D F, &</s>
            <s xml:id="echoid-s8939" xml:space="preserve">c.</s>
            <s xml:id="echoid-s8940" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8941" xml:space="preserve">Cum enim ex puncto D in circuli peripheriam cadant rectæ D A, D F,
              <lb/>
            D B, &</s>
            <s xml:id="echoid-s8942" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8943" xml:space="preserve">patet, ex elementis, D A, in qua eſt centrum, _MAXIMAM_ eſſe,
              <lb/>
            nempe maiorem D F, ſed eſt obliqua D F maior perpendiculari D H, er-
              <lb/>
            go D A eò magis maior erit D H. </s>
            <s xml:id="echoid-s8944" xml:space="preserve">Quod D A quoque ſit maior D B, pa-
              <lb/>
            tet cum ipſa ſit diametri ſegmentum, in quo eſt centrum, & </s>
            <s xml:id="echoid-s8945" xml:space="preserve">hoc ſemper
              <lb/>
            oſtendetur de quibuslibet alijs perpendicularibus ad contingentes; </s>
            <s xml:id="echoid-s8946" xml:space="preserve">ergo D
              <lb/>
            A, in qua centrum reperitur, eſt _MAXIMA_ in vtraque figura, etiam ſi da-
              <lb/>
            tum punctum cadat in ipſam peripheriam.</s>
            <s xml:id="echoid-s8947" xml:space="preserve"/>
          </p>
          <figure number="256">
            <image file="0321-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0321-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s8948" xml:space="preserve">In prima verò, iam eſt D B minor D A; </s>
            <s xml:id="echoid-s8949" xml:space="preserve">item eſt D B minor D G, eſtq;
              <lb/>
            </s>
            <s xml:id="echoid-s8950" xml:space="preserve">D G minor D H, ergo D B eò ampliùs eſt minor D H, & </s>
            <s xml:id="echoid-s8951" xml:space="preserve">hoc ſemper de
              <lb/>
            qualibet perpendiculari ad quamcunque contingentem, pręter ad punctum
              <lb/>
            D; </s>
            <s xml:id="echoid-s8952" xml:space="preserve">quare, dum datum punctum D cadit intra circulum, _MINIMA_ eſt D
              <lb/>
            B reliquum diametri ſe gmentum, dempta _MAXIMA_.</s>
            <s xml:id="echoid-s8953" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8954" xml:space="preserve">Si autem datum punctum incidat in ipſam peripheriam, vt in B: </s>
            <s xml:id="echoid-s8955" xml:space="preserve">patet
              <lb/>
            perpendicularem ex B, ſuper contingentem ex eodem B ductam, pun-
              <lb/>
            ctum euadere, ac propterea non dari _MINIMAM_, niſi dicatur illud idem
              <lb/>
            punctum eſſe _MINIMAM_.</s>
            <s xml:id="echoid-s8956" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8957" xml:space="preserve">Si tandem punctum D cadat extra, vt in ſecunda figura: </s>
            <s xml:id="echoid-s8958" xml:space="preserve">ducta ex D
              <lb/>
            circulum contingente D I, conſtat pariter perpendicularem ductam ex D
              <lb/>
            ſuper ipſam D I in punctum abire, ac ideo in hoc etiam caſu non dari _MINI-_
              <lb/>
            _MAM_, &</s>
            <s xml:id="echoid-s8959" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8960" xml:space="preserve">Quod vltimò probandum erat.</s>
            <s xml:id="echoid-s8961" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum