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

Page concordance

< >
Scan Original
241 57
242 58
243 59
244 60
245 61
246 62
247 63
248 64
249 65
250 66
251 67
252 68
253 69
254 70
255 71
256 72
257 73
258 74
259 75
260 76
261 77
262 78
263
264
265 79
266 80
267 81
268 82
269 83
270 84
< >
page |< < (64) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div717" type="section" level="1" n="287">
          <p>
            <s xml:id="echoid-s6852" xml:space="preserve">
              <pb o="64" file="0248" n="248" rhead=""/>
            portio M F N maior portione H F I (totum ſua parte) ſed portio M F N æ-
              <lb/>
            qualis eſt portioni A B C (cum ſit D F ad F L, vt D B ad B E)
              <note symbol="a" position="left" xlink:label="note-0248-01" xlink:href="note-0248-01a" xml:space="preserve">40. h.</note>
            portio A B C erit maior H F I, & </s>
            <s xml:id="echoid-s6853" xml:space="preserve">hoc ſemper de qualibet alia portione, cu-
              <lb/>
            ius diameter æqualis ſit axi B E: </s>
            <s xml:id="echoid-s6854" xml:space="preserve">ergo portio A B C eſt _MAXIMA_ portio-
              <lb/>
            num æqualium diametrorum. </s>
            <s xml:id="echoid-s6855" xml:space="preserve">Quod erat vltimò demonſtrandum.</s>
            <s xml:id="echoid-s6856" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div720" type="section" level="1" n="288">
          <head xml:id="echoid-head297" xml:space="preserve">THEOR. XXX. PROP. XLIX.</head>
          <p>
            <s xml:id="echoid-s6857" xml:space="preserve">MAXIMA portionum ſemi- Ellipſi minorum, & </s>
            <s xml:id="echoid-s6858" xml:space="preserve">æqualium dia-
              <lb/>
            metrorum eſt ea, cuius diameter ſit minoris ſemi-axis ſegmentum.
              <lb/>
            </s>
            <s xml:id="echoid-s6859" xml:space="preserve">MINIMA verò, cuius diameter ſit ſegmentum maioris ſemi-axis.</s>
            <s xml:id="echoid-s6860" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6861" xml:space="preserve">ESto A B C D Ellipſis, cuius axis maior ſit B D, minor A C, centrum
              <lb/>
            E, ſitque ex minori ſemi-axe A E demptum ſegmentum A G, & </s>
            <s xml:id="echoid-s6862" xml:space="preserve">ex
              <lb/>
            maiori B E ipſi A G ſit æquale B F perque puncta G, F applicatæ ſint
              <lb/>
            axibus rectæ L G M, H F I. </s>
            <s xml:id="echoid-s6863" xml:space="preserve">Dico portionem L A M eſſe _MAXIMAM_, & </s>
            <s xml:id="echoid-s6864" xml:space="preserve">
              <lb/>
            H B I _MINIMAM_ aliarum portionum eiuſdem Ellipſis circa diametros ipſis
              <lb/>
            A G, B F æquales.</s>
            <s xml:id="echoid-s6865" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6866" xml:space="preserve">Quod L A M ſit maior H B I patet ſic.
              <lb/>
            </s>
            <s xml:id="echoid-s6867" xml:space="preserve">
              <figure xlink:label="fig-0248-01" xlink:href="fig-0248-01a" number="204">
                <image file="0248-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0248-01"/>
              </figure>
            Nam cum ſit E A minor E B, A G verò
              <lb/>
            æqualis B F, habebit. </s>
            <s xml:id="echoid-s6868" xml:space="preserve">E A ad A G mi-
              <lb/>
            norem rationem quàm E B ad B F: </s>
            <s xml:id="echoid-s6869" xml:space="preserve">fiat
              <lb/>
            ergo E B ad B N, vt E A ad A G, & </s>
            <s xml:id="echoid-s6870" xml:space="preserve">ha-
              <lb/>
            bebit E B ad B N minorem rationem
              <lb/>
            quàm E B ad B F, ſiue B N erit maior
              <lb/>
            B F; </s>
            <s xml:id="echoid-s6871" xml:space="preserve">quare applicata O N P cadet infra
              <lb/>
            H I: </s>
            <s xml:id="echoid-s6872" xml:space="preserve">& </s>
            <s xml:id="echoid-s6873" xml:space="preserve">cum ſit vt E A ad A G, ita E B
              <lb/>
            ad B N, erit portio L A M ęqualis
              <note symbol="b" position="left" xlink:label="note-0248-02" xlink:href="note-0248-02a" xml:space="preserve">ibidem.</note>
            tioni O B P, ſed hæc maior eſt portione
              <lb/>
            H B I, totum parte, ergo L A M maior
              <lb/>
            eſt H B I.</s>
            <s xml:id="echoid-s6874" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6875" xml:space="preserve">Præterea, ducta inter ſemi-axes qua-
              <lb/>
            cunque ſemi-diametro E Q, ex ipſa, quę
              <lb/>
            maior eſt E A (eo quod hæc ſit ſemi-dia-
              <lb/>
            metrorum _MINIMA_ ) & </s>
            <s xml:id="echoid-s6876" xml:space="preserve">eò maior
              <note symbol="c" position="left" xlink:label="note-0248-03" xlink:href="note-0248-03a" xml:space="preserve">86. pri-
                <lb/>
              mi huius.</note>
            A G, dematur Q R æqualis ipſi A G, vel B F, appliceturque S R T. </s>
            <s xml:id="echoid-s6877" xml:space="preserve">Iam
              <lb/>
            cum ſit E A minor E Q, & </s>
            <s xml:id="echoid-s6878" xml:space="preserve">A G æqualis Q R, habebit E A ad A G mi-
              <lb/>
            norem rationem, quàm E Q ad Q R, ac ideò vti ſuperiùs oſtendimus, por-
              <lb/>
            tio L A M erit maior portione S Q T. </s>
            <s xml:id="echoid-s6879" xml:space="preserve">Eadem ratione, cum ſit E Q minor
              <lb/>
            E B, (eò quod hæc ſit ſemi-diametrorum _MAXIMA_) & </s>
            <s xml:id="echoid-s6880" xml:space="preserve">Q R ęqualis B
              <note symbol="d" position="left" xlink:label="note-0248-04" xlink:href="note-0248-04a" xml:space="preserve">ibidem.</note>
            habebit E Q ad Q R minorem rationem quàm E B ad B F, quapropter
              <lb/>
            portio S Q T maior erit portione H B I, & </s>
            <s xml:id="echoid-s6881" xml:space="preserve">hoc ſemper de qualibet portio-
              <lb/>
            ne, cuius diameter ſit inter ſemi- axes; </s>
            <s xml:id="echoid-s6882" xml:space="preserve">quare portio L A M erit _MAXIMA_,
              <lb/>
            & </s>
            <s xml:id="echoid-s6883" xml:space="preserve">H B I _MINIMA_ portionum æqualium diametrorum. </s>
            <s xml:id="echoid-s6884" xml:space="preserve">Quod erat demon-
              <lb/>
            ſtrandum.</s>
            <s xml:id="echoid-s6885" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum