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

Page concordance

< >
Scan Original
221 39
222 40
223 41
224 42
225 43
226 44
227 45
228 46
229 47
230 48
231 49
232 50
233
234
235 51
236 52
237 53
238 54
239 55
240 56
241 57
242 58
243 59
244 60
245 61
246 62
247 63
248 64
249 65
250 66
< >
page |< < (39) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div642" type="section" level="1" n="256">
          <p>
            <s xml:id="echoid-s6186" xml:space="preserve">
              <pb o="39" file="0221" n="221" rhead=""/>
            quare angulus D A M, ſiue in ſimili triangulo D L I, angulus D L I erit
              <lb/>
            maior angulo A H M, ſiue angulo parallelarum externo I B L: </s>
            <s xml:id="echoid-s6187" xml:space="preserve">cum
              <note symbol="*" position="right" xlink:label="note-0221-01" xlink:href="note-0221-01a" xml:space="preserve">27. h.</note>
            tur in triangulo I B L ſit angulus I B L minor I L B, erit latus I L minus
              <lb/>
            latere I B.</s>
            <s xml:id="echoid-s6188" xml:space="preserve"/>
          </p>
          <figure number="183">
            <image file="0221-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0221-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s6189" xml:space="preserve">Præterea, cum trian-
              <lb/>
            gula A P O, B P H
              <note symbol="a" position="right" xlink:label="note-0221-02" xlink:href="note-0221-02a" xml:space="preserve">I. tertij
                <lb/>
              conic.</note>
            æqualia, addito commu-
              <lb/>
            ni triangulo A P B, erunt
              <lb/>
            triangula A O B, A H B
              <lb/>
            ſuper eadem baſi A B in-
              <lb/>
            ter ſe ęqualia, quare O H
              <lb/>
            æquidiſtabit A B, ideo-
              <lb/>
            que vt D O ad O A, vel
              <lb/>
            D B ad B M, ita D H ad
              <lb/>
            H B, vel D A ad A I.
              <lb/>
            </s>
            <s xml:id="echoid-s6190" xml:space="preserve">Sunt ergo D M, D I pro-
              <lb/>
            portionaliter ſectæ in B,
              <lb/>
            A, quibus additæ ſunt D
              <lb/>
            E, D G, æquales ipſis D
              <lb/>
            B, D A, vtraq; </s>
            <s xml:id="echoid-s6191" xml:space="preserve">vtrique,
              <lb/>
            ſuntq; </s>
            <s xml:id="echoid-s6192" xml:space="preserve">rectangula triãgu-
              <lb/>
            la D M A, D I L ſimilia
              <lb/>
            inter ſe, quare recta ngu-
              <lb/>
            lum E M B ad quadratũ
              <lb/>
            M A, ſiue E B ad B
              <note symbol="b" position="right" xlink:label="note-0221-03" xlink:href="note-0221-03a" xml:space="preserve">21. primi
                <lb/>
              conic.</note>
            eſt vt rectãgulum G
              <note symbol="c" position="right" xlink:label="note-0221-04" xlink:href="note-0221-04a" xml:space="preserve">28. h.</note>
            ad quadratum I L, cumque ſit I L minor I B, erit quadratum I L minus
              <lb/>
            quadrato I B, ideoque rectangulum G I A ad quadratum I L, hoc eſt tranſ-
              <lb/>
            uerſum E B ad rectum B F, habebit maiorem rationem, quàm rectangu-
              <lb/>
            lum G I A ad quadratum I B, vel quàm tranſuerſum G A ad rectum A K;</s>
            <s xml:id="echoid-s6193" xml:space="preserve">
              <note symbol="d" position="right" xlink:label="note-0221-05" xlink:href="note-0221-05a" xml:space="preserve">21 pri-
                <lb/>
              mi conic.</note>
            ergo prima E B, ad ſecundam B F, maiorem habet rationem quàm tertia G
              <lb/>
            A ad quartam A K, ſed eſt prima E B minor tertia G A, ergo, & </s>
            <s xml:id="echoid-s6194" xml:space="preserve">
              <note symbol="e" position="right" xlink:label="note-0221-06" xlink:href="note-0221-06a" xml:space="preserve">24. h.</note>
            da B F erit minor quarta A K; </s>
            <s xml:id="echoid-s6195" xml:space="preserve">& </s>
            <s xml:id="echoid-s6196" xml:space="preserve">ſic de reliquis diametrorum rectis
              <note symbol="f" position="right" xlink:label="note-0221-07" xlink:href="note-0221-07a" xml:space="preserve">29. h.</note>
            teribus: </s>
            <s xml:id="echoid-s6197" xml:space="preserve">quare B F, rectum axis tranſuerſi, eſt _MINIMVM_, & </s>
            <s xml:id="echoid-s6198" xml:space="preserve">c.</s>
            <s xml:id="echoid-s6199" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6200" xml:space="preserve">Si autem axis E B æqualis fuerit eius recto B F; </s>
            <s xml:id="echoid-s6201" xml:space="preserve">cum demonſtratum ſit re-
              <lb/>
            ctangulum G I A ad quadratum I L eſſe vt tranſuerſus axis E B ad rectum
              <lb/>
            B F; </s>
            <s xml:id="echoid-s6202" xml:space="preserve">patet rectangulum quoque G I A æquari quadrato I L, ſed quando
              <lb/>
            E B æquatur B F, rectangulum etiam D M H æquatur quadrato M A, &</s>
            <s xml:id="echoid-s6203" xml:space="preserve">
              <note symbol="g" position="right" xlink:label="note-0221-08" xlink:href="note-0221-08a" xml:space="preserve">37. primi
                <lb/>
              conic.</note>
            tunc angulus D A M, ęqualis eſt angulo A H M, ergo etiam angulus D L
              <note symbol="h" position="right" xlink:label="note-0221-09" xlink:href="note-0221-09a" xml:space="preserve">27. h.</note>
            æquabitur angulo I B L, hoc eſt linea I B æqualis erit I L, ſed erat rectan-
              <lb/>
            gulum G I A æquale quadrato I L, ergo idem rectangulum G I A æqua-
              <lb/>
            bitur quadrato I B, ſiue tranſuerſa diameter A G, eius recto A K æqualis
              <lb/>
            erit, & </s>
            <s xml:id="echoid-s6204" xml:space="preserve">hoc ſemper, quæcunque ſit ducta tranſuerſa diameter præter axim.</s>
            <s xml:id="echoid-s6205" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6206" xml:space="preserve">Cum ergo Hyperbole fuerit rectangula æquilatera, ad aliam quoque
              <lb/>
            diametri applicationem æquilatera erit, ſed axis eſt tranſuerſorum
              <note symbol="i" position="right" xlink:label="note-0221-10" xlink:href="note-0221-10a" xml:space="preserve">24. h.</note>
            _MIMVS_: </s>
            <s xml:id="echoid-s6207" xml:space="preserve">ergo in Hyperbola, cuius axis tranſuerſus eius rectum adæquet,
              <lb/>
            rectum axis aliorum rectorum eſt _MINIMVM_. </s>
            <s xml:id="echoid-s6208" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s6209" xml:space="preserve">c.</s>
            <s xml:id="echoid-s6210" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum