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

List of thumbnails

< >
31
31 (11) 		32
32 (12)
33
33 (13) 		34
34 (14)
35
35 (15) 		36
36 (16)
37
37 (17) 		38
38 (18)
39
39 (19) 		40
40 (20)
< >
page |< < (15) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div40" type="section" level="1" n="28">
          <pb o="15" file="0035" n="35" rhead=""/>
        </div>
        <div xml:id="echoid-div43" type="section" level="1" n="29">
          <head xml:id="echoid-head34" xml:space="preserve">MONITVM.</head>
          <p style="it">
            <s xml:id="echoid-s628" xml:space="preserve">VT aliquando ad rem noſtram accedamus, quoniam in hac de
              <lb/>
            MAXIMIS, & </s>
            <s xml:id="echoid-s629" xml:space="preserve">MINIMIS tractatione frequenter nobis eſt
              <lb/>
            opus conicas ſectiones circà datam diametrum, per datum ver-
              <lb/>
            ticem, cum datis lateribus, cumque applicatis angulum dato
              <lb/>
            æqualem cum diametro efficientibus deſcribere, quæ omnia quidem nos docet
              <lb/>
            Apoll. </s>
            <s xml:id="echoid-s630" xml:space="preserve">in 52. </s>
            <s xml:id="echoid-s631" xml:space="preserve">53. </s>
            <s xml:id="echoid-s632" xml:space="preserve">54. </s>
            <s xml:id="echoid-s633" xml:space="preserve">primi conic. </s>
            <s xml:id="echoid-s634" xml:space="preserve">ad quas itaque vſu exigente confugien-
              <lb/>
            dum eſſet; </s>
            <s xml:id="echoid-s635" xml:space="preserve">attamen cum hæo ſint forſan longiſsimæ, ac difficillimæ omnium
              <lb/>
            demonſtrationum in quatuor conicorum libris contentarum, eò quod ipſarum
              <lb/>
            quælibet in duos caſus diſtribuatur, variaque ibi Lemmata requirantur à
              <lb/>
            Pappo, Eutocio, & </s>
            <s xml:id="echoid-s636" xml:space="preserve">Commandino ſuppleta; </s>
            <s xml:id="echoid-s637" xml:space="preserve">conſentaneum viſum eſt noſtras
              <lb/>
            hic quoque horum problematum ſolutiones afferre, quæ expeditiores, admo-
              <lb/>
            dumque faciles nobis videntur, vniuerſaliter ſingulas oſtendendo, abſque
              <lb/>
            vſu prædictorum, vel aliorum Lemmatum, vt mox videre licet.</s>
            <s xml:id="echoid-s638" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div44" type="section" level="1" n="30">
          <head xml:id="echoid-head35" xml:space="preserve">PROBL. III. PROP. V.</head>
          <p>
            <s xml:id="echoid-s639" xml:space="preserve">Data in quodam plano recta linea ad vnum punctum terminata,
              <lb/>
              <note position="right" xlink:label="note-0035-01" xlink:href="note-0035-01a" xml:space="preserve">Prop. 52.
                <lb/>
              pri. con.</note>
            inuenire in dato plano coni-ſectionem, quæ Parabole appellatur,
              <lb/>
            cuius diameter ſit data linea, vertex eius terminus, rectum verò la-
              <lb/>
            tus ſit altera quædam linea magnitudine data, & </s>
            <s xml:id="echoid-s640" xml:space="preserve">diametrō
              <unsure/>
            ordina-
              <lb/>
            tim ductæ in dato angulo applicentur.</s>
            <s xml:id="echoid-s641" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s642" xml:space="preserve">SIt in ſubiecto plano recta linea A B
              <lb/>
              <figure xlink:label="fig-0035-01" xlink:href="fig-0035-01a" number="11">
                <image file="0035-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0035-01"/>
              </figure>
            data poſitione ad punctum A ter-
              <lb/>
            minata, altera autem recta magnitu-
              <lb/>
            dine data ſit AC, & </s>
            <s xml:id="echoid-s643" xml:space="preserve">datus angulus ſit
              <lb/>
            D. </s>
            <s xml:id="echoid-s644" xml:space="preserve">Oportet in ſubiecto plano Para-
              <lb/>
            bolen deſcribere, cuius diameter ſit
              <lb/>
            AB vertex A, rectum figuræ latus ſit
              <lb/>
            AC, & </s>
            <s xml:id="echoid-s645" xml:space="preserve">ordinatim ductæ ad diametrũ
              <lb/>
            in angulo D applicentur.</s>
            <s xml:id="echoid-s646" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s647" xml:space="preserve">Sumatur in AB quodcunque pun-
              <lb/>
            ctum B, per quod in ſubiecto plano, in
              <lb/>
            quo AB, ducatur recta EBF ad angu-
              <lb/>
            lum ABF, qui dato D ſit æqualis, ſu-
              <lb/>
            manturque hinc inde B E, & </s>
            <s xml:id="echoid-s648" xml:space="preserve">B F inter
              <lb/>
            ſe æquales, vtraque verò ſit media
              <lb/>
            proportionalis inter B A, & </s>
            <s xml:id="echoid-s649" xml:space="preserve">datam
              <lb/>
            AC, & </s>
            <s xml:id="echoid-s650" xml:space="preserve">per rectã EF intelligatur quod-
              <lb/>
            cunque planum GEHF, quod non ſit
              <lb/>
            idem cum plano per rectas E F, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum