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

List of thumbnails

< >
91
91 (67) 		92
92 (68)
93
93 (69) 		94
94 (70)
95
95 (71) 		96
96 (72)
97
97 (73) 		98
98 (74)
99
99 (75) 		100
100 (76)
< >
page |< < (79) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div250" type="section" level="1" n="113">
          <pb o="79" file="0103" n="103" rhead=""/>
        </div>
        <div xml:id="echoid-div252" type="section" level="1" n="114">
          <head xml:id="echoid-head119" xml:space="preserve">THEOR. XXIV. PROP. XXXXV.</head>
          <p>
            <s xml:id="echoid-s2672" xml:space="preserve">Similes Hyperbolæ per diuerſos vertices ſimul adſcriptæ, & </s>
            <s xml:id="echoid-s2673" xml:space="preserve">
              <lb/>
            quarum eadem ſit regula, ſunt inter ſe nunquam coeuntes, & </s>
            <s xml:id="echoid-s2674" xml:space="preserve">in in-
              <lb/>
            finitum productæ ad ſe propiùs accedentes, ſed ad interuallum
              <lb/>
            nunquam perueniunt æquale cuidam dato interuallo.</s>
            <s xml:id="echoid-s2675" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2676" xml:space="preserve">SInt duæ Hyperbolæ ABC, DEF per diuerſos vertices B, E ſimul adſcri-
              <lb/>
            ptæ, quarum eadem ſit regula GH (ſic enim
              <unsure/>
            ſimiles erunt,
              <note symbol="a" position="right" xlink:label="note-0103-01" xlink:href="note-0103-01a" xml:space="preserve">6. ſecúd.
                <lb/>
              defin.</note>
            ductis contingentibus BI, EL; </s>
            <s xml:id="echoid-s2677" xml:space="preserve">eſt tranſuerſum GB ad rectum BI, vt tranſuer-
              <lb/>
            ſum GE ad rectum EL.) </s>
            <s xml:id="echoid-s2678" xml:space="preserve">Dico primùm, has in infinitum productas, nun-
              <lb/>
            quam ſimul conuenire.</s>
            <s xml:id="echoid-s2679" xml:space="preserve"/>
          </p>
          <figure number="71">
            <image file="0103-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0103-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s2680" xml:space="preserve">Protracta enim contingente LE, ſectionem ABC ſecane in M, N, quæ
              <lb/>
            erit ipſi ordinata, cum ſectiones ponantur ſimul adſcriptæ; </s>
            <s xml:id="echoid-s2681" xml:space="preserve">patet ſectionem
              <lb/>
            DEF totam cadere infra contingentem MN. </s>
            <s xml:id="echoid-s2682" xml:space="preserve">Iam ſumpto in ſectione DEF
              <lb/>
            quolibet puncto D, per ipſum ordinatim applicetur ADOH alteram ſectio-
              <lb/>
            nem ſecans in A, regulam verò in H: </s>
            <s xml:id="echoid-s2683" xml:space="preserve">erit quadratum AO, ad quadratum
              <lb/>
            DO, vt rectangulum BOH ad rectangulum EOH (ob ęqualitatem) vel
              <note symbol="b" position="right" xlink:label="note-0103-02" xlink:href="note-0103-02a" xml:space="preserve">Coroll.
                <lb/>
              1. huius.</note>
            altitudo BO ad altitudinem EO, ſed eſt BO maior EO, quare quadratum
              <lb/>
            AO maius erit quadrato DO, ex quo punctum D cadit intra Hyperbolen
              <lb/>
            ABC; </s>
            <s xml:id="echoid-s2684" xml:space="preserve">& </s>
            <s xml:id="echoid-s2685" xml:space="preserve">ſic de quibuſcunque alijs punctis Hyperbolę DEF: </s>
            <s xml:id="echoid-s2686" xml:space="preserve">quare huiuſmo-
              <lb/>
            di ſectiones inter ſe nunquam conueniunt. </s>
            <s xml:id="echoid-s2687" xml:space="preserve">Quod primò, &</s>
            <s xml:id="echoid-s2688" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2689" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2690" xml:space="preserve">Iam ſi datæ Hyperbolæ, per verticem E, adſcribatur Hyperbole P E Q
              <lb/>
            cuius latera ER, ES æqualia ſint lateribus BG, BI, vtrunque vtrique, ipſæ
              <lb/>
            Hyperbolæ ABC, PEQ, congruentes erunt, eritque, (ob
              <note symbol="c" position="right" xlink:label="note-0103-03" xlink:href="note-0103-03a" xml:space="preserve">1. Co-
                <lb/>
              roll. 19. h.</note>
            RE ad ES, vt GB ad BI, vel vt GE ad EL, quare Hyperbolæ DEF, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum