Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

Table of figures

< >
< >
page |< < (110) of 393 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div434" type="section" level="1" n="43">
          <pb o="110" file="0288" n="303" rhead=""/>
        </div>
        <div xml:id="echoid-div456" type="section" level="1" n="44">
          <head xml:id="echoid-head47" xml:space="preserve">APPENDICULA 1.</head>
          <p>
            <s xml:id="echoid-s14209" xml:space="preserve">HIc demùm etſi præter inſtitutum ſit particularia nunc attingere;
              <lb/>
            </s>
            <s xml:id="echoid-s14210" xml:space="preserve">qualibus ſanè, hæc generalia conſequentibus, admodum pro-
              <lb/>
            clive foret turgidum Volumen compingere (_amico tamen morem ge-_
              <lb/>
            _rens operâ_ dignum cenſenti) ſubtexam ad _Circuli Tangentes Secantéſq_; </s>
            <s xml:id="echoid-s14211" xml:space="preserve">
              <lb/>
            ſpectantia nonnulla, pleraque de ſuprà poſitis emergentia.</s>
            <s xml:id="echoid-s14212" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div457" type="section" level="1" n="45">
          <head xml:id="echoid-head48" style="it" xml:space="preserve">Præparatio Communis.</head>
          <note position="left" xml:space="preserve">Fig. 166.</note>
          <p>
            <s xml:id="echoid-s14213" xml:space="preserve">Eſto _cirtuli Quadrans_ ACB, quam tangant rectæ AH, BG; </s>
            <s xml:id="echoid-s14214" xml:space="preserve">& </s>
            <s xml:id="echoid-s14215" xml:space="preserve">
              <lb/>
            in productis HA, AC ſumantur AK, CE ſingulæ pares _radio_ CA;
              <lb/>
            </s>
            <s xml:id="echoid-s14216" xml:space="preserve">& </s>
            <s xml:id="echoid-s14217" xml:space="preserve">_aſymptotis_ AC, CZ per K deſcripta ſit _Hyperbola_ KZZ; </s>
            <s xml:id="echoid-s14218" xml:space="preserve">_aſymp-_
              <lb/>
            _totis_ BC, BG per E _byperbola_ LEO. </s>
            <s xml:id="echoid-s14219" xml:space="preserve">Sumatur etiam in arcu AB
              <lb/>
              <note position="left" xlink:label="note-0288-02" xlink:href="note-0288-02a" xml:space="preserve">Fig. 167.</note>
            _punctum arbitrarium_ M, per quod ducantur recta CMS (tangenti
              <lb/>
            AH occurrens in S) recta MT circulum tangens; </s>
            <s xml:id="echoid-s14220" xml:space="preserve">recta MFZ ad
              <lb/>
            BC parallela, recta MPL ad AC parallela. </s>
            <s xml:id="echoid-s14221" xml:space="preserve">Sit denuò recta α β æ-
              <lb/>
            qualis _arcui_ AB, & </s>
            <s xml:id="echoid-s14222" xml:space="preserve">α μ arcui AM; </s>
            <s xml:id="echoid-s14223" xml:space="preserve">& </s>
            <s xml:id="echoid-s14224" xml:space="preserve">rectæ α γ, ξ μ π ψ rectæ α β
              <lb/>
            perpendiculares; </s>
            <s xml:id="echoid-s14225" xml:space="preserve">quarum α γ = AC; </s>
            <s xml:id="echoid-s14226" xml:space="preserve">μξ = AS; </s>
            <s xml:id="echoid-s14227" xml:space="preserve">μψ = CS; </s>
            <s xml:id="echoid-s14228" xml:space="preserve">μπ
              <lb/>
            = MP.</s>
            <s xml:id="echoid-s14229" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14230" xml:space="preserve">I. </s>
            <s xml:id="echoid-s14231" xml:space="preserve">Recta CS æquatur rectæ FZ; </s>
            <s xml:id="echoid-s14232" xml:space="preserve">adeoque _ſumma ſecantium ad_
              <lb/>
            _arcum_ AM pertinentium, & </s>
            <s xml:id="echoid-s14233" xml:space="preserve">ad rectam AC applicatarum æquatur
              <lb/>
            _ſpatio byperbolico_ AF ZK.</s>
            <s xml:id="echoid-s14234" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14235" xml:space="preserve">Eſt enim CF. </s>
            <s xml:id="echoid-s14236" xml:space="preserve">CA:</s>
            <s xml:id="echoid-s14237" xml:space="preserve">: (CM. </s>
            <s xml:id="echoid-s14238" xml:space="preserve">CS:</s>
            <s xml:id="echoid-s14239" xml:space="preserve">:) CA. </s>
            <s xml:id="echoid-s14240" xml:space="preserve">CS. </s>
            <s xml:id="echoid-s14241" xml:space="preserve">adeòque CF
              <lb/>
            x CS = CAq. </s>
            <s xml:id="echoid-s14242" xml:space="preserve">item CF x FZ = CA x AK = CAq. </s>
            <s xml:id="echoid-s14243" xml:space="preserve">ergo CS = FZ.</s>
            <s xml:id="echoid-s14244" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14245" xml:space="preserve">II. </s>
            <s xml:id="echoid-s14246" xml:space="preserve">_Spatium_ αμξ (hoc eſt _Smmma tangentium in arcu_ AM ad re-
              <lb/>
              <note position="left" xlink:label="note-0288-03" xlink:href="note-0288-03a" xml:space="preserve">Fig. 167.</note>
            ctam αμ applicatarum) æquatur _ſpatio byperbolico_ AFZK.</s>
            <s xml:id="echoid-s14247" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14248" xml:space="preserve">Patet ex hujuſce Lectionis 9.</s>
            <s xml:id="echoid-s14249" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum