Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

Page concordance

< >
Scan Original
41 332
42 333
43 334
44 335
45 336
46 337
47 338
48 339
49 340
50
51
52
53
54
55
56 344
57 345
58 346
59 347
60 348
61 349
62 350
63
64
65
66
67
68
69
70 358
< >
page |< < (332) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div41" type="section" level="1" n="18">
          <p>
            <s xml:id="echoid-s535" xml:space="preserve">
              <pb o="332" file="0038" n="41" rhead="ΕΞΕΤΑΣΙΣ CYCLOM."/>
            habent quam baſes quibus inſiſtunt, certum eſſe quod dixi-
              <lb/>
            mus, ſegmentum circuli C H G ad G H E F, eſſe ut ſoli-
              <lb/>
            dum ex ductu plani A Y Q in pl. </s>
            <s xml:id="echoid-s536" xml:space="preserve">A H X Q ad ſolidum ex
              <lb/>
            ductu plani Q Y V N in pl. </s>
            <s xml:id="echoid-s537" xml:space="preserve">Q X T N.</s>
            <s xml:id="echoid-s538" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s539" xml:space="preserve">Hæc ita enucleatè ſcribere volui, ne cui ignaro fortaſſe na-
              <lb/>
            turæ demonſtrationum quibus Cl. </s>
            <s xml:id="echoid-s540" xml:space="preserve">V. </s>
            <s xml:id="echoid-s541" xml:space="preserve">utitur, ſcrupulus re-
              <lb/>
            ſtare poſſet, quod ubi ille in d. </s>
            <s xml:id="echoid-s542" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s543" xml:space="preserve">52, lib. </s>
            <s xml:id="echoid-s544" xml:space="preserve">10, duo cir-
              <lb/>
            culi ſegmenta conſiderat, quale ferè eſt G H E F, ego pro
              <lb/>
            altero eorum ſumpſerim ſegmentum C H G: </s>
            <s xml:id="echoid-s545" xml:space="preserve">Quodque in
              <lb/>
            linea A B ab ipſo termino A æquales partes capiam A Q,
              <lb/>
            Q N. </s>
            <s xml:id="echoid-s546" xml:space="preserve">Ipſum autem Cl. </s>
            <s xml:id="echoid-s547" xml:space="preserve">Virum hæc remorari non poſſunt,
              <lb/>
            neque hîc, neque in ſequentibus; </s>
            <s xml:id="echoid-s548" xml:space="preserve">quia cum in d. </s>
            <s xml:id="echoid-s549" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s550" xml:space="preserve">52.
              <lb/>
            </s>
            <s xml:id="echoid-s551" xml:space="preserve">& </s>
            <s xml:id="echoid-s552" xml:space="preserve">44, lib. </s>
            <s xml:id="echoid-s553" xml:space="preserve">10. </s>
            <s xml:id="echoid-s554" xml:space="preserve">præcipit in linea a b æquales inter ſe ſumi
              <lb/>
            h i, k l, ſcit hoc nullam limitationem admittere; </s>
            <s xml:id="echoid-s555" xml:space="preserve">ſicut & </s>
            <s xml:id="echoid-s556" xml:space="preserve">
              <lb/>
            in ſchemate communi prop. </s>
            <s xml:id="echoid-s557" xml:space="preserve">39, lib. </s>
            <s xml:id="echoid-s558" xml:space="preserve">10, ubivis in linea a b
              <lb/>
            ſumitur i k, quæ dividitur in duas æquales i m, m k. </s>
            <s xml:id="echoid-s559" xml:space="preserve">Idem
              <lb/>
            contingit in prop. </s>
            <s xml:id="echoid-s560" xml:space="preserve">ſequenti 40.</s>
            <s xml:id="echoid-s561" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s562" xml:space="preserve">Revertor autem ad propoſitum, & </s>
            <s xml:id="echoid-s563" xml:space="preserve">conſtat nunc quidem,
              <lb/>
            ſi detur Ratio ſolidi quod fit ex ductu plani A Y Q in pl.
              <lb/>
            </s>
            <s xml:id="echoid-s564" xml:space="preserve">A H X Q, ad ſolidum ex ductu plani Q Y V N in pl. </s>
            <s xml:id="echoid-s565" xml:space="preserve">
              <lb/>
            Q X T N, eo ipſo dari quoque rationem ſegmenti C H G
              <lb/>
            ad ſegmentum G H E F, ac proinde continuò tunc inveni-
              <lb/>
            ri poſſe quam rationem circulus habeat ad inſcriptum hexa-
              <lb/>
            gonum regulare.</s>
            <s xml:id="echoid-s566" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s567" xml:space="preserve">Vocemus autem brevitatis gratia, id quod fieri diximus
              <lb/>
            ex ductu plani A Y Q in planum A H X Q, ſolidum H Y.
              <lb/>
            </s>
            <s xml:id="echoid-s568" xml:space="preserve">Item quod ſit ex ductu plani Q Y V N in planum Q X T N,
              <lb/>
            ſolidum X V. </s>
            <s xml:id="echoid-s569" xml:space="preserve">Similiter quod oritur ex ductu plani C Θ R
              <lb/>
            in planum C K Δ R, vocemus ſolidum K Θ; </s>
            <s xml:id="echoid-s570" xml:space="preserve">eâdemque
              <lb/>
            brevitate dicamus ſolida Δ Γ, Μ Ξ, Λ Σ, quibus quæ de-
              <lb/>
            notentur jam ſatis intelligitur.</s>
            <s xml:id="echoid-s571" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s572" xml:space="preserve">His ſic conſtitutis, ſciendum eſt, omnem ſpem & </s>
            <s xml:id="echoid-s573" xml:space="preserve">fundamen-
              <lb/>
            tum perficiendæ Quadraturæ Cl. </s>
            <s xml:id="echoid-s574" xml:space="preserve">Viro in eo poſitum eſſe,
              <lb/>
            quod exiſtimet rationem ſolidi H Y ad ſolidum X V (quam
              <lb/>
            unicam tantum deſiderari jam admonui) facile inveniri poſ-
              <lb/>
            ſe, ſi cognitæ ſint duæ rationes hæ, nimirum ratio </s>
          </p>
        </div>
      </text>
    </echo>
Impressum