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

Table of Notes

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          <p>
            <s xml:id="echoid-s2082" xml:space="preserve">
              <pb o="391" file="0105" n="112" rhead="ILLUST.QUORUND.PROB.CONSTRUCT."/>
            atque ipſi E F. </s>
            <s xml:id="echoid-s2083" xml:space="preserve">quod ſane manifeſtum eſt; </s>
            <s xml:id="echoid-s2084" xml:space="preserve">nam C E eſt æ-
              <lb/>
            qualis C H; </s>
            <s xml:id="echoid-s2085" xml:space="preserve">B D æqualis B G; </s>
            <s xml:id="echoid-s2086" xml:space="preserve">D E vero utriſque ſimul
              <lb/>
            G H, & </s>
            <s xml:id="echoid-s2087" xml:space="preserve">F E. </s>
            <s xml:id="echoid-s2088" xml:space="preserve">Ergo conſtat propoſitum.</s>
            <s xml:id="echoid-s2089" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2090" xml:space="preserve">Sumpſimus autem arcum B C ſemicircumferentiâ mino-
              <lb/>
            rem quoniam in conſtructione problematis ejuſmodi ſemper
              <lb/>
            invenitur. </s>
            <s xml:id="echoid-s2091" xml:space="preserve">Nam lemma ad quoſvis arcus pertinet, eſtque
              <lb/>
            in ſemicircumferentiâ majoribus demonſtratio parum diverſa.</s>
            <s xml:id="echoid-s2092" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div112" type="section" level="1" n="49">
          <head xml:id="echoid-head76" xml:space="preserve">
            <emph style="sc">Probl</emph>
          . II.</head>
          <head xml:id="echoid-head77" style="it" xml:space="preserve">Cubum invenire dati cubi duplum.</head>
          <p>
            <s xml:id="echoid-s2093" xml:space="preserve">AD hoc imperfectam primò conſtructionem proponemus
              <lb/>
            ad mechanicen utilem; </s>
            <s xml:id="echoid-s2094" xml:space="preserve">deinde accuratam ſubjiciemus,
              <lb/>
            quæ tamen non niſi ſæpius tentando perficiatur. </s>
            <s xml:id="echoid-s2095" xml:space="preserve">Etenim ſoli-
              <lb/>
            da problemata omnia vel hoc exigunt vel ſectionum conica-
              <lb/>
            rum deſcriptionem.</s>
            <s xml:id="echoid-s2096" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2097" xml:space="preserve">Sit itaque datus cubus cujus latus A B, oporteatque in-
              <lb/>
              <note position="right" xlink:label="note-0105-01" xlink:href="note-0105-01a" xml:space="preserve">TAB. XLI.
                <lb/>
              Fig. 3.</note>
            venire latus cubi dupli.</s>
            <s xml:id="echoid-s2098" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2099" xml:space="preserve">Radio B A ſemicirculus deſcribatur A F C. </s>
            <s xml:id="echoid-s2100" xml:space="preserve">Sitque arcus
              <lb/>
            A F ſemicircumferentiæ triens, C D vero quadrans; </s>
            <s xml:id="echoid-s2101" xml:space="preserve">& </s>
            <s xml:id="echoid-s2102" xml:space="preserve">du-
              <lb/>
            cantur C F, A D, quarum interſectio ad E punctum. </s>
            <s xml:id="echoid-s2103" xml:space="preserve">Erit
              <lb/>
            A E latus cubi quæſiti; </s>
            <s xml:id="echoid-s2104" xml:space="preserve">exiguo tamen excedens, quodque
              <lb/>
            minus ſit {1/2000} ſui parte, ut facile numeris explorari poteſt.
              <lb/>
            </s>
            <s xml:id="echoid-s2105" xml:space="preserve">Fit enim A E ſecans anguli p. </s>
            <s xml:id="echoid-s2106" xml:space="preserve">37. </s>
            <s xml:id="echoid-s2107" xml:space="preserve">ſcr. </s>
            <s xml:id="echoid-s2108" xml:space="preserve">30. </s>
            <s xml:id="echoid-s2109" xml:space="preserve">quæ proinde ma-
              <lb/>
            jor eſt partibus 12600 qualium A F vel A B 10000. </s>
            <s xml:id="echoid-s2110" xml:space="preserve">Minor
              <lb/>
            autem quam 12605. </s>
            <s xml:id="echoid-s2111" xml:space="preserve">Itaque cum cubus ex 12600 ſit major
              <lb/>
            quam duplus ejus qui ex A B 10000, erit & </s>
            <s xml:id="echoid-s2112" xml:space="preserve">cubus A E
              <lb/>
            major duplo cubo ex A B. </s>
            <s xml:id="echoid-s2113" xml:space="preserve">Rurſus quia A E major eſt par-
              <lb/>
            tibus 12600 erit {1/2000} A E major part. </s>
            <s xml:id="echoid-s2114" xml:space="preserve">6. </s>
            <s xml:id="echoid-s2115" xml:space="preserve">Tota vero A E mi-
              <lb/>
            nor eſt quam 12605. </s>
            <s xml:id="echoid-s2116" xml:space="preserve">Ergo auferendo ab A E partem bis-
              <lb/>
            milleſimam ſui ipſius reliqua minor erit partibus 12599, tot
              <lb/>
            enim ſuperſunt cum ex 12605 deducuntur 6. </s>
            <s xml:id="echoid-s2117" xml:space="preserve">Atqui cubus
              <lb/>
            ex 12599 minor eſt duplo cubo ex 10000. </s>
            <s xml:id="echoid-s2118" xml:space="preserve">Ergo omnino
              <lb/>
            quoque A E diminuta parte ſui biſmilleſima cubum mino-
              <lb/>
            rem producet quam ſit duplus cubus à latere A B.</s>
            <s xml:id="echoid-s2119" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2120" xml:space="preserve">Porro ad perfectam conſtructionem, C F quidem uti </s>
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