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

Table of Notes

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              <pb o="471" file="0191" n="201" rhead="AD ANIMADV. HUGENII."/>
            quiſitionem Septimæ eſſe univerſalem. </s>
            <s xml:id="echoid-s4167" xml:space="preserve">Dico igitur & </s>
            <s xml:id="echoid-s4168" xml:space="preserve">de-
              <lb/>
            claro me intelligere, nullam quantitatem indefinitam præter
              <lb/>
            ipſos terminos convergentes compoſitionem poſſe ingredi.
              <lb/>
            </s>
            <s xml:id="echoid-s4169" xml:space="preserve">Atque ita corruunt tres ultimæ Hugenii ſive diverſæ obje-
              <lb/>
            ctiones, ſive ejuſdem portiones; </s>
            <s xml:id="echoid-s4170" xml:space="preserve">neſcio enim, quare in tot
              <lb/>
            partes dividatur.</s>
            <s xml:id="echoid-s4171" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4172" xml:space="preserve">Præcedentibus perceptis, evidentiſſimum eſt, Circuli, El-
              <lb/>
            lipſeos, vel Hyperbolæ ſectorem eſſe terminationem ſeriei
              <lb/>
            convergentis, cujus primi termini a
              <emph style="super">3</emph>
            + a
              <emph style="super">2</emph>
            b, ab
              <emph style="super">2</emph>
            + b
              <emph style="super">3</emph>
            , & </s>
            <s xml:id="echoid-s4173" xml:space="preserve">
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            ſecundi ba
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            a,
              <emph style="sub">2</emph>
            b
              <emph style="super">2</emph>
            a & </s>
            <s xml:id="echoid-s4174" xml:space="preserve">proinde Sectorem eodem
              <note symbol="*" position="right" xlink:label="note-0191-01" xlink:href="note-0191-01a" xml:space="preserve">Schol. 5.</note>
              <note symbol="*" position="right" xlink:label="note-0191-02" xlink:href="note-0191-02a" xml:space="preserve">Conſ. 10.</note>
            do componi ex primis terminis quo ex ſecundis ; </s>
            <s xml:id="echoid-s4175" xml:space="preserve">atque evidens eſt, nullam dari quantitatem eodem modo ana-
              <lb/>
            lyticè compoſitam ex primis terminis quo ex ſecundis, quo-
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            niam primos eodem modo analyticè tractando quo ſe-
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            cundos, ſemper reſtat altior poteſtas ipſius a in primorum
              <lb/>
            producto, quam in producto ſecundorum; </s>
            <s xml:id="echoid-s4176" xml:space="preserve">de hoc (ſi non cre-
              <lb/>
            datur) fiat experientia, & </s>
            <s xml:id="echoid-s4177" xml:space="preserve">conſtabit non ſolum aſſertionis veri-
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            tas, ſed etiam ejuſdem demonſtratio; </s>
            <s xml:id="echoid-s4178" xml:space="preserve">quando autem altior eſt
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            ejuſdem poteſtas in una quantitate quàm in altera, nulla datur
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            indefinita æquatio, de qua hic tantum loquimur, hoc eſt,
              <lb/>
            ut (poſitis a, b, ad libitum,) æqualitas ſemper rite proce-
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            dat. </s>
            <s xml:id="echoid-s4179" xml:space="preserve">Atque hæc eſt ſumma non ſolum propoſitionis unde-
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            cimæ ſed etiam totius noſtræ Circ. </s>
            <s xml:id="echoid-s4180" xml:space="preserve">& </s>
            <s xml:id="echoid-s4181" xml:space="preserve">Hyp. </s>
            <s xml:id="echoid-s4182" xml:space="preserve">Quadraturæ,
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            ab Hugenio adhuc intactæ. </s>
            <s xml:id="echoid-s4183" xml:space="preserve">Gratias tamen ago nobiliſſimo
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            viro, quod meas qualeſcunque lucubrationes examinare di-
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            gnatus eſt, hinc enim mihi data eſt occaſio illas fuſius ex-
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            plicandi & </s>
            <s xml:id="echoid-s4184" xml:space="preserve">confirmandi. </s>
            <s xml:id="echoid-s4185" xml:space="preserve">Num Hugeniana methodus cir-
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            culum menſurandi mea ſit præciſior, experientiæ relinquo
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            judicandum; </s>
            <s xml:id="echoid-s4186" xml:space="preserve">quod autem noſtra, Hyperbolam quadrandi,
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            illi etiam innotuerat, de hoc nihil habeo quod dicam, niſi
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            quod mihi gratuler, inventa mea ipſo Hugenio non æſtima-
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            @i indigna.</s>
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