Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

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          <pb o="98" file="0146" n="158" rhead="CHRISTIANI HUGENII"/>
          <p>
            <s xml:id="echoid-s2173" xml:space="preserve">Hanc cycloidis dimenſionem primus invenit, via tamen
              <lb/>
              <note position="left" xlink:label="note-0146-01" xlink:href="note-0146-01a" xml:space="preserve">
                <emph style="sc">De linea-</emph>
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                <emph style="sc">RUM CUR-</emph>
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                <emph style="sc">VARUM</emph>
                <lb/>
                <emph style="sc">EVOLUTIO-</emph>
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                <emph style="sc">NE</emph>
              .</note>
            longe alia, eximius geometra Chriſtophorus Wren Anglus,
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            eamque deinde eleganti demonſtratione confirmavit, quæ
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            edita eſt in libro de cycloide viri clariſſimi Ioannis Walliſij.
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            </s>
            <s xml:id="echoid-s2174" xml:space="preserve">De eadem vero linea, alia quoque multa extant pulcherrima
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            inventa noſtri temporis mathematicorum, quibus præcipuè
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            occaſionem præbuere problemata quædam à Blaſio Paſchalio
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            Gallo propoſita, qui in his ſtudiis præcellebat. </s>
            <s xml:id="echoid-s2175" xml:space="preserve">Is cum ſua,
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            tum aliorum inventa recenſens, primum omnium Merſennum
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            lineam hanc in rerum natura advertiſſe ait. </s>
            <s xml:id="echoid-s2176" xml:space="preserve">Primum Roberval-
              <lb/>
            lium tangentes ejus definiviſſe, ac plana & </s>
            <s xml:id="echoid-s2177" xml:space="preserve">ſolida dimenſum eſſe. </s>
            <s xml:id="echoid-s2178" xml:space="preserve">
              <lb/>
            Item centra gravitatis tum plani, tum partium ejus inveniſſe. </s>
            <s xml:id="echoid-s2179" xml:space="preserve">
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            Primum Wrennium curvæ cycloidis æqualem rectam dediſ-
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            ſe. </s>
            <s xml:id="echoid-s2180" xml:space="preserve">Me quoque primum reperiſſe dimenſionem abſolutam por-
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            tionis cycloidis, quæ rectâ, baſi parallelâ, abſcinditur per
              <lb/>
            punctum axis, quod quarta parte ejus à vertice abeſt. </s>
            <s xml:id="echoid-s2181" xml:space="preserve">quæ
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            nimirum portio æquatur dimidio hexagono æquilatero, intra
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            circulum genitorem deſcripto. </s>
            <s xml:id="echoid-s2182" xml:space="preserve">Seipſum denique ſolidorum
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            ac ſemiſolidorum, tam circa baſin quàm circa axem, centra
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            gravitatis definiviſſe, itemque partium eorum. </s>
            <s xml:id="echoid-s2183" xml:space="preserve">Lineæ etiam
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            ipſius (Sed hæc poſt acceptam à Wrennio dimenſionem)
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            centrum gravitatis inveniſſe, & </s>
            <s xml:id="echoid-s2184" xml:space="preserve">dimenſionem ſuperficierum
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            convexarum, quibus ſolida iſta eorumque partes comprehen-
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            duntur; </s>
            <s xml:id="echoid-s2185" xml:space="preserve">earumque ſuperficierum centra gravitatis. </s>
            <s xml:id="echoid-s2186" xml:space="preserve">Ac denique
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            dimenſionem curvarum cujuſvis cycloidis, tam protractæ quam
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            contractæ: </s>
            <s xml:id="echoid-s2187" xml:space="preserve">hoc eſt earum quæ deſcribuntur à puncto intra
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            vel extra circumferentiam circuli genitoris ſumpto. </s>
            <s xml:id="echoid-s2188" xml:space="preserve">Et ho-
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            rum quidem demonſtrationes à Paſchalio ſunt editæ. </s>
            <s xml:id="echoid-s2189" xml:space="preserve">A qui-
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            bus ſuas quoque, de eadem linea, ſubtiliſſimas meditationes
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            expoſuit Cl. </s>
            <s xml:id="echoid-s2190" xml:space="preserve">Walliſius, atque eadem illa omnia ſuo Marte
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            ſe reperiſſe, ac problemata à Paſchalio propoſita ſolviſſe con-
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            tendit. </s>
            <s xml:id="echoid-s2191" xml:space="preserve">Quod idem & </s>
            <s xml:id="echoid-s2192" xml:space="preserve">doctiſſimus Lovera ſibi vindicat. </s>
            <s xml:id="echoid-s2193" xml:space="preserve">Quan-
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            tum vero unicuique debeatur, ex ſcriptis eorum eruditi dijudi-
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            cent. </s>
            <s xml:id="echoid-s2194" xml:space="preserve">Nos propterea tantum præcedentia retulimus, quod ſi-
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            lentio prætereunda non videbantur egregia adeo inventa, qui-
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            bus factum eſt, ut, ex lineis omnibus, nulla nunc melius </s>
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