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

Table of Notes

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              <pb o="329" file="0035" n="38" rhead="ΕΞΕΤΑΣΙΣ CYCLOM. GR. à S. VINC."/>
            ventionis hiſtoriam & </s>
            <s xml:id="echoid-s433" xml:space="preserve">progreſſum paucis expoſuit, nullius
              <lb/>
            modi præter hunc unum meminerit. </s>
            <s xml:id="echoid-s434" xml:space="preserve">Potuit autem & </s>
            <s xml:id="echoid-s435" xml:space="preserve">aliam
              <lb/>
            rationem habuiſſe tres poſteriores quadraturas illic ſilentio
              <lb/>
            prætereundi, eam videlicet, quod quatuor omnes ſciret ex
              <lb/>
            iiſdem principiis deductas & </s>
            <s xml:id="echoid-s436" xml:space="preserve">demonſtratas eſſe. </s>
            <s xml:id="echoid-s437" xml:space="preserve">Sed mihi vel
              <lb/>
            alterutra harum conſiderationum ſufficere viſa eſt, ut per-
              <lb/>
            ſuaderet unam pro omnibus fore diſcuſſionem quæ quadra-
              <lb/>
            turam primariam infirmatura eſſet, reliquarum agmen du-
              <lb/>
            centem. </s>
            <s xml:id="echoid-s438" xml:space="preserve">Si enim erratum in ea oſtenderimus quæ minus
              <lb/>
            obſcuritatis habet, non video quâ ratione melior ſuc-
              <lb/>
            ceſſus expectandus ſit in tribus ſequentibus, quæ maximâ
              <lb/>
            caligine involvuntur, quaſque Auctor ipſe vel uni illi poſt-
              <lb/>
            habere videtur. </s>
            <s xml:id="echoid-s439" xml:space="preserve">Principia quæ communia eſſe omnibus qua-
              <lb/>
            draturis dixi, ea ſunt nova inventa de Proportionalitatibus
              <lb/>
            Geometricis ſive de Proportionum proportionibus, & </s>
            <s xml:id="echoid-s440" xml:space="preserve">de
              <lb/>
            Ductibus plani in planum. </s>
            <s xml:id="echoid-s441" xml:space="preserve">Quæ quidem prorſus non impu-
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            gnabo, nam & </s>
            <s xml:id="echoid-s442" xml:space="preserve">ſolida corpora quæcunque in Geometria con-
              <lb/>
            ſiderare licere exiſtimo, & </s>
            <s xml:id="echoid-s443" xml:space="preserve">alia omnia adhiberi poſſe, quæ
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            modò ullo auxilio fore credimus ad inveſtigationem veri. </s>
            <s xml:id="echoid-s444" xml:space="preserve">U-
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            num tamen prætermittere nequeo quin dicam, Clar. </s>
            <s xml:id="echoid-s445" xml:space="preserve">Virum
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            non ſatis feliciter quædam inventa in materia Proportiona-
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            litatum ad Quadraturam applicaſſe, atque hinc, meâ opi-
              <lb/>
            nione, ipſi extitiſſe erroris cauſam. </s>
            <s xml:id="echoid-s446" xml:space="preserve">Primùm omnium id in
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            propoſ. </s>
            <s xml:id="echoid-s447" xml:space="preserve">39. </s>
            <s xml:id="echoid-s448" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s449" xml:space="preserve">10. </s>
            <s xml:id="echoid-s450" xml:space="preserve">Oper. </s>
            <s xml:id="echoid-s451" xml:space="preserve">Geom. </s>
            <s xml:id="echoid-s452" xml:space="preserve"> obſervaveram. </s>
            <s xml:id="echoid-s453" xml:space="preserve">Poſitis enim numeris fortuitò aſſumptis, 2, 3, 4, 5; </s>
            <s xml:id="echoid-s454" xml:space="preserve">deinde horum
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            quadratis 4, 9, 16, 25; </s>
            <s xml:id="echoid-s455" xml:space="preserve">& </s>
            <s xml:id="echoid-s456" xml:space="preserve">quadratorum, quadratis, 16,
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            81, 256, 625; </s>
            <s xml:id="echoid-s457" xml:space="preserve">videbam duodecim hiſce eandem demonſtra-
              <lb/>
            tionem convenire, quæ in dicta prop. </s>
            <s xml:id="echoid-s458" xml:space="preserve">39. </s>
            <s xml:id="echoid-s459" xml:space="preserve">ſcripta eſt de to-
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            tidem parallelepipedis. </s>
            <s xml:id="echoid-s460" xml:space="preserve">Et quum tamen concluſio nullam ido-
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            neam admitteret interpretationem, non dubitabam quin æ-
              <lb/>
            què ipſius ac mea argumentatio, quam iiſdem verbis forma-
              <lb/>
            veram, aliquid abſurdi contineret. </s>
            <s xml:id="echoid-s461" xml:space="preserve">Poſterior autem demon-
              <lb/>
            ſtrationis pars rectè ſe habebat, ideoque arguebat peccatum
              <lb/>
              <note symbol="*" position="foot" xlink:label="note-0035-01" xlink:href="note-0035-01a" xml:space="preserve">In hac Propoſ. 39. etiam Carteſius paralogiſmum oſtendit Epiſt. ad
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              Schotenium.</note>
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