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

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              <pb o="241" file="0319" n="346" rhead="CONTROVERSIA."/>
            Rogantur hac occaſione eruditi, ut examinent, qualem le-
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            gem communicationis celeritatum obſervent corpora mota,
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            quæ ex una parte innituntur firmo fulcimento, ex altera alii
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            corpori itidem, ſed tardius moto: </s>
            <s xml:id="echoid-s5272" xml:space="preserve">ſi namque celeritatis ex-
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            ceſſus, qui hinc inde communicandus eſt, in eadem ratione
              <lb/>
            diſtribueretur, in qua diſtribuitur onus aliquod, quod vecti
              <lb/>
            duobus ſuſtento fulcris impoſitum eſt, nimirum in ratione
              <lb/>
            reciproca diſtantiarum mobilis a fulcris, tum imitando ra-
              <lb/>
            tiocinium Dn. </s>
            <s xml:id="echoid-s5273" xml:space="preserve">Catelani, deprehenderemus, ſummam altitu-
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            dinum, ad quas aſcendunt ſeparata penduli pondera, viciſ-
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            ſim nunc minorem eſſe ſumma altitudinum, e quibus antea
              <lb/>
            conjunctim deſcenderant, quod iterum Hugenianam Propo-
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            ſitionem everteret.</s>
            <s xml:id="echoid-s5274" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5275" xml:space="preserve">En calculum: </s>
            <s xml:id="echoid-s5276" xml:space="preserve">Eſto altitudo A L = 1 ped.</s>
            <s xml:id="echoid-s5277" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5278" xml:space="preserve">Altitudo B N = 4 ped.</s>
            <s xml:id="echoid-s5279" xml:space="preserve"/>
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          <note position="right" xml:space="preserve">
            <lb/>
          Celeritas ponderis A acquiſita in puncto L, ubi deſcendit
            <lb/>
          ſeparatim # = 1
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          Celeritas ponderis B acquiſita in puncto N, quando cadit
            <lb/>
          ſeparatim # = 2
            <lb/>
          Celeritas ponderis A acquiſita in puncto L, quando deſcen-
            <lb/>
          dit conjunctim # = x
            <lb/>
          Igitur Exceſſus celeritatis ponderis A, qui tam in axem,
            <lb/>
          quam in pondus B redundat # = 1 - x
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          Et pars hujus exceſſus, quæ ſoli ponderi B communicatur
            <lb/>
          # = {1/4} - {1/2} x
            <lb/>
          Tota ergo celeritas ponderis B in puncto N cum conjun-
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          ctim cadit # = 2 {1/4} - {1/4} x
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s5280" xml:space="preserve">Atqui vero 2 {1/4} - {1/4} x, x:</s>
            <s xml:id="echoid-s5281" xml:space="preserve">: 4, 1. </s>
            <s xml:id="echoid-s5282" xml:space="preserve">Igitur x = {9/17} & </s>
            <s xml:id="echoid-s5283" xml:space="preserve">4 x = {36/17} eorum-
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            que quadrata {81/289} & </s>
            <s xml:id="echoid-s5284" xml:space="preserve">{1296/289} quorum ſumma 4 {13/17} minor eſt 1 + 4 = 5.
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            </s>
            <s xml:id="echoid-s5285" xml:space="preserve">Antequam finiam, in favorem Dn. </s>
            <s xml:id="echoid-s5286" xml:space="preserve">Catelani hoc monebo,
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            quod etiamſi commune gravitatis centrum juxta illum altius
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            aſcendere deberet, quam deſcendit, nondum tamen ſequa-
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            tur, repertum fore motum perpetuum, ut ſibi perſuadet Ill. </s>
            <s xml:id="echoid-s5287" xml:space="preserve">
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            Hugenius; </s>
            <s xml:id="echoid-s5288" xml:space="preserve">quoniam in iſtis abſtrahi ſolet ab aëris reſiſtentia,
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            a diminutione celeritatis, quæ neceſſario ſequitur disruptio-
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            nem vinculi, quo connectebantur partes penduli, </s>
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