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

Table of figures

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[161] Fig. 8.R G M K N D B V C A
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[162] Fig. 7.R d D G g B h H E V C u A c
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[163] Fig. 2.B F G C H A K D E
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[164] Fig. 4.A B G F E C D
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[165] Fig. 6.T G D H B E M L N C K I S P F V R Q O A
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[166] Fig. 3.A E G B D F C
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[167] Fig. 5.N K F E C B A H L V W R G
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[168] Fig. 9.Z R A X H C B D M K S Q G
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            quibus Hugenius loquitur, ut probet propoſitionem meam
              <lb/>
            falſam, ſint anguli rectilinei agitati circa verticem, non
              <lb/>
            habentes requiſitam conditionem, me non feriunt. </s>
            <s xml:id="echoid-s5014" xml:space="preserve">Si
              <lb/>
            concipiamus tales angulos moveri circa Axem, per verti-
              <lb/>
            ces illorum transeuntem, patet ſummas diſtantiarum Axis ab
              <lb/>
            omnibus punctis linearum, quæ Pendula componunt, eſſe
              <lb/>
            inæquales, prout illæ lineæ efficiunt cum Axe angulos ma-
              <lb/>
            gis minusve acutos. </s>
            <s xml:id="echoid-s5015" xml:space="preserve">Et meâ regulâ detego ſummas diſtantia-
              <lb/>
            rum eſſe æquales Parabolis habentibus pro Diametro maxi-
              <lb/>
            mam ab Axe diſtantiam, & </s>
            <s xml:id="echoid-s5016" xml:space="preserve">pro Parametro 4
              <emph style="super">am</emph>
            proportiona-
              <lb/>
            lem poſitis hiſce tribus, linea datâ, quæ eadem eſt in quo-
              <lb/>
            vis Pendulo, maximâ diſtantiâ, quæ variat pro variis angu-
              <lb/>
            lis, & </s>
            <s xml:id="echoid-s5017" xml:space="preserve">unitate; </s>
            <s xml:id="echoid-s5018" xml:space="preserve">unde ſequitur, tempus Oſcillationis valere {2/3} ma-
              <lb/>
            ximæ ab Axe diſtantiæ, & </s>
            <s xml:id="echoid-s5019" xml:space="preserve">non in omni caſu idem eſſe; </s>
            <s xml:id="echoid-s5020" xml:space="preserve">tanto
              <lb/>
            enim brevius eſt, quanto angulus eſt obtuſior, id eſt, quan-
              <lb/>
            to Pendulum magis Axi vicinum eſt.</s>
            <s xml:id="echoid-s5021" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5022" xml:space="preserve">Si Hugenius deſiderat propoſitionem quæ conveniat Pen-
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            dulis, circa punctum motis, mutanda tantum erunt verba
              <lb/>
            quædam in principio Pendulorum habentibum Axem; </s>
            <s xml:id="echoid-s5023" xml:space="preserve">loco
              <lb/>
            radices diſtantiarum illarum, legendum ſummæ linearum re-
              <lb/>
            ctarum, quæ repræſentant tempora Oſcillationum omnium par-
              <lb/>
            tium ſeparatim ſumtarum.</s>
            <s xml:id="echoid-s5024" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5025" xml:space="preserve">Hoc modo propoſitio inſerviet ambobus caſibus. </s>
            <s xml:id="echoid-s5026" xml:space="preserve">Sed res
              <lb/>
            melius intelligitur per generale Principium, quod propoſui
              <lb/>
            & </s>
            <s xml:id="echoid-s5027" xml:space="preserve">ita ſe habet. </s>
            <s xml:id="echoid-s5028" xml:space="preserve">In eodem Pendulo, cum omnes partes niſi
              <lb/>
            ſimul moveri nequeant, propter ſuam conjunctionem, vibra-
              <lb/>
            tio minus diſtantium ab Axe, vel puncto ſuſpenſionis, ita
              <lb/>
            retardatur a vibratione remotiorum, & </s>
            <s xml:id="echoid-s5029" xml:space="preserve">reciproce Oſcillatio
              <lb/>
            remotiorum ita acceleratur per Oſcillationem aliarum, ut de-
              <lb/>
            tur inter illas compenſatio celeritatum proportionalis arcubus,
              <lb/>
            vel cur varum portionibus, quas deſcribunt, ita ut tempus Oſcil-
              <lb/>
            lationis totius Penduli ſit medium inter tempora Vibratio-
              <lb/>
            num, quas peragerent illæ partes, ſi non inter ſe forent con-
              <lb/>
            junctæ, id eſt, ut ſit æquale ſummæ temporum illorum diviſæ
              <lb/>
            per numerum partium, quas debemus conſiderare ut æquales
              <lb/>
            & </s>
            <s xml:id="echoid-s5030" xml:space="preserve">infinite parvas.</s>
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