Gravesande, Willem Jacob 's, Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1

Table of handwritten notes

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              <pb o="(33)" file="0525" n="577" rhead="MATHEMATICA, LIB. III. CAP. VIII."/>
            modo ac ſi vitrum non daretur. </s>
            <s xml:id="echoid-s13442" xml:space="preserve">Diſponatur pixis, ut unus
              <lb/>
            ex radiis per centrum ſuperficiei ſphæricæ aquæ tranſeat, a-
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            lii ad hunc accedent, & </s>
            <s xml:id="echoid-s13443" xml:space="preserve">in F cum hoc concurrent.</s>
            <s xml:id="echoid-s13444" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13445" xml:space="preserve">Detur iterum X medium denſius, Z rarius, ſeparentur
              <lb/>
              <note position="right" xlink:label="note-0525-01" xlink:href="note-0525-01a" xml:space="preserve">TAB. VI.
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              fig. 3.</note>
            ſuperficie ſphæricâ ES, cujus centrum eſt C, & </s>
            <s xml:id="echoid-s13446" xml:space="preserve">cujus con-
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            vexitas eſt ad partem medii rarioris; </s>
            <s xml:id="echoid-s13447" xml:space="preserve">Ex puncto radiante R
              <lb/>
              <note position="right" xlink:label="note-0525-02" xlink:href="note-0525-02a" xml:space="preserve">661.</note>
            procedant radii, & </s>
            <s xml:id="echoid-s13448" xml:space="preserve">in medium denſius per memoratam ſuperfi-
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            ciem penetrent, ita ut inter hos radius RO continuatus per
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            centrum C tranſeat; </s>
            <s xml:id="echoid-s13449" xml:space="preserve">hic non refringitur dum aquam intrat,
              <lb/>
            & </s>
            <s xml:id="echoid-s13450" xml:space="preserve">ad hunc refractione reliqui omnes accedunt, & </s>
            <s xml:id="echoid-s13451" xml:space="preserve">quando
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            parum diſperguntur in unum punctum, ut F, colliguntur, eo-
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            dem modo ac de radiis parallelis dictum; </s>
            <s xml:id="echoid-s13452" xml:space="preserve">cum hac differen-
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            tiâ, quod focus F in hoc caſu magis diſtet. </s>
            <s xml:id="echoid-s13453" xml:space="preserve">Eadem etiam de-
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            monſtratio hìc locum habet ac circa radios parallelos, quæ
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            hoc fundamento nititur, quod angulus incidentiæ, cum ar-
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            cu n O in eadem ratione creſcat, quod & </s>
            <s xml:id="echoid-s13454" xml:space="preserve">hìc obtinet, ſiarcus
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            n O gradus 15. </s>
            <s xml:id="echoid-s13455" xml:space="preserve">non ſuperet. </s>
            <s xml:id="echoid-s13456" xml:space="preserve">Detur radius R n, per n ex
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            centro C ducatur C np: </s>
            <s xml:id="echoid-s13457" xml:space="preserve">angulus R np erit angulus inci-
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            dentiæ; </s>
            <s xml:id="echoid-s13458" xml:space="preserve">dividatur hic in duas partes lineâ nq, parallelâ li-
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            neæ ROC; </s>
            <s xml:id="echoid-s13459" xml:space="preserve">pars pnq æqualis eſt angulo n CO, qui arcu
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            n O menſuratur, & </s>
            <s xml:id="echoid-s13460" xml:space="preserve">qui ideo cum hoc arcu eandem ſequitur
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            proportionem; </s>
            <s xml:id="echoid-s13461" xml:space="preserve">quam etiam, poſito hoc exiguo, ſequitur
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            angulus n RO, æqualis ſecundæ parti anguli incidentiæ,
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            qui igitur in totum etiam cum arcu n O in eadem ratione
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            creſcit & </s>
            <s xml:id="echoid-s13462" xml:space="preserve">minuitur, quæ enim ratio in ſingulis partibus lo-
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            cum habet, reſpectu totius etiam obtinet.</s>
            <s xml:id="echoid-s13463" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13464" xml:space="preserve">Similis demonſtratio poteſt applicari radiis quibuſcunque
              <lb/>
              <note position="right" xlink:label="note-0525-03" xlink:href="note-0525-03a" xml:space="preserve">662.</note>
            divergentibus, aut convergentibus, qui in quocunque caſu
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            in ſuperficie ſphæricâ refringuntur, & </s>
            <s xml:id="echoid-s13465" xml:space="preserve">qui ut hac demonſtra-
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            tione conſtat, in exiguâ diſperſione, focum habent aut ve-
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            rum, aut imaginarium, aut paralleli ſunt inter ſe. </s>
            <s xml:id="echoid-s13466" xml:space="preserve">Quod in
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            genere hic notaſſe ſufficiat.</s>
            <s xml:id="echoid-s13467" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s13468" xml:space="preserve">Focus F radiorum ab R procedentium, accedente R rece-
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              <note position="right" xlink:label="note-0525-04" xlink:href="note-0525-04a" xml:space="preserve">663.</note>
            dit & </s>
            <s xml:id="echoid-s13469" xml:space="preserve">vice verſa. </s>
            <s xml:id="echoid-s13470" xml:space="preserve">Accedente puncto radiante, ſi maneat
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            punctum n, augetur angulus incidentiæ, quo creſcente, au-
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            getur etiam angulus refractionis F n C, & </s>
            <s xml:id="echoid-s13471" xml:space="preserve">n F ad majorem
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            diſtantiam interſecat RC.</s>
            <s xml:id="echoid-s13472" xml:space="preserve"/>
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