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

Table of contents

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[181.] Problema III.
[182.] Problema IV.
[183.] Problema V.
[184.] FINIS.
[185.] CHRISTIANI HUGENII NOVUS CYCLUS HARMONICUS.
[186.] CHRISTIANI HUGENII NOVUS CYCLUS HARMONICUS. Litteræ D. Hugenii de Cyclo Harmonico.
[187.] Tabulæ Explicatio.
[188.] FINIS.
[189.] CHRISTIANI HUGENII VARIA DE OPTICA.
[190.] CHRISTIANI HUGENII VARIA DE OPTICA. I. Excerpta ex literis Dni Hugenii, Academiæ Regiæ Scientiarum Socii, ad Autorem Diarii Eruditoruns de Catoptrico conſpicillo Dni Newtoni.
[191.] II. CONSTRUCTIO PROBLEMATIS OPTICI. Propoſitio 39 Libri v. Alhazeni, & 22 lib. VI. Vitellionis.
[192.] III. ALITER. Dato Speculo Cavo aut Convexo, itemque Oculo & Puncto Rei viſæ, invenire Punctum Reflexionis.
[193.] IV. COMPENDIUM.
[194.] V. ALIA SOLUTIO.
[195.] VI. Excerpta ex litteris Dni. Hugenii Acad. Reg. ſcient. Socii, ad auctorem Diarii Paris. de novo Mi-croſcopio ex Hollandia allato.
[196.] FINIS.
[197.] CHRISTIANI HUGENII EXPERIMENTA PHYSICA.
[198.] CHRISTIANI HUGENII EXPERIMENTA PHYSICA. Excerpta ex literis Dni Hugenii, Academiæ regiæ ſcien-tiarum Socii, ad Auctorem Diarii Eruditorum, de Phænomenis aquæ aëre purgatæ.
[199.] EXPERIMENTUMI. Aqua, ſublatâ aëris preſſione, hæret in tubo.
[200.] EXPERIMENTUM II. Notabile quid in deſcenſu aquæ aëre purgatæ.
[201.] EXPERIMENTUM III. Adhibito ſpiritu vini loco aquæ.
[202.] EXPERIMENTUM IV. Aër, ex Spiritu vini aut aqua exhauſtus, hæc corpora iterum intrat.
[203.] EXPERIMENTUM V. Laminæ metallicæ arcte inter ſe cohærent in vacuo licet nihil inter has detur.
[204.] EXPERIMENTUM VI. Effectus Siphonis in vacuo.
[205.] FINIS.
[206.] INDEX RERUM Quatuor Tomis contentarum. TOMUS PRIMUS OPERA MECHANICA.
[207.] TOMUS SECUNDUS. OPERA GEOMETRICA.
[208.] TOMUS TERTIUS. OPERA ASTRONOMICA.
[209.] TOMUS QUARTUS OPERA MISCELLANEA.
[210.] FINIS.
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            ſequentes Vqab, {aa.</s>
            <s xml:id="echoid-s3133" xml:space="preserve">/Vqab} ſumma terminorum convergentium
              <emph style="super">a + b</emph>
              <lb/>
            multiplicata in terminum convergentem primum
              <emph style="sub">a</emph>
            efficit
              <lb/>
            aa + ab: </s>
            <s xml:id="echoid-s3134" xml:space="preserve">& </s>
            <s xml:id="echoid-s3135" xml:space="preserve">ſumma terminorum convergentium immediate ſe-
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            quentium nempe Vqab + {aa/Vqab} multiplicata in primum terminum
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            convergentem
              <emph style="super">Vqab</emph>
            efficit etiam aa + ab; </s>
            <s xml:id="echoid-s3136" xml:space="preserve">ex his invenienda ſit ſe-
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            riei propoſitæ terminatio. </s>
            <s xml:id="echoid-s3137" xml:space="preserve">manifeſtum eſt quantitatem aa + ab
              <lb/>
            eodem modo fieri à terminis convergentibus
              <emph style="super">a, b,</emph>
            quo à termi-
              <lb/>
            nis convergentibus immediatè ſequentibus Vqab, {aa/Vqab:</s>
            <s xml:id="echoid-s3138" xml:space="preserve">} & </s>
            <s xml:id="echoid-s3139" xml:space="preserve">quo-
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            niam quantitates
              <emph style="super">a, b,</emph>
            indefinitæ ponuntur pro quibuslibet to-
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            tius ſeriei terminis convergentibus, evidens eſt ſummam quo-
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            rumcunque terminorum convergentium propoſitæ ſeriei mul-
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            tiplicatam in primum terminum convergentem efficere quan-
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            titatem æqualem illi, quæ fit à ſumma terminorum conver-
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            gentium immediatè ſequentium multiplicata etiam in primum
              <lb/>
            ſuum terminum convergentem; </s>
            <s xml:id="echoid-s3140" xml:space="preserve">cumque duo termini conver-
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            gentes duos terminos convergentes ſemper immediatè ſe-
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            quuntur, manifeſtum eſt ſummam duorum quorumlibet ter-
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            minorum convergentium multiplicatam in primum ſemper
              <lb/>
            efficere eandem quantitatem nempe aa + ab, atque ultimi ter-
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            mini convergentes ſunt æquales, & </s>
            <s xml:id="echoid-s3141" xml:space="preserve">proinde ſit ultimus ille
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            terminus ſeu ſeriei terminatio
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            , quæ ſibi addita & </s>
            <s xml:id="echoid-s3142" xml:space="preserve">in ſum-
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            mam multiplicata efficit
              <emph style="super">2 zz</emph>
            , quæ quantitas debet eſſe æqua-
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            lis quantitati aa + ab, & </s>
            <s xml:id="echoid-s3143" xml:space="preserve">æquatione reſoluta dabitur
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            ſeu ſeriei
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            terminatio {Vq aa + ab,/2} quam invenire oportuit.</s>
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            <s xml:id="echoid-s3145" xml:space="preserve">Et proinde ad inveniendam cujuscunque ſeriei convergen-
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            tis terminationem; </s>
            <s xml:id="echoid-s3146" xml:space="preserve">opus eſt ſolummodo invenire quantitatem
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            eodem modo compoſitam ex terminis convergentibus primis,
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            quo componitur eadem quantitas ex terminis convergentibus
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            ſecundis.</s>
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          <head xml:id="echoid-head113" xml:space="preserve">CONSECTARIUM.</head>
          <p>
            <s xml:id="echoid-s3148" xml:space="preserve">Quoniam non refert in problemate ſive termini conver-
              <lb/>
            gentes a, b, ſint primi, ſecundi, vel tertii &</s>
            <s xml:id="echoid-s3149" xml:space="preserve">c; </s>
            <s xml:id="echoid-s3150" xml:space="preserve">manifeſtum </s>
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