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

Table of contents

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[191.] II. CONSTRUCTIO PROBLEMATIS OPTICI. Propoſitio 39 Libri v. Alhazeni, & 22 lib. VI. Vitellionis.
Page: 525 (759)
[192.] III. ALITER. Dato Speculo Cavo aut Convexo, itemque Oculo & Puncto Rei viſæ, invenire Punctum Reflexionis.
Page: 526 (760)
[193.] IV. COMPENDIUM.
Page: 527 (761)
[194.] V. ALIA SOLUTIO.
Page: 527 (761)
[195.] VI. Excerpta ex litteris Dni. Hugenii Acad. Reg. ſcient. Socii, ad auctorem Diarii Paris. de novo Mi-croſcopio ex Hollandia allato.
Page: 530 (764)
[196.] FINIS.
Page: 531 (765)
[197.] CHRISTIANI HUGENII EXPERIMENTA PHYSICA.
Page: 533
[198.] CHRISTIANI HUGENII EXPERIMENTA PHYSICA. Excerpta ex literis Dni Hugenii, Academiæ regiæ ſcien-tiarum Socii, ad Auctorem Diarii Eruditorum, de Phænomenis aquæ aëre purgatæ.
Page: 535 (769)
[199.] EXPERIMENTUMI. Aqua, ſublatâ aëris preſſione, hæret in tubo.
Page: 536 (770)
[200.] EXPERIMENTUM II. Notabile quid in deſcenſu aquæ aëre purgatæ.
Page: 537 (771)
[201.] EXPERIMENTUM III. Adhibito ſpiritu vini loco aquæ.
Page: 538 (772)
[202.] EXPERIMENTUM IV. Aër, ex Spiritu vini aut aqua exhauſtus, hæc corpora iterum intrat.
Page: 539 (773)
[203.] EXPERIMENTUM V. Laminæ metallicæ arcte inter ſe cohærent in vacuo licet nihil inter has detur.
Page: 541 (775)
[204.] EXPERIMENTUM VI. Effectus Siphonis in vacuo.
Page: 542 (776)
[205.] FINIS.
Page: 542 (776)
[206.] INDEX RERUM Quatuor Tomis contentarum. TOMUS PRIMUS OPERA MECHANICA.
Page: 546
[207.] TOMUS SECUNDUS. OPERA GEOMETRICA.
Page: 550
[208.] TOMUS TERTIUS. OPERA ASTRONOMICA.
Page: 554
[209.] TOMUS QUARTUS OPERA MISCELLANEA.
Page: 557
[210.] FINIS.
Page: 559
[211.] CATALOGUS QUORUNDAM LIBRORUM, Qui apud Janssonios Van der Aa, Bibliopolas Lugduni Batavorum, venales proſtant.
Page: 560
[212.] AVIS AU RELIEUR.
Page: 563
[213.] BERIGT AAN DEN BOEKBINDER.
Page: 563
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            eadem F major eſt. </s>
            <s xml:id="echoid-s3510" xml:space="preserve">eadem modo utramque ſeriem in infini-
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            tum continuando, ſemper demonſtratur terminum quemlibet
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            ſeriei A B, C D, minorem eſſe quam idem numero terminus
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            ſeriei. </s>
            <s xml:id="echoid-s3511" xml:space="preserve">A B, G H; </s>
            <s xml:id="echoid-s3512" xml:space="preserve">& </s>
            <s xml:id="echoid-s3513" xml:space="preserve">igitur terminatio ſeriei A B, C D, nem-
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            pe Z minor erit terminatione ſeriei A B, G H, nempe X;
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            </s>
            <s xml:id="echoid-s3514" xml:space="preserve">atque ex hujus 7, terminatio ſeriei A B, G H, ſeu X æqua-
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            lis eſt majori duarum mediarum arithmeticè continuè propor-
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            tionalium inter A & </s>
            <s xml:id="echoid-s3515" xml:space="preserve">B, & </s>
            <s xml:id="echoid-s3516" xml:space="preserve">ideo Z eadem minor eſt, quod
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        <div xml:id="echoid-div190" type="section" level="1" n="91">
          <head xml:id="echoid-head127" xml:space="preserve">PROP. XXII. THEOREMA.</head>
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            <s xml:id="echoid-s3518" xml:space="preserve">IIsdem poſitis quæ ſupra; </s>
            <s xml:id="echoid-s3519" xml:space="preserve">dico Z
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              A B # A B
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              C D # G H
                <lb/>
              E F # M N
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              K L # O P
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              Z # X
                <lb/>
              </note>
            ſeu ſectorem circuli vel ellipſeos
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            minorem eſſe quam major duarum
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            mediarum geometricè continuè pro-
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            portionalium inter A & </s>
            <s xml:id="echoid-s3520" xml:space="preserve">B. </s>
            <s xml:id="echoid-s3521" xml:space="preserve">inter A
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            & </s>
            <s xml:id="echoid-s3522" xml:space="preserve">B ſit media geometrica G, & </s>
            <s xml:id="echoid-s3523" xml:space="preserve">inter
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            G & </s>
            <s xml:id="echoid-s3524" xml:space="preserve">B ſit media geometrica H; </s>
            <s xml:id="echoid-s3525" xml:space="preserve">Item
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            inter G & </s>
            <s xml:id="echoid-s3526" xml:space="preserve">H media Geometrica M, & </s>
            <s xml:id="echoid-s3527" xml:space="preserve">inter M & </s>
            <s xml:id="echoid-s3528" xml:space="preserve">H media Geo-
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            metrica N; </s>
            <s xml:id="echoid-s3529" xml:space="preserve">continuetúrque hæc ſeries convergens A B, G H,
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            M N, O P, &</s>
            <s xml:id="echoid-s3530" xml:space="preserve">c, in infinitum, ut fiat ejus terminatio X. </s>
            <s xml:id="echoid-s3531" xml:space="preserve">ſatis
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            patet ex prædictis C & </s>
            <s xml:id="echoid-s3532" xml:space="preserve">G eſſe inter ſe æquales, item H majorem
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            eſſe quam D; </s>
            <s xml:id="echoid-s3533" xml:space="preserve">atque ob hanc rationem M media Geometrica in-
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            ter G & </s>
            <s xml:id="echoid-s3534" xml:space="preserve">H major eſt quam E media geometrica inter G & </s>
            <s xml:id="echoid-s3535" xml:space="preserve">D.
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            </s>
            <s xml:id="echoid-s3536" xml:space="preserve">deinde N media Geometrica inter M & </s>
            <s xml:id="echoid-s3537" xml:space="preserve">H major eſt media har-
              <lb/>
            monica inter easdem; </s>
            <s xml:id="echoid-s3538" xml:space="preserve">& </s>
            <s xml:id="echoid-s3539" xml:space="preserve">quoniam M major eſt quam E & </s>
            <s xml:id="echoid-s3540" xml:space="preserve">H
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            major quam D, erit media harmonica inter M & </s>
            <s xml:id="echoid-s3541" xml:space="preserve">H major quam
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            F media harmonica inter E & </s>
            <s xml:id="echoid-s3542" xml:space="preserve">D; </s>
            <s xml:id="echoid-s3543" xml:space="preserve">& </s>
            <s xml:id="echoid-s3544" xml:space="preserve">ideo N media Geometrica
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            inter M & </s>
            <s xml:id="echoid-s3545" xml:space="preserve">H major erit quam F. </s>
            <s xml:id="echoid-s3546" xml:space="preserve">eadem methodo utramque
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            ſeriem in infinitum continuando ſemper demonſtratur termi-
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            num quemlibet ſeriei A B, C D, minorem eſſe quam idem
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            numero terminus ſeriei A B, G H; </s>
            <s xml:id="echoid-s3547" xml:space="preserve">& </s>
            <s xml:id="echoid-s3548" xml:space="preserve">igitur terminatio ſeriei
              <lb/>
            A B, C D, nempe Z minor erit terminatione ſeriei A B,
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            G H, nempè X; </s>
            <s xml:id="echoid-s3549" xml:space="preserve">atque ex hujus 9 terminatio ſeriei A B,
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            G H, ſeu X, æqualis eſt majori duarum mediarum Geometri-
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            cè continuè proportionalium inter A & </s>
            <s xml:id="echoid-s3550" xml:space="preserve">B; </s>
            <s xml:id="echoid-s3551" xml:space="preserve">& </s>
            <s xml:id="echoid-s3552" xml:space="preserve">ideo Z eadem
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            minor eſt, quod demonſtrare oportuit.</s>
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