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

Table of contents

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[171.] Propositio VIII. Nunc verò ponamus tres eſſe colluſores, quorum pri-mo ut & ſecundo unus luſus deficiat, ſed tertio duo luſus.
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[172.] Propositio IX.
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[173.] Tabula pro 3 colluſoribus.
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[174.] Propositio X. Invenire, quot vicibus ſuſcipere quis poſſit, ut unâ teſſerâ 6 puncta jaciat.
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[175.] Propositio XI. Invenire, quot vicibus ſuſcipere quis poſſit, ut dua-bus teſſeris 12 puncta jaciat.
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[176.] Propositio XII. Invenire quot teſſeris ſuſcipere quis poſſit, ut primâ vice duos ſenarios jaciat.
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[177.] Propositio XIII.
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[178.] Propositio XIV.
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[179.] Coronidis loco ſubjungantur ſequentia Problemata. Problema I.
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[180.] Problema II.
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[181.] Problema III.
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[182.] Problema IV.
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[183.] Problema V.
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[184.] FINIS.
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[185.] CHRISTIANI HUGENII NOVUS CYCLUS HARMONICUS.
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[186.] CHRISTIANI HUGENII NOVUS CYCLUS HARMONICUS. Litteræ D. Hugenii de Cyclo Harmonico.
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[187.] Tabulæ Explicatio.
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[188.] FINIS.
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[189.] CHRISTIANI HUGENII VARIA DE OPTICA.
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[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.
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[191.] II. CONSTRUCTIO PROBLEMATIS OPTICI. Propoſitio 39 Libri v. Alhazeni, & 22 lib. VI. Vitellionis.
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[192.] III. ALITER. Dato Speculo Cavo aut Convexo, itemque Oculo & Puncto Rei viſæ, invenire Punctum Reflexionis.
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[193.] IV. COMPENDIUM.
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[194.] V. ALIA SOLUTIO.
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[195.] VI. Excerpta ex litteris Dni. Hugenii Acad. Reg. ſcient. Socii, ad auctorem Diarii Paris. de novo Mi-croſcopio ex Hollandia allato.
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[196.] FINIS.
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[197.] CHRISTIANI HUGENII EXPERIMENTA PHYSICA.
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[198.] CHRISTIANI HUGENII EXPERIMENTA PHYSICA. Excerpta ex literis Dni Hugenii, Academiæ regiæ ſcien-tiarum Socii, ad Auctorem Diarii Eruditorum, de Phænomenis aquæ aëre purgatæ.
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[199.] EXPERIMENTUMI. Aqua, ſublatâ aëris preſſione, hæret in tubo.
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[200.] EXPERIMENTUM II. Notabile quid in deſcenſu aquæ aëre purgatæ.
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          <head xml:id="echoid-head100" xml:space="preserve">PROP. III. THEOREMA.</head>
          <head xml:id="echoid-head101" style="it" xml:space="preserve">Dico triangulum B A P, & trapezium A B I P ſimul,
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          eſſe ad trapezium A B I P, ut duplum trapezii A B I P ad polygonum A B D L P.</head>
          <note position="right" xml:space="preserve">TAB. XLIII.
            <lb/>
          Fig. 1. 2. 3.</note>
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            <s xml:id="echoid-s2831" xml:space="preserve">In antecedente demonſtratum eſt trapezia A B F P, A B I P
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            ſimul, eſſe ad duplum trapezii A B I P, ſicut trapezium
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            A B F P ad polygonum A B D L P: </s>
            <s xml:id="echoid-s2832" xml:space="preserve">& </s>
            <s xml:id="echoid-s2833" xml:space="preserve">permutando tra-
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            pezia A B F P, A B I P ſimul, ſunt ad trapezium A B F P,
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            ut duplum trapezii A B I P ad polygonum A B D L P. </s>
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            quoniam trapezium A B F P, trapezium A B I P & </s>
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            gulum A B P, ſunt continuè proportionalia; </s>
            <s xml:id="echoid-s2837" xml:space="preserve">erit trape-
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            zium A B I P ad trapezium A B F P, ut triangulum A B P
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            ad trapezium A B I P; </s>
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            <s xml:id="echoid-s2839" xml:space="preserve">componendo, ut trapezia A B I P,
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            A B F P ſimul, ad trapezium A B F P, ita triangulum
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            A B P & </s>
            <s xml:id="echoid-s2840" xml:space="preserve">trapezium A B I P ſimul, ad trapezium A B I P:
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            </s>
            <s xml:id="echoid-s2841" xml:space="preserve">erat autem, ut trapezia A B I P, A B F P, ſimul, ad tra-
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            pezium A B F P, ita duplum trapezii A B I P ad polygo-
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            num A B D L P; </s>
            <s xml:id="echoid-s2842" xml:space="preserve">& </s>
            <s xml:id="echoid-s2843" xml:space="preserve">igitur ut triangulum A B P & </s>
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            zium A B I P ſimul, ad trapezium A B I P, ita duplum
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            trapezii A B I P ad polygonum A B D L P, quod demon-
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            ſtrare oportuit.</s>
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            <s xml:id="echoid-s2846" xml:space="preserve">Producantur (ſi opus ſit) rectæ A D, A L, ſegmentum
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            ſecantes in punctis E & </s>
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            <s xml:id="echoid-s2848" xml:space="preserve">rectas B I, I P, in H & </s>
            <s xml:id="echoid-s2849" xml:space="preserve">M:
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            <s xml:id="echoid-s2850" xml:space="preserve">deinde jungantur rectæ B E, E I, I O, O P, ut complea-
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            tur polygonum A B E I O P.</s>
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          <head xml:id="echoid-head102" xml:space="preserve">PROP. IV. THEOREMA.</head>
          <head xml:id="echoid-head103" style="it" xml:space="preserve">Dico polygonum A B E I O P eſſe medium pro-
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          portionale inter polygonum A B D L & trapezium A B I P.</head>
          <note position="right" xml:space="preserve">TAB. XLIII.
            <lb/>
          Fig. 1. 2. 3.</note>
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            <s xml:id="echoid-s2852" xml:space="preserve">Ex hujus prima manifeſtum eſt trapezium A I L P, tra-
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            pezium A I O P & </s>
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