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

Table of contents

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[101.] PROP. XXXI. PROBLEMA. Ex dato arcu invenire ſinum.
[102.] PROP. XXXII. PROBLEMA. Invenire quadratum æquale ſpatio hyperbolico con-tento à curva hyperbolica, uno aſymptoto & dua-bus rectis alteri aſymptoto parallelis; quod ſpatium æquale eſt ſectori hyperbolico cujus baſis eſt eadem curva.
[103.] PROP. XXXIII. PROBLEMA. Propoſiti cujuscunque numeri logorithmum invenire.
[104.] SCHOLIUM.
[105.] PROP. XXXIV. PROBLEMA. Ex dato logorithmo invenire ejus numerum.
[106.] Tom. II. Mmm
[107.] PROP. XXXV. PROBLEMA. Rectâ per datum punctum in diametro ductâ, ſemicirculum in ratione data dividere.
[108.] SCHOLIUM.
[109.] FINIS.
[110.] II. HUGENII OBSERVATIONES IN LIBRUM JACOBI GREGORII, DE VERA CIRCULI ET HYPERBOLÆ QUADRATURA.
[111.] III. DOMINI GREGORII RESPONSUM AD ANIMADVERSIONES DOMINI HUGENII, IN EJUS LIBRUM, DE VERA CIRCULI ET HYPERBOLÆ QUADRATURA.
[112.] PROP. X. PROBLEMA.
[113.] Tom. II. Nnn
[114.] CONSECTARIUM.
[115.] IV. EXCERPTA EX LITERIS Dni. HUGENII DE RESPONSO, QUOD Dnus. GREGORIUS DEDIT AD EXAMEN LIBRI, CUI TITULUS EST, VERA CIRCULI ET HYPERBOLÆ QUADRATURA.
[116.] V. EXCERPTA EX EPISTOLA D. JACOBI GREGORII, CONTINENTE QUASDAM EJUS CONSIDERATIO-NES, SUPER EPISTOLA D. HUGENII, IMPRESSA IN VINDICATIONEM EXAMINIS SUI LIBRI, DE VERA CIRCULI ET HY-PERBOLÆ QUADRATURA.
[117.] FINIS.
[118.] CHRISTIANI HUGENII GEOMETRICA VARIA. Tom. II. Ppp
[119.] I. CONSTRUCTIO LOCI AD HYPERBOLAM PER ASYMPTOTOS.
[120.] DEMONSTRATIO.
[121.] II. DEMONSTRATIO REGULÆ DE MAXIMIS ET MINIMIS.
[122.] Tom. II. Qqq
[123.] III. REGULA Ad inveniendas Tangentes linearum curvarum.
[124.] Tom. II. Rrr
[125.] IV. CHRISTIANI HUGENII EPISTOLA DE CURVIS QUIBUSDAM PECULIARIBUS.
[126.] V. PROBLEMA AB ERUDITIS SOLVENDUM: A JOHANNE BERNOULLIO IN ACTIS LIPSIENSIBUS ANNI MDCXCIII. PROPOSITUM.
[127.] Tom. II. Ttt
[128.] VI. C. H. Z. DE PROBLEMATE BERNOULLIANO IN ACTIS LIPSIENSIBUS PROPOSITO.
[129.] VII. C. H. Z. CONSTRUCTIO UNIVERSALIS PROBLEMATIS A CLARISSIMO VIRO JOH. BERNOULLIO PROPOSITI.
[130.] FINIS.
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            tione, diviſione, & </s>
            <s xml:id="echoid-s3240" xml:space="preserve">radicum extractione trianguli A B P & </s>
            <s xml:id="echoid-s3241" xml:space="preserve">
              <lb/>
            trapezii A B F P: </s>
            <s xml:id="echoid-s3242" xml:space="preserve">triangulum autem A B P & </s>
            <s xml:id="echoid-s3243" xml:space="preserve">trapezium
              <lb/>
            A B F P ſupponimus eſſe quantitates inter ſe analyticas; </s>
            <s xml:id="echoid-s3244" xml:space="preserve">& </s>
            <s xml:id="echoid-s3245" xml:space="preserve">
              <lb/>
            proinde ſector A B I P illis analytica eſſe non poteſt, hoc
              <lb/>
            eſt ex quantitatum ipſis A B P, A B F P analyticarum addi-
              <lb/>
            tione, ſubductione, multiplicatione, diviſione & </s>
            <s xml:id="echoid-s3246" xml:space="preserve">radicum
              <lb/>
            extractione componi non poteſt; </s>
            <s xml:id="echoid-s3247" xml:space="preserve">& </s>
            <s xml:id="echoid-s3248" xml:space="preserve">proinde ex hoc capite
              <lb/>
            nulla poteſt exhiberi ratio inter triangulum A B P & </s>
            <s xml:id="echoid-s3249" xml:space="preserve">ſecto-
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            rem A B I P, cum evidens ſit illam non eſſe analyticam. </s>
            <s xml:id="echoid-s3250" xml:space="preserve">ſed
              <lb/>
            dicet fortè aliquis rationem inter triangulum A B P & </s>
            <s xml:id="echoid-s3251" xml:space="preserve">ſecto-
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            rem A B I P omnifariam variari poſſe; </s>
            <s xml:id="echoid-s3252" xml:space="preserve">& </s>
            <s xml:id="echoid-s3253" xml:space="preserve">proinde poſſe eſſe
              <lb/>
            inter ſe in ratione qualibet data ſive analytica ſive etiam com-
              <lb/>
            menſurabili: </s>
            <s xml:id="echoid-s3254" xml:space="preserve">reſpondeo hoc eſſe veriſſimum, ſed in hoc ca-
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            ſu ratio inter triangulum A B P & </s>
            <s xml:id="echoid-s3255" xml:space="preserve">trapezium A B F P non
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            erit analytica; </s>
            <s xml:id="echoid-s3256" xml:space="preserve">& </s>
            <s xml:id="echoid-s3257" xml:space="preserve">proinde ex dato circulo ellipſe vel hyper-
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            bola nunquam dabitur in analyticis triangulum A B P, quod
              <lb/>
            ex prædictis clariſſimè patet. </s>
            <s xml:id="echoid-s3258" xml:space="preserve">etiamſi ex prædicto capite non
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            poſſimus comprehendere rationem inter triangulum A B P & </s>
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            ſectorem A B I P, poſſumus tamen ejus aliquam habere cogni-
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            tionem, ex eo quod ſector A B I P ſit terminatio ſeriei con-
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            vergentis datæ; </s>
            <s xml:id="echoid-s3260" xml:space="preserve">& </s>
            <s xml:id="echoid-s3261" xml:space="preserve">ex hac conſideratione poſſibile eſt inve-
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            nire quantitatem datæ commenſurabilem cujus differentia à
              <lb/>
            ſectore A B I P minor fuerit quacunque quantitate propoſi-
              <lb/>
            ta, ad hoc enim ſemper recurrendum eſt, cum de quantita-
              <lb/>
            tibus quibuscunque incommenſurabilibus tractant practici,
              <lb/>
            & </s>
            <s xml:id="echoid-s3262" xml:space="preserve">in hac noſtra approximatione praxis non erit operoſior
              <lb/>
            quam in multis aliis etiam quantitatum analyticarum appro-
              <lb/>
            ximationibus, immo multo brevior, facilior & </s>
            <s xml:id="echoid-s3263" xml:space="preserve">paratior erit
              <lb/>
            illis Vietæ ſectionibus angularibus, quæ tamen ſummæ ma-
              <lb/>
            theſeos utilitati in praxem reducuntur. </s>
            <s xml:id="echoid-s3264" xml:space="preserve">non video ergo qua-
              <lb/>
            re circuli quadratura diutius æſtimetur ignorari: </s>
            <s xml:id="echoid-s3265" xml:space="preserve">cum enim
              <lb/>
            demonſtratum ſit rationem circuli ad diametri quadratum
              <lb/>
            non eſſe analyticam, vanum certè erit & </s>
            <s xml:id="echoid-s3266" xml:space="preserve">ineptum illam ſicut
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            talem impoſterum quærere: </s>
            <s xml:id="echoid-s3267" xml:space="preserve">at rejectis quantitatibus analyti-
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            cis, vix credo ullam poſſe eſſe notiorem hisce noſtrarum ſe-
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            rierum convergentium terminationibus, ſicut ex ſequentibus
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            pleniſſimè apparebit.</s>
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