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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          <p>
            <s xml:id="echoid-s5153" xml:space="preserve">
              <pb o="517" file="0241" n="253" rhead="GEOMET. VARIA."/>
            portionales fieri poſſit, ubi ratio tangentis ad abſciſ-
              <lb/>
            ſam eſt ea quæ numeri ad numerum, hinc apparuit curvam
              <lb/>
            quæſitam tunc iis accenſendam quæ geometricæ vocantur,
              <lb/>
            alias eſſe ex heterogeneis; </s>
            <s xml:id="echoid-s5154" xml:space="preserve">ac tamen conſtructionem dari
              <lb/>
            poſita lineæ logarithmicæ deſcriptione, quam quidem hic ad-
              <lb/>
            ducerem, niſi viderem haud difficulter ex ipſa Jacobi Ber-
              <lb/>
            noullii doctiſſima ſimul breviſſimaque ſolutione omnia erui
              <lb/>
            poſſe, ut jam ab aliis occupatam dubitem.</s>
            <s xml:id="echoid-s5155" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5156" xml:space="preserve">Colligitur vero ex his illud animadverſione dignum,
              <lb/>
            nempe quandocunque in inveſtigatione curvarum ex tan-
              <lb/>
            gentibus aut ſubtangentibus ejus, ad ſimiles ei, quam dixi,
              <lb/>
            æquationes pervenietur, aut in quibus habeatur utrinque
              <lb/>
            elementum ſpatii ad trapezium hyperbolicum reductibilis;
              <lb/>
            </s>
            <s xml:id="echoid-s5157" xml:space="preserve">tunc idem hoc, quod mirabile hic accidit, eventurum, ut
              <lb/>
            curvæ geometricæ diverſorum generum graduumque exi-
              <lb/>
            ſtant, ſi hyperbolarum ad quas devenitur rectangula
              <lb/>
            quæ in aſymptotis, ſint commenſurabilia. </s>
            <s xml:id="echoid-s5158" xml:space="preserve">Præterea
              <lb/>
            obſervanda venit in hoc problemate inuſitata ac ſin-
              <lb/>
            gularis analyſis via, quæ ad alia multa in hac Tan-
              <lb/>
            gentium doctrina aditum aperit, ut egregie jam ani-
              <lb/>
            madvertit Vir Celeberrimus calculi differentialis inven-
              <lb/>
            tor, ſine quo vix eſſet, ut ad haſce geometriæ ſubti-
              <lb/>
            litates admitteremur. </s>
            <s xml:id="echoid-s5159" xml:space="preserve">Porro quod ad curvarum, de qui-
              <lb/>
            bus agitur, deſignationem in plano attinet, poſſem, ſi
              <lb/>
            operæ pretium eſſet, alios modos ac fortaſſe com-
              <lb/>
            modiores indicare quam qui a Cl. </s>
            <s xml:id="echoid-s5160" xml:space="preserve">Bernoullio præſcri-
              <lb/>
            bitur, atque etiam docere qua ratione optime peraga-
              <lb/>
            tur deſcriptio noſtræ quadratricis hyperbolæ, quæ in-
              <lb/>
            ter Tractorias (ita enim vocari poſſunt) ſimpliciſſi-
              <lb/>
            ma cenſenda eſt, cum ad eam filis nihil opus ſit,
              <lb/>
            ſed bacillo tantum utrimque cuſpidem lateri infixam
              <lb/>
            habente, quo fit ut & </s>
            <s xml:id="echoid-s5161" xml:space="preserve">regreſſu explorari poſſit quam
              <lb/>
            recte exarata ſit. </s>
            <s xml:id="echoid-s5162" xml:space="preserve">Sed his ſuperſedendum arbitror, do-
              <lb/>
            nec inſignis uſus aliquis harum linearum in lucem
              <lb/>
            proferatur. </s>
            <s xml:id="echoid-s5163" xml:space="preserve">Interim aliam quandam utiliſſimam </s>
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