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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          <head xml:id="echoid-head166" xml:space="preserve">II.
            <lb/>
          DEMONSTRATIO
            <lb/>
          REGULÆ
            <lb/>
          DE
            <lb/>
          MAXIMIS ET MINIMIS.</head>
          <p>
            <s xml:id="echoid-s4604" xml:space="preserve">Ad inveſtiganda Maxima & </s>
            <s xml:id="echoid-s4605" xml:space="preserve">Minima in Geometricis quæ-
              <lb/>
            ſtionibus, regulam certam primus, quod ſciam, Fer-
              <lb/>
            matius adhibuit: </s>
            <s xml:id="echoid-s4606" xml:space="preserve">cujus originem ab ipſo non traditam cum
              <lb/>
            exquirerem, inveni ſimul quo pacto ea ipſa regula ad mira-
              <lb/>
            bilem brevitatem perduci poſſet, utque inde eadem illa exiſte-
              <lb/>
            ret quam poſtea vir ampliſſimus Joh. </s>
            <s xml:id="echoid-s4607" xml:space="preserve">Huddenius dederat, tan-
              <lb/>
            quam partem regulæ ſuæ generalioris atque elegantiſſimæ,
              <lb/>
            quæ ab alio prorſus principio pendet. </s>
            <s xml:id="echoid-s4608" xml:space="preserve">Hæc à Fr. </s>
            <s xml:id="echoid-s4609" xml:space="preserve">Schote-
              <lb/>
            nio edita eſt unà cum Carteſianis de Geometria libris. </s>
            <s xml:id="echoid-s4610" xml:space="preserve">Fer-
              <lb/>
            matianæ autem regulæ examen quod inſtitui eſt hujuſ-
              <lb/>
            modi.</s>
            <s xml:id="echoid-s4611" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4612" xml:space="preserve">Quoties Maximum aut Minimum in problemate aliquo de-
              <lb/>
              <note position="left" xlink:label="note-0210-01" xlink:href="note-0210-01a" xml:space="preserve">TAB. XLV.
                <lb/>
              fig. 1.</note>
            terminandum proponitur, certum eſt utrinque æqualitatis
              <lb/>
            caſum exiſtere: </s>
            <s xml:id="echoid-s4613" xml:space="preserve">ut ſi data ſit poſitione recta E D & </s>
            <s xml:id="echoid-s4614" xml:space="preserve">puncta A,
              <lb/>
            B, oporteatque invenire in E D punctum C, unde ductis C A,
              <lb/>
            C B, quadrata earum ſimul ſumpta, ſint minima quæ eſſe poſ-
              <lb/>
            ſint; </s>
            <s xml:id="echoid-s4615" xml:space="preserve">neceſſe eſt ab utraque parte puncti C, eſſe puncta G & </s>
            <s xml:id="echoid-s4616" xml:space="preserve">
              <lb/>
            F, à quibus ducendo rectas G A, G B; </s>
            <s xml:id="echoid-s4617" xml:space="preserve">F A, F B oriatur ſum-
              <lb/>
            ma quadratorum G A, G B æqualis ſummæ quadratorum F A,
              <lb/>
            F B, & </s>
            <s xml:id="echoid-s4618" xml:space="preserve">utraque ſumma major quadratis C A, C B ſimul
              <lb/>
            ſumptis.</s>
            <s xml:id="echoid-s4619" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4620" xml:space="preserve">Ut igitur inveniam punctum C, unde ductis C A, C B
              <lb/>
            fiat ſumma quadratorum ab ipſis omnium minima; </s>
            <s xml:id="echoid-s4621" xml:space="preserve">ductis A E,
              <lb/>
            B D perpendicularibus in E D, quarum A E dicatur a; </s>
            <s xml:id="echoid-s4622" xml:space="preserve">B D,
              <lb/>
            b; </s>
            <s xml:id="echoid-s4623" xml:space="preserve">intervallum verò E, D, c: </s>
            <s xml:id="echoid-s4624" xml:space="preserve">fingo primùm G F, </s>
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