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

Table of contents

< >
[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.
[131.] CHRISTIANI HUGENII OPERA ASTRONOMICA. Tomus Tertius.
[132.] Tomi tertii contenta.
[133.] CHRISTIANI HUGENII DE SATURNILUNA OBSERVATIO NOVA. Tom. III. Ttt
[134.] CHRISTIANI HUGENII DE SATURNI LUNA OBSERVATIO NOVA.
[135.] Tom. III. Vvv.
[136.] CHRISTIANI HUGENII ZULICHEMII, CONST. F. SYSTEMA SATURNIUM, SIVE DE CAUSIS MIRANDORUM SATURNI PHÆNOMENON; ET COMITE EJUS PLANETA NOVO.
[137.] SERENISSIMO PRINCIPI LEOPOLDO AB HETRURIA Chriſtianus Hugenius S.D.
[138.] Tom. III. Xxx
[139.] NICOLAUS HEINSIUS, D. F. AD AUCTOREM SYSTEMATIS.
[140.] CHRISTIANI HUGENII Zulichemii, Cθnst. F. SYSTEMA SATURNIUM.
< >
page |< < (467) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div225" type="section" level="1" n="111">
          <p>
            <s xml:id="echoid-s4053" xml:space="preserve">
              <pb o="467" file="0187" n="197" rhead="JAC. GREG. RESPONS."/>
            perientiam enim feci ſolummodo de primis & </s>
            <s xml:id="echoid-s4054" xml:space="preserve">ſecundis ter-
              <lb/>
            minis, non conſiderando tertios cum primis coincidere, nam
              <lb/>
            ratiociniis inſiſtebam, de exemplis parum ſolicitus. </s>
            <s xml:id="echoid-s4055" xml:space="preserve">Ut au-
              <lb/>
            tem appareat in hoc nihil contineri contra noſtram Doctri-
              <lb/>
            nam, agedum hoc loco 10: </s>
            <s xml:id="echoid-s4056" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s4057" xml:space="preserve">totidem verbis, ſed cum
              <lb/>
            legitimo exemplo repetamus.</s>
            <s xml:id="echoid-s4058" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div226" type="section" level="1" n="112">
          <head xml:id="echoid-head154" xml:space="preserve">PROP. X. PROBLEMA.</head>
          <p style="it">
            <s xml:id="echoid-s4059" xml:space="preserve">Ex data quantitate eodem modo compoſita à duobus
              <lb/>
            terminis convergentibus cujuſcunque ſeriei convergen-
              <lb/>
            tis, quo componitur ex terminis convergentibus ejuſ-
              <lb/>
            dem ſeriei immediate ſequentibus; </s>
            <s xml:id="echoid-s4060" xml:space="preserve">ſeriei propoſitæ
              <lb/>
            terminationem invenire.</s>
            <s xml:id="echoid-s4061" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4062" xml:space="preserve">Sit ſeries convergens, cujus duo termini convergentes qui-
              <lb/>
            cunque ſint a, b, & </s>
            <s xml:id="echoid-s4063" xml:space="preserve">termini convergentes immediatè ſe-
              <lb/>
            quentes {2 a b/a + b}, {a + b/2}, termini priores inter ſe multiplicati effi-
              <lb/>
            ciunt eandem a b, item ſequentes inter ſe multiplicati effi-
              <lb/>
            ciunt eandem a b; </s>
            <s xml:id="echoid-s4064" xml:space="preserve">ex his invenienda ſit propoſitæ ſeriei ter-
              <lb/>
            minatio. </s>
            <s xml:id="echoid-s4065" xml:space="preserve">Manifeſtum eſt, quantitatem a b eodem modo
              <lb/>
            fieri à terminis convergentibus a, b, quo à terminis conver-
              <lb/>
            gentibus immediatè ſequentibus {2 a b/a + b}, {a + b/z}: </s>
            <s xml:id="echoid-s4066" xml:space="preserve">& </s>
            <s xml:id="echoid-s4067" xml:space="preserve">quoniam quan-
              <lb/>
            titates a, b, indefinitè ponuntur pro quibuslibet totius ſe-
              <lb/>
            riei terminis convergentibus, evidens eſt, duos quoſcunque
              <lb/>
            terminos convergentes propoſitæ ſeriei inter ſe multiplica-
              <lb/>
            tos idem efficere productum, quod faciunt termini imme-
              <lb/>
            diatè ſequentes etiam inter ſe multiplicati; </s>
            <s xml:id="echoid-s4068" xml:space="preserve">cumque duo ter-
              <lb/>
            mini convergentes duos terminos convergentes ſemper im-
              <lb/>
            mediatè ſequantur, manifeſtum eſt, duos quoſcunque ter-
              <lb/>
            minos convergentes inter ſe multiplicatos idem ſemper effi-
              <lb/>
            cere productum, nempe a b; </s>
            <s xml:id="echoid-s4069" xml:space="preserve">atque ultimi termini conver-
              <lb/>
            gentes ſunt æquales, & </s>
          </p>
        </div>
        <div xml:id="echoid-div227" type="section" level="1" n="113">
          <head xml:id="echoid-head155" style="it" xml:space="preserve">Tom. II. Nnn</head>
          <p>
            <s xml:id="echoid-s4070" xml:space="preserve">proinde ſit ultimus ille terminus, ſeu
              <lb/>
            ſeriei terminatio Z, quæ in ſe ipſam multiplicata facit
              <lb/>
            </s>
          </p>
        </div>
      </text>
    </echo>