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

Table of contents

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[91.] PROP. XXII. THEOREMA.
[92.] SCHOLIUM.
[93.] PROP. XXIII. THEOREMA.
[94.] PROP. XXIV. THEOREMA.
[95.] PROP. XXV. THEOREMA.
[96.] PROP. XXVI. THEOREMA.
[97.] PROP. XXVII. THEOREMA.
[98.] PROP. XXVIII. THEOREMA.
[99.] PROP. XXIX. PROBLEMA. Dato circulo æquale invenire quadratum.
[100.] PROP. XXX. PROBLEMA. Ex dato ſinu invenire arcum.
[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.
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          <pb o="472" file="0192" n="202" rhead="HUGENII EXCEPSIO"/>
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          <head xml:id="echoid-head157" xml:space="preserve">IV.
            <lb/>
          EXCERPTA EX LITERIS
            <lb/>
          D
            <emph style="super">ni</emph>
          . HUGENII
            <lb/>
          DE RESPONSO, QUOD
            <lb/>
          D
            <emph style="super">nus</emph>
          . GREGORIUS
            <lb/>
          DEDIT AD EXAMEN LIBRI, CUI TITULUS EST,
            <lb/>
          VERA CIRCULI ET HYPERBOLÆ QUADRATURA.</head>
          <p>
            <s xml:id="echoid-s4188" xml:space="preserve">In circuli quadraturam inquirentes Geometræ, va-
              <lb/>
            ria & </s>
            <s xml:id="echoid-s4189" xml:space="preserve">quidem pulcherrima detexere, ideo ne u-
              <lb/>
            tili exercitio deſtituantur adverſus Gregorium de-
              <lb/>
            fendere conſtitui, quadraturam hanc detegi poſ-
              <lb/>
            ſe; </s>
            <s xml:id="echoid-s4190" xml:space="preserve">neque huc uſque reſponſionem hanc diſtuliſſem, niſi oc-
              <lb/>
            caſione controverſiæ noſtræ examen ſuſcepiſſem exactiſſimum
              <lb/>
            de proxima Circuli & </s>
            <s xml:id="echoid-s4191" xml:space="preserve">Hyperboles Quadratura: </s>
            <s xml:id="echoid-s4192" xml:space="preserve">in quo me
              <lb/>
            interpellarunt ſæpe alia impedimenta.</s>
            <s xml:id="echoid-s4193" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4194" xml:space="preserve">Dico nunc primo; </s>
            <s xml:id="echoid-s4195" xml:space="preserve">Quod ſpectat impoſſibilitatem analy-
              <lb/>
            ticam quadraturæ illarum figurarum, tantum abeſſe etiam poſt
              <lb/>
            ſupplementum demonſtrationum, quod D
              <emph style="super">nus</emph>
            Gregorius dedit,
              <lb/>
            impoſſibilitatem hanc bene probatam eſſe, ut adhuc dum in-
              <lb/>
            certum maneat, num Circulus & </s>
            <s xml:id="echoid-s4196" xml:space="preserve">quadratum diametri ejus ſint
              <lb/>
            incommenſurabilia, id eſt an non horum ratio per numeros
              <lb/>
            poſſit exprimi; </s>
            <s xml:id="echoid-s4197" xml:space="preserve">quod etiam applicari poteſt portioni deter-
              <lb/>
            minatæ Hyperboles & </s>
            <s xml:id="echoid-s4198" xml:space="preserve">figuræ huic inſcriptæ. </s>
            <s xml:id="echoid-s4199" xml:space="preserve">Quod ut demon-
              <lb/>
            ſtremus ſufficit obſervaſſe; </s>
            <s xml:id="echoid-s4200" xml:space="preserve">quod XI ejus Propoſitio & </s>
            <s xml:id="echoid-s4201" xml:space="preserve">ſup-
              <lb/>
            plementum nil probent quando in ejus ſerie convergen-
              <lb/>
            te determinantur quantitates a & </s>
            <s xml:id="echoid-s4202" xml:space="preserve">b per numeros ra-
              <lb/>
            tionales vel ſurdos; </s>
            <s xml:id="echoid-s4203" xml:space="preserve">quoniam tunc terminatio et-
              <lb/>
            iam poterit eſſe numerus quidam ſimilis; </s>
            <s xml:id="echoid-s4204" xml:space="preserve">& </s>
            <s xml:id="echoid-s4205" xml:space="preserve">con-
              <lb/>
            trarium per illam propoſitionem demonſtrari non </s>
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