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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          <head xml:id="echoid-head42" xml:space="preserve">PRÆFATIO.</head>
          <p style="it">
            <s xml:id="echoid-s1100" xml:space="preserve">CIrca antiquum Tetragoniſmiproble-
              <lb/>
            ma, quo vel apud Mathematum ig-
              <lb/>
            naros nihil eſt celebrius, recens ope-
              <lb/>
            ræ pretium nos feciſſe rati, & </s>
            <s xml:id="echoid-s1101" xml:space="preserve">quæ-
              <lb/>
            dam hactenus compertis meliora ut
              <lb/>
            putamus conſecuti, Geometris ea de-
              <lb/>
            monſtrata impertiri volumus. </s>
            <s xml:id="echoid-s1102" xml:space="preserve">Nam-
              <lb/>
            que & </s>
            <s xml:id="echoid-s1103" xml:space="preserve">ſtudiis eorum profutura arbitramur, & </s>
            <s xml:id="echoid-s1104" xml:space="preserve">no-
              <lb/>
            vitate ipſâ ad rerum abditarum inveſtigationem
              <lb/>
            incitamento futura, reputantibus in eo quoque ar-
              <lb/>
            gumento, ubi omnes pridem ſummâ contentione ver-
              <lb/>
            ſati ſint, aliqua ſuperfuiſſe haud indigna diligen-
              <lb/>
            tiæ præmia. </s>
            <s xml:id="echoid-s1105" xml:space="preserve">Plurimi quidem antehac inventæ Qua-
              <lb/>
            draturæ gloriam ſibi aſſerere conati ſunt, varia-
              <lb/>
            que ſubinde commenta protulere, falſis vera mi-
              <lb/>
            ſcentes. </s>
            <s xml:id="echoid-s1106" xml:space="preserve">Verum à peritioribus omnia veleverſa fuiſ-
              <lb/>
            ſe vel contempta ſcimus, neque aliud adhuc rece-
              <lb/>
            ptum, quo omnis circuli dimenſio niteretur, præ-
              <lb/>
            ter unum illud, majorem eſſe eum inſcripto ſibi
              <lb/>
            polygono, circumſcripto minorem. </s>
            <s xml:id="echoid-s1107" xml:space="preserve">Nos autem pro-
              <lb/>
            piorem determinationem nunc exhibemus oſtendi-
              <lb/>
            muſque, quod duobus ſumptis polygonis propor-
              <lb/>
            tione mediis inter inſcriptum circumſcriptum-
              <lb/>
            que ipſis ſimile, minoris eorum perimeter cir-
              <lb/>
            cumferentia circuli major exiſtit, reliquum </s>
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