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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            <s xml:id="echoid-s4484" xml:space="preserve">
              <pb o="482" file="0202" n="212" rhead="J. GREG. CONS. SUPER HUG. EXCEPT."/>
            minor quam ejuſdem {1/3000000}. </s>
            <s xml:id="echoid-s4485" xml:space="preserve">Sed hæc levia mihi videntur,
              <lb/>
            cum poſſim Approximationes exhibere, quæ ab ipſa
              <lb/>
            ſemi-circumferentia differant minori intervallo, quam quæ-
              <lb/>
            libet ejus pars aſſignata, neque nobis amplius apparent hæc
              <lb/>
            mirabilia, cum demonſtratio ſolida innoteſcat. </s>
            <s xml:id="echoid-s4486" xml:space="preserve">Ad reliqua
              <lb/>
            ab Hugenio publicata, cum à meo inſtituto ſint aliena, nihil
              <lb/>
            dico, niſi quod ipſa Hugenii dicta (non obſtante exactiſſi-
              <lb/>
            ma ſua, ut ait, materiæ hujus examinatione) à meæ Ap-
              <lb/>
            pendiculæ factis ni fallor, longè ſuperentur. </s>
            <s xml:id="echoid-s4487" xml:space="preserve">Vale. </s>
            <s xml:id="echoid-s4488" xml:space="preserve">Decemb.
              <lb/>
            </s>
            <s xml:id="echoid-s4489" xml:space="preserve">15. </s>
            <s xml:id="echoid-s4490" xml:space="preserve">1668.</s>
            <s xml:id="echoid-s4491" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4492" xml:space="preserve">Figura Hugenii hæc eſt, quam ipſe hoc ſenſu, licet Gal-
              <lb/>
            licè, ſic explicat. </s>
            <s xml:id="echoid-s4493" xml:space="preserve">Sit Arcus Circuli, qui non excedat ſemicir-
              <lb/>
            cumferentiam, A B C, cujus ſubtenſa ſit A C, & </s>
            <s xml:id="echoid-s4494" xml:space="preserve">dividan-
              <lb/>
            tur ambo in partes æquales per lineam B D. </s>
            <s xml:id="echoid-s4495" xml:space="preserve">Ducta ſubtenſa
              <lb/>
            A B, capias inde {2/3}, eaſque jungas inde ab A ad E in linea
              <lb/>
            C A protracta. </s>
            <s xml:id="echoid-s4496" xml:space="preserve">Dein, reſecta lineæ D E parte decima E F,
              <lb/>
            ducas F B, & </s>
            <s xml:id="echoid-s4497" xml:space="preserve">tandem B G, ipſi perpendicularem: </s>
            <s xml:id="echoid-s4498" xml:space="preserve">& </s>
            <s xml:id="echoid-s4499" xml:space="preserve">habe-
              <lb/>
            bis lineam A G æqualem Arcui A B C, cujus exceſſus tantil-
              <lb/>
            lus erit, ut etiam tunc, quando hic arcus æqualis erit ſemi-
              <lb/>
            circumferentiæ Circuli, futura non ſit differentia {1/3400} ſuæ
              <lb/>
            longitudinis; </s>
            <s xml:id="echoid-s4500" xml:space="preserve">at quando non eſt niſi tertiæ partis circumfe-
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            ferentiæ, differentia non erit {1/13000}; </s>
            <s xml:id="echoid-s4501" xml:space="preserve">& </s>
            <s xml:id="echoid-s4502" xml:space="preserve">ſi non ſit niſi quar-
              <lb/>
            tæ partis, non differet niſi {1/90000}, ſuæ longitudinis.</s>
            <s xml:id="echoid-s4503" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div238" type="section" level="1" n="117">
          <head xml:id="echoid-head161" xml:space="preserve">FINIS.</head>
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