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

Table of contents

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[11.] Theorema III.
[12.] Theorema IV.
[13.] Lemma.
[14.] Theorema V.
[15.] Theorema VI.
[16.] Theorema VII.
[17.] Theorema VIII.
[18.] ἘΞἘΤΑΣΙΣ CYCLOMETRIÆ CLARISSIMI VIRI, GREGORII à S. VINCENTIO, S. J. Editæ Anno D. cIↄ Iↄc XLVII.
[19.] FINIS.
[20.] CHRISTIANI HUGENII, Const. F. AD C. V. FRAN. XAVERIUM AINSCOM. S.I. EPISTOLA, Qua diluuntur ea quibus Ε’ξε{τα}{σι}ς Cyclometriæ Gregorii à Sto. Vincentio impugnata fuit.
[21.] CHRISTIANI HUGENII, Const. F. AD C. V. FRAN. XAVERIUM AINSCOM. S. I. EPISTOLA. Cl. Viro D°. XAVERIO AINSCOM CHRISTIANUS HUGENIUS S. D.
[22.] CHRISTIANI HUGENII, Const. F. DE CIRCULI MAGNITUDINE INVENTA. ACCEDUNT EJUSDEM Problematum quorundam illuſtrium Conſtructiones.
[23.] PRÆFATIO.
[24.] CHRISTIANI HUGENII, Const. f. DE CIRCULI MAGNITUDINE INVENTA. Theorema I. Propositio I.
[25.] Theor. II. Prop. II.
[26.] Theor. III. Prop. III.
[27.] Theor. IV. Prop. IV.
[28.] Theor. V. Prop. V.
[29.] Theor. VI. Prop. VI.
[30.] Theor. VII. Prop. VII.
[31.] Theor. VIII. Prop. VIII.
[32.] Theor. IX. Prop. IX.
[33.] Problema I. Prop. X. Peripheriæ ad diametrum rationem invenire quamlibet veræ propinquam.
[34.] Problema II. Prop. XI.
[35.] Aliter.
[36.] Aliter.
[37.] Problbma III. Prop. XII. Dato arcui cuicunque rectam æqualem ſumere.
[38.] Theor. X. Prop. XIII.
[39.] Lemma.
[40.] Theor. XI. Prop. XIV.
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            <s xml:id="echoid-s53" xml:space="preserve">
              <pb o="316" file="0016" n="16" rhead="THEOR. DE QUADRAT."/>
            minor erit dato ſpatio; </s>
            <s xml:id="echoid-s54" xml:space="preserve">ſit ea parallelogrammum B F, & </s>
            <s xml:id="echoid-s55" xml:space="preserve">di-
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            vidatur baſis A C in partes æquales ipſi D F, punctis
              <lb/>
            G, H, K &</s>
            <s xml:id="echoid-s56" xml:space="preserve">c. </s>
            <s xml:id="echoid-s57" xml:space="preserve">atque inde ducantur ad ſectionem rectæ
              <lb/>
            G L, H M, K N &</s>
            <s xml:id="echoid-s58" xml:space="preserve">c. </s>
            <s xml:id="echoid-s59" xml:space="preserve">diametro B D parallelæ, & </s>
            <s xml:id="echoid-s60" xml:space="preserve">perfi-
              <lb/>
            ciantur parallelogramma D O, G P, H Q, K R &</s>
            <s xml:id="echoid-s61" xml:space="preserve">c. </s>
            <s xml:id="echoid-s62" xml:space="preserve">Di-
              <lb/>
            co figuram ex omnibus iſtis parallelogrammis compoſitam
              <lb/>
            (quæ impoſterum ordinatè circumſcripta vocabitur) ſupera-
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            re portionem A B C minori quàm datum ſit ſpatio.</s>
            <s xml:id="echoid-s63" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s64" xml:space="preserve">Jungantur enim A N, N M, M L, L B, B S, &</s>
            <s xml:id="echoid-s65" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s66" xml:space="preserve">eritque hac ratione inſcripta quoque portioni figura quædam
              <lb/>
            rectilinea; </s>
            <s xml:id="echoid-s67" xml:space="preserve">majorque erit exceſſus figuræ circumſcriptæ quæ
              <lb/>
            ex parallelogrammis compoſita eſt, ſuper inſcriptam, quàm
              <lb/>
            ſupra portionem A B C. </s>
            <s xml:id="echoid-s68" xml:space="preserve">Exceſſus autem circumſcriptæ ſuper
              <lb/>
            inſcriptam ex triangulis conſtat, quorum quæ ſunt ab una
              <lb/>
            diametri parte, ut A R N, N Q M, M P L, L O B,
              <lb/>
            æquantur dimidio parallelogrammi O D vel B F, quia ſin-
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            gulorum baſes baſi D F æquales ſunt, & </s>
            <s xml:id="echoid-s69" xml:space="preserve">omnium ſimul al-
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            titudo, parallelogrammi B F altitudini. </s>
            <s xml:id="echoid-s70" xml:space="preserve">Eâdem ratione trian-
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            gula qu& </s>
            <s xml:id="echoid-s71" xml:space="preserve">ſunt ab altera diametri parte, æquantur dimidio
              <lb/>
            parallelogrammi B F: </s>
            <s xml:id="echoid-s72" xml:space="preserve">Ergo omnia ſimul triangula ſive di-
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            ctus exceſſus æqualis eſt parallelogrammo B F, eóque mi-
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            nor ſpatio dato. </s>
            <s xml:id="echoid-s73" xml:space="preserve">Sed eodem exceſſu adhuc minor erat ex-
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            ceſſus figuræ circumſcriptæ ſupra portionem A B C: </s>
            <s xml:id="echoid-s74" xml:space="preserve">igitur
              <lb/>
            hic exceſſus dato ſpatio multo minor eſt. </s>
            <s xml:id="echoid-s75" xml:space="preserve">Et apparet fieri
              <lb/>
            poſſe quod proponebatur.</s>
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            <emph style="sc">Theorema</emph>
          II.</head>
          <p style="it">
            <s xml:id="echoid-s77" xml:space="preserve">DAtâ portione hyperboles, vel ellipſis vel circuli
              <lb/>
            portione, dimidiâ ellipſi dimidiove circulo non
              <lb/>
            majore, & </s>
            <s xml:id="echoid-s78" xml:space="preserve">dato triangulo qui baſin habeat baſi por-
              <lb/>
            tionis æqualem; </s>
            <s xml:id="echoid-s79" xml:space="preserve">poteſt utrique figura circumſcribi ex
              <lb/>
            parallelogrammis quorum ſit omnium eadem latitu-
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            do, ita ut uterque ſimulexceſſus quo figuræ circum-
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            ſcriptæ portionem & </s>
            <s xml:id="echoid-s80" xml:space="preserve">triangulum ſuperant, ſit minor
              <lb/>
            ſpatio quovis dato.</s>
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