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-s179" xml:space="preserve">
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            rantur duæ æquales E S, B P, & </s>
            <s xml:id="echoid-s180" xml:space="preserve">inſuper alia P D. </s>
            <s xml:id="echoid-s181" xml:space="preserve">Dico
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            iterum, id quo rectangulum E D B excedit E P B, æquari
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            rectangulo S D P. </s>
            <s xml:id="echoid-s182" xml:space="preserve">Rectangulum enim E D B æquale eſt iſtis
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            duobus, rectangulo E D P, & </s>
            <s xml:id="echoid-s183" xml:space="preserve">rectangulo ſub E D, P B;
              <lb/>
            </s>
            <s xml:id="echoid-s184" xml:space="preserve">horum autem E D P rurſus æquale eſt duobus, rectangulo ni-
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            mirum S D P, & </s>
            <s xml:id="echoid-s185" xml:space="preserve">ei quod continetur ſub E S, D P, ſive
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            rectangulo D P B. </s>
            <s xml:id="echoid-s186" xml:space="preserve">Igitur rectangulum E D B iſtis tribus æ-
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            quale eſt rectangulis, S D P, D P B, & </s>
            <s xml:id="echoid-s187" xml:space="preserve">rectangulo ſub
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            E D, P B; </s>
            <s xml:id="echoid-s188" xml:space="preserve">horum vero duo poſtrema æquantur rectangu-
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            lo E P B; </s>
            <s xml:id="echoid-s189" xml:space="preserve">ergo rectangulum E D B æquale eſt duobus, re-
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            ctangulo nimirum S D P & </s>
            <s xml:id="echoid-s190" xml:space="preserve">E P B, unde apparet exceſ-
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            ſum rectanguli E D B ſupra rectangulum E P B æquari re-
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            ctangulo S D P.</s>
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            <emph style="sc">Theorema</emph>
          V.</head>
          <p style="it">
            <s xml:id="echoid-s192" xml:space="preserve">DAtâ portione hyperboles, vel ellipſis vel cir-
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            culi portione, dimidiâ figurâ non majore; </s>
            <s xml:id="echoid-s193" xml:space="preserve">ſi ad
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            diametrum conſtituatur triangulus hujuſmodi, qui
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            verticem habeat in centro figuræ, & </s>
            <s xml:id="echoid-s194" xml:space="preserve">baſin portio-
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            nis baſi æqualem & </s>
            <s xml:id="echoid-s195" xml:space="preserve">parallelam; </s>
            <s xml:id="echoid-s196" xml:space="preserve">eam verò quæ de-
              <lb/>
            inceps à vertice ad mediam baſin pertingit tantam,
              <lb/>
            ut poſſit ipſa rectangulum comprehenſum lineis, quæ
              <lb/>
            inter portionis baſin & </s>
            <s xml:id="echoid-s197" xml:space="preserve">terminos diametri figuræ in-
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            terjiciuntur. </s>
            <s xml:id="echoid-s198" xml:space="preserve">Erit magnitudinis, quæ ex portione & </s>
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            præſcripto triangulo componitur, centrum gravita-
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            tis punctum idem quod eſt trianguli vertex, cen-
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            trum nimirum figuræ.</s>
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          </p>
          <p>
            <s xml:id="echoid-s201" xml:space="preserve">Data ſit portio hyberboles, vel ellipſis vel circuli portio
              <lb/>
              <note position="left" xlink:label="note-0020-01" xlink:href="note-0020-01a" xml:space="preserve">TAB. XXXV.
                <lb/>
              Fig. 1. 2. 3.</note>
            dimidiâ figurâ non major, A B C. </s>
            <s xml:id="echoid-s202" xml:space="preserve">Diameter ejus ſit B D,
              <lb/>
            & </s>
            <s xml:id="echoid-s203" xml:space="preserve">figuræ diameter B E, in cujus medio centrum figuræ F.
              <lb/>
            </s>
            <s xml:id="echoid-s204" xml:space="preserve">Et ſumatur F G quæ poſſit rectangulum B D E, ductâque
              <lb/>
            K G H æquali & </s>
            <s xml:id="echoid-s205" xml:space="preserve">parallelâ baſi A C, quæque ad G </s>
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