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

Table of contents

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[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.
[41.] Theor. XII. Prop. XV.
[42.] Theor. XIII. Prop. XVI.
[43.] Theorema XIV. Propos. XVII.
[44.] Theor. XV. Propos. XVIII.
[45.] Theor. XVI. Propos. XIX.
[46.] Problema IV. Propos. XX.
[47.] Christiani Hugenii C. F. ILLVSTRIVM QVORVNDAM PROBLEMATVM CONSTRVCTIONES. Probl. I. Datam ſphæram plano ſecare, ut portiones inter ſe rationem habeant datam.
[48.] LEMMA.
[49.] Probl. II. Cubum invenire dati cubi duplum.
[50.] Probl. III. Datis duabus rectis duas medias propor-tionales invenire.
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            <emph style="sc">Theorema</emph>
          VIII.</head>
          <p style="it">
            <s xml:id="echoid-s354" xml:space="preserve">IN ſemicirculo & </s>
            <s xml:id="echoid-s355" xml:space="preserve">quolibet circuli ſectore, habet
              <lb/>
            arcus ad duas tertias rectæ ſibi ſubtenſæ hanc ra-
              <lb/>
            tionem, quam ſemidiameter ad eam, quæ ex centro
              <lb/>
            ducitur ad ſectoris centrum gravitatis.</s>
            <s xml:id="echoid-s356" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s357" xml:space="preserve">Eſto primùm ſemicirculus A B C, deſcriptus centro D,
              <lb/>
              <note position="left" xlink:label="note-0028-01" xlink:href="note-0028-01a" xml:space="preserve">TAB. XXXVI.
                <lb/>
              Fig. 3.</note>
            ſectuſque bifariam rectâ B D, in qua centrum gravitatis
              <lb/>
            ſemicirculi ſit E . </s>
            <s xml:id="echoid-s358" xml:space="preserve">Dico arcum A B C eſſe ad duas
              <note symbol="1" position="left" xlink:label="note-0028-02" xlink:href="note-0028-02a" xml:space="preserve">Theor. 4. h.</note>
            A C, ſicut B D ad D E. </s>
            <s xml:id="echoid-s359" xml:space="preserve">Jungantur enim A B, B C. </s>
            <s xml:id="echoid-s360" xml:space="preserve">Igi-
              <lb/>
            tur, ut ſemicirculus ad triangulum A B C, ſic ſunt duæ ter-
              <lb/>
            tiæ B D ad D E , eſt enim B D æqualis diametro
              <note symbol="2" position="left" xlink:label="note-0028-03" xlink:href="note-0028-03a" xml:space="preserve">Theor. 7. h.</note>
            nis reliquæ. </s>
            <s xml:id="echoid-s361" xml:space="preserve">Verùm etiam ut ſemicirculus, id eſt, ut trian-
              <lb/>
            gulus habens baſin æqualem arcui A B C & </s>
            <s xml:id="echoid-s362" xml:space="preserve">altitudinem B D,
              <lb/>
            ad A B C triangulum, ita eſt arcus A B C ad A C re-
              <lb/>
            ctam; </s>
            <s xml:id="echoid-s363" xml:space="preserve">ergo ut arcus A B C ad A C, ita ſunt duæ tertiæ
              <lb/>
            B D ad D E, & </s>
            <s xml:id="echoid-s364" xml:space="preserve">permutando, ut arcus A B C ad duas tertias
              <lb/>
            B D, ita A C ad D E, ſive ita {2/3} A C ad {2/3} D E, unde rur-
              <lb/>
            ſus permutando, ut arcus A B C ad {2/3} A C, ita {2/3} B D ad {2/3}
              <lb/>
            D E, ſive ita, B D ad D E.</s>
            <s xml:id="echoid-s365" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">TAB. XXXVI.
            <lb/>
          Fig. 4.</note>
          <p>
            <s xml:id="echoid-s366" xml:space="preserve">Sit deinde ſector D A B C, ſemicirculo minor, bifariam
              <lb/>
            ſectus rectâ D B, in qua ſectoris centrum gravitatis ponatur
              <lb/>
            E punctum, & </s>
            <s xml:id="echoid-s367" xml:space="preserve">ducatur ſubtenſa A C. </s>
            <s xml:id="echoid-s368" xml:space="preserve">Dico rurſus, arcum
              <lb/>
            A B C ad duas tertias rectæ A C eam habere rationem,
              <lb/>
            quam B D ad D E. </s>
            <s xml:id="echoid-s369" xml:space="preserve">Jungantur enim A B, B C, & </s>
            <s xml:id="echoid-s370" xml:space="preserve">totius
              <lb/>
            circuli ſit diameter K D B, quæ producatur in Q, ut fiat
              <lb/>
            Q F, ad B F, ſicut portio A C B ad A B C triangulum,
              <lb/>
            & </s>
            <s xml:id="echoid-s371" xml:space="preserve">jungantur A Q, Q C; </s>
            <s xml:id="echoid-s372" xml:space="preserve">erit jam triangulus A Q C portio-
              <lb/>
            ni A C B æqualis. </s>
            <s xml:id="echoid-s373" xml:space="preserve">Ponantur deinde centra gravitatis, G tri-
              <lb/>
            anguli A C D, & </s>
            <s xml:id="echoid-s374" xml:space="preserve">H portionis A C B; </s>
            <s xml:id="echoid-s375" xml:space="preserve">& </s>
            <s xml:id="echoid-s376" xml:space="preserve">ſicut D Q ad
              <lb/>
            Q F, ita ſit H D ad D R.</s>
            <s xml:id="echoid-s377" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s378" xml:space="preserve">Quia igitur ſicut portio A C B ſive triangulus A Q C ad
              <lb/>
            triangulum A B C, id eſt, ut Q F ad B F, ita {2/3} K F ad
              <lb/>
            D H , erit rectangulum ſub Q F, D H, æquale
              <note symbol="3" position="left" xlink:label="note-0028-05" xlink:href="note-0028-05a" xml:space="preserve">Theor. 7. h.</note>
            </s>
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