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

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        <div xml:id="echoid-div79" type="section" level="1" n="37">
          <p>
            <s xml:id="echoid-s1511" xml:space="preserve">
              <pb o="371" file="0081" n="86" rhead="DE CIRCULI MAGNIT. INVENTA."/>
            jor quam 5176 {3/8}. </s>
            <s xml:id="echoid-s1512" xml:space="preserve">cujus dupla F H major quam 10352 {3/4}. </s>
            <s xml:id="echoid-s1513" xml:space="preserve">unde
              <lb/>
            G H major quam 352 {3/4}; </s>
            <s xml:id="echoid-s1514" xml:space="preserve">& </s>
            <s xml:id="echoid-s1515" xml:space="preserve">H I major quam 117 {7/12}. </s>
            <s xml:id="echoid-s1516" xml:space="preserve">Tota igi-
              <lb/>
            tur F I major quam 10470 {1/3}. </s>
            <s xml:id="echoid-s1517" xml:space="preserve">Arcus autem C D, ſextans pe-
              <lb/>
            ripheriæ, minor eſt quam 10472. </s>
            <s xml:id="echoid-s1518" xml:space="preserve">Ergo deficiunt lineæ F I
              <lb/>
            partium earundem pauciores quam 1 {2/3}. </s>
            <s xml:id="echoid-s1519" xml:space="preserve">Quæ non æquant {1/6000}
              <lb/>
            F I. </s>
            <s xml:id="echoid-s1520" xml:space="preserve">Porro cum arcus quadrante major datus erit, dividen-
              <lb/>
            dus eſt in partes æquales 4 vel 6 vel plures, prout accura-
              <lb/>
            tiori dimenſione uti voluerimus; </s>
            <s xml:id="echoid-s1521" xml:space="preserve">ſed numero pares: </s>
            <s xml:id="echoid-s1522" xml:space="preserve">Earum-
              <lb/>
            que partium ſubtenſis ſimul ſumptis adjungendus eſt triens
              <lb/>
            exceſſus quo ipſæ ſuperant aggregatum earum quæ arcubus
              <lb/>
            duplis ſubtenduntur. </s>
            <s xml:id="echoid-s1523" xml:space="preserve">Ita namque componetur longitudo ar-
              <lb/>
            cus totius. </s>
            <s xml:id="echoid-s1524" xml:space="preserve">Vel hac etiam ratione eadem habebitur, ſi arcus
              <lb/>
            reliqui ad ſemicircumferentiam longitudo inveniatur aut ſu-
              <lb/>
            pra eandem exceſſus, aut reliqui ad circumferentiam totam,
              <lb/>
            ſi dodrante major fuerit datus; </s>
            <s xml:id="echoid-s1525" xml:space="preserve">eaque longitudo adjungatur
              <lb/>
            vel auferatur à dimidiæ vel totius circumferentiæ longitudi-
              <lb/>
            ne, quam antea invenire docuimus.</s>
            <s xml:id="echoid-s1526" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div81" type="section" level="1" n="38">
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            <emph style="sc">Theor</emph>
          . X.
            <emph style="sc">Prop</emph>
          . XIII.</head>
          <p style="it">
            <s xml:id="echoid-s1527" xml:space="preserve">
              <emph style="bf">L</emph>
            Atus Polygoni æquilateri circulo inſcripti, pro-
              <lb/>
            portione medium eſt inter latus polygoni ſimi-
              <lb/>
            lis circumſcripti, & </s>
            <s xml:id="echoid-s1528" xml:space="preserve">dimidium latus polygoni in-
              <lb/>
            ſcriptiſub duplo laterum numero.</s>
            <s xml:id="echoid-s1529" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1530" xml:space="preserve">IN circulo cujus centrum A, radius A B, ſit latus inſcri-
              <lb/>
              <note position="right" xlink:label="note-0081-01" xlink:href="note-0081-01a" xml:space="preserve">TAB. XXXIX.
                <lb/>
              Fig. 4.</note>
            pti polygoni æquilateri B C; </s>
            <s xml:id="echoid-s1531" xml:space="preserve">& </s>
            <s xml:id="echoid-s1532" xml:space="preserve">latus circumſcripti ſimilis
              <lb/>
            polygoni D E ipſi B C parallelum. </s>
            <s xml:id="echoid-s1533" xml:space="preserve">Ergo producta A B trans-
              <lb/>
            ibit per D, & </s>
            <s xml:id="echoid-s1534" xml:space="preserve">A C per E. </s>
            <s xml:id="echoid-s1535" xml:space="preserve">Et ſi ducatur C F ipſi A B ad
              <lb/>
            angulos rectos, ea erit dimidium latus polygoni inſcripti ſub-
              <lb/>
            duplo numero laterum. </s>
            <s xml:id="echoid-s1536" xml:space="preserve">Itaque oſtendendum eſt, B C me-
              <lb/>
            diam eſſe proportione inter E D & </s>
            <s xml:id="echoid-s1537" xml:space="preserve">C F. </s>
            <s xml:id="echoid-s1538" xml:space="preserve">Ducatur A G, quæ
              <lb/>
            dividat E D bifariam, itaque erit ipſa quoque circuli ſemi-
              <lb/>
            diameter & </s>
            <s xml:id="echoid-s1539" xml:space="preserve">æqualis A B. </s>
            <s xml:id="echoid-s1540" xml:space="preserve">Et quoniam eſt ut E D ad C B,
              <lb/>
            ſic D A ad A B, hoc eſt, D A ad A G; </s>
            <s xml:id="echoid-s1541" xml:space="preserve">ſicut autem D </s>
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