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

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        <div xml:id="echoid-div85" type="section" level="1" n="40">
          <p style="it">
            <s xml:id="echoid-s1572" xml:space="preserve">
              <pb o="373" file="0083" n="88" rhead="DE CIRCULI MAGNIT. INVENTA."/>
            ptum. </s>
            <s xml:id="echoid-s1573" xml:space="preserve">Et circulus minor eſt polygono iſtis ſimili cu-
              <lb/>
            jus ambitus majori mediarum æquetur.</s>
            <s xml:id="echoid-s1574" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1575" xml:space="preserve">Eſto circulus B D, cujus centrum A. </s>
            <s xml:id="echoid-s1576" xml:space="preserve">Et inſcribatur ei po-
              <lb/>
              <note position="right" xlink:label="note-0083-01" xlink:href="note-0083-01a" xml:space="preserve">TAB. XXXIX.
                <lb/>
              Fig. 6.</note>
            lygonum æquilaterum B C D L, ſimileque circumſcri-
              <lb/>
            batur lateribus parallelis H K M N. </s>
            <s xml:id="echoid-s1577" xml:space="preserve">Sitque perimetro po-
              <lb/>
            lygoni H K M N æqualis recta T, perimetro autem B C D L
              <lb/>
            æqualis Z. </s>
            <s xml:id="echoid-s1578" xml:space="preserve">Et inter Z & </s>
            <s xml:id="echoid-s1579" xml:space="preserve">T duæ ſint mediæ proportionales
              <lb/>
            X & </s>
            <s xml:id="echoid-s1580" xml:space="preserve">V, quarum X minor. </s>
            <s xml:id="echoid-s1581" xml:space="preserve">Dico circumferentiam circuli
              <lb/>
            B D minorem eſſe rectâ X. </s>
            <s xml:id="echoid-s1582" xml:space="preserve">Et ſi fiat polygonum in quo Y,
              <lb/>
            cujus perimeter æquetur rectæ V, ſimile autem ſit polygono
              <lb/>
            B C D L aut H K M N; </s>
            <s xml:id="echoid-s1583" xml:space="preserve">Dico circulum B N minorem
              <lb/>
            haberi polygono Y. </s>
            <s xml:id="echoid-s1584" xml:space="preserve">Ducatur enim diameter circuli P E,
              <lb/>
            quæ dividat bifariam latera parallela B C, H K, inſcripti
              <lb/>
            circumſcriptique polygoni in R & </s>
            <s xml:id="echoid-s1585" xml:space="preserve">E; </s>
            <s xml:id="echoid-s1586" xml:space="preserve">erit autem E punctum
              <lb/>
            contactus lateris H K, & </s>
            <s xml:id="echoid-s1587" xml:space="preserve">B C ſecabitur in R ad angulos
              <lb/>
            rectos. </s>
            <s xml:id="echoid-s1588" xml:space="preserve">Ducatur etiam ex centro recta A C K, quæ utriuſ-
              <lb/>
            que polygoni angulos C & </s>
            <s xml:id="echoid-s1589" xml:space="preserve">K bifariam ſecet, nam hoc ab
              <lb/>
            eadem recta fieri conſtat; </s>
            <s xml:id="echoid-s1590" xml:space="preserve">& </s>
            <s xml:id="echoid-s1591" xml:space="preserve">jungatur C E. </s>
            <s xml:id="echoid-s1592" xml:space="preserve">Ipſi autem C E
              <lb/>
            ponatur æqualis C F; </s>
            <s xml:id="echoid-s1593" xml:space="preserve">ſitque duabus his C R, C F tertia
              <lb/>
            proportionalis C G. </s>
            <s xml:id="echoid-s1594" xml:space="preserve">Ergo qualis polygoni inſcripti latus eſt
              <lb/>
            C E ſive C F, talis circumſcripti latus erit C G . </s>
            <s xml:id="echoid-s1595" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0083-02" xlink:href="note-0083-02a" xml:space="preserve">per 13. huj.</note>
            duæ tertiæ C F cum triente C G ſimul majores erunt arcu
              <lb/>
            E C . </s>
            <s xml:id="echoid-s1596" xml:space="preserve">Sit autem duabus tertiis C F cum triente C G
              <note symbol="*" position="right" xlink:label="note-0083-03" xlink:href="note-0083-03a" xml:space="preserve">per 9. huj.</note>
            lis recta S. </s>
            <s xml:id="echoid-s1597" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s1598" xml:space="preserve">hæc major erit arcu E C.</s>
            <s xml:id="echoid-s1599" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1600" xml:space="preserve">Et quoniam ſe habet C R ad C F, ut C F ad C G;
              <lb/>
            </s>
            <s xml:id="echoid-s1601" xml:space="preserve">erit quoque dupla C R una cum C F ad triplam C R,
              <lb/>
            hoc eſt, utraque ſimul B C, C F ad utramque B C, C R,
              <lb/>
            ut dupla C F una cum C G ad triplam C F: </s>
            <s xml:id="echoid-s1602" xml:space="preserve">vel ſumptis
              <lb/>
            horum trientibus, ut {2/3} C F una cum {1/3} C G ad C F, hoc
              <lb/>
            eſt, ut S ad C F. </s>
            <s xml:id="echoid-s1603" xml:space="preserve">Quare etiam triplicata ratio ejus quam ha-
              <lb/>
            bet utraque ſimul B C, C F ad utramque B C, C R ea-
              <lb/>
            dem erit triplicatæ rationi S ad C F. </s>
            <s xml:id="echoid-s1604" xml:space="preserve">Major autem eſt ratio
              <lb/>
            R B ad B F quam triplicata ejus, quam habet utraque ſi-
              <lb/>
            mul B C, C F ad utramque B C, C R . </s>
            <s xml:id="echoid-s1605" xml:space="preserve">Ergo major
              <note symbol="*" position="right" xlink:label="note-0083-04" xlink:href="note-0083-04a" xml:space="preserve">per lemm@
                <lb/>
              præ.</note>
            dem ratio R B ad B F quam triplicata ejus quam habet S </s>
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