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

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              <pb o="375" file="0085" n="90" rhead="DE CIRCULI MAGNIT. INVENTA."/>
            R B ad S, quam R C ad E K. </s>
            <s xml:id="echoid-s1630" xml:space="preserve">Eſt autem S major oſtenſa
              <lb/>
            arcu E C. </s>
            <s xml:id="echoid-s1631" xml:space="preserve">Ergo omnino major erit ratio triplicata R B ſeu
              <lb/>
            R C ad æqualem arcui E C, quam R C ad E K. </s>
            <s xml:id="echoid-s1632" xml:space="preserve">Sicut au-
              <lb/>
            tem R C ad arcum E C, ita eſt perimeter polygoni B C D L,
              <lb/>
            hoc eſt, linea Z ad circumferentiam circuli B D; </s>
            <s xml:id="echoid-s1633" xml:space="preserve">Et ſicut
              <lb/>
            R C ad E K, ita perimeter polygoni B C D L ad perime-
              <lb/>
            trum polygoni H K M N, hoc eſt, ita Z ad T. </s>
            <s xml:id="echoid-s1634" xml:space="preserve">Ergo ma-
              <lb/>
            jor quoque triplicata ratio Z ad circumferentiam totam B D,
              <lb/>
            quam Z ad T. </s>
            <s xml:id="echoid-s1635" xml:space="preserve">Ratio autem triplicata Z ad X eadem eſt
              <lb/>
            rationi Z ad T. </s>
            <s xml:id="echoid-s1636" xml:space="preserve">Itaque major eſt ratio ipſius Z ad dictam
              <lb/>
            circumferentiam, quam Z ad X. </s>
            <s xml:id="echoid-s1637" xml:space="preserve">Ac proinde circumferentia
              <lb/>
            minor quam recta X. </s>
            <s xml:id="echoid-s1638" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s1639" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1640" xml:space="preserve">Sciendum eſt autem ipſam X minorem eſſe duabus tertiis
              <lb/>
            Z & </s>
            <s xml:id="echoid-s1641" xml:space="preserve">triente T: </s>
            <s xml:id="echoid-s1642" xml:space="preserve">hoc eſt, duabus tertiis perimetri polygoni
              <lb/>
            inſcripti & </s>
            <s xml:id="echoid-s1643" xml:space="preserve">triente circumſcripti, quibus alioqui minorem eſſe
              <lb/>
            circuli circumferentiam conſtat ex præcedentibus. </s>
            <s xml:id="echoid-s1644" xml:space="preserve">Nam {2/3} Z
              <lb/>
            cum {1/3} T æquantur minori duarum mediarum ſecundum Ari-
              <lb/>
            thmeticam proportionem, quæ major eſt minore mediarum
              <lb/>
            ſecundum proportionem Geometricam.</s>
            <s xml:id="echoid-s1645" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1646" xml:space="preserve">Jam vero & </s>
            <s xml:id="echoid-s1647" xml:space="preserve">de polygono Y demonſtrabimus, ipſum videlicet
              <lb/>
            circulo B D majus eſſe. </s>
            <s xml:id="echoid-s1648" xml:space="preserve">Quia enim polygonum Y habet ad po-
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            lygonum ſimile H K M N rationem duplicatam ejus quam peri-
              <lb/>
            meter ad perimetrum: </s>
            <s xml:id="echoid-s1649" xml:space="preserve">perimeter autem polygoni Y æquatur
              <lb/>
            rectæ V, & </s>
            <s xml:id="echoid-s1650" xml:space="preserve">perim. </s>
            <s xml:id="echoid-s1651" xml:space="preserve">H K M N ipſi T. </s>
            <s xml:id="echoid-s1652" xml:space="preserve">habebit proinde polygon. </s>
            <s xml:id="echoid-s1653" xml:space="preserve">Y
              <lb/>
            ad polyg. </s>
            <s xml:id="echoid-s1654" xml:space="preserve">H K M N rationem duplicatam ejus quam V ad
              <lb/>
            T, hoc eſt, eam quam X ad T. </s>
            <s xml:id="echoid-s1655" xml:space="preserve">Sicut autem polygonum
              <lb/>
            H K M N ad circulum B D, ita eſt perimeter ipſius poly-
              <lb/>
            goni, hoc eſt, linea T ad circuli B D circumferentiam; </s>
            <s xml:id="echoid-s1656" xml:space="preserve">quo-
              <lb/>
            niam polygonum æquale eſt triangulo baſin habenti perime-
              <lb/>
            tro ſuæ æqualem & </s>
            <s xml:id="echoid-s1657" xml:space="preserve">altitudinem radii A E, circulus autem
              <lb/>
            æqualis ejuſdem altitudinis triangulo cujus baſis circumferen-
              <lb/>
            tiæ æquetur. </s>
            <s xml:id="echoid-s1658" xml:space="preserve">Ex æquali igitur, erit polygonum Y ad circu-
              <lb/>
            lum B D ſicut X ad circumferentiam B D. </s>
            <s xml:id="echoid-s1659" xml:space="preserve">Eſt autem X
              <lb/>
            major oſtenſa quam B D circumferentia. </s>
            <s xml:id="echoid-s1660" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s1661" xml:space="preserve">polygo-
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            num Y majus erit circulo B D. </s>
            <s xml:id="echoid-s1662" xml:space="preserve">Quod erat demonſtran-
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            dum.</s>
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