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

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            <s xml:id="echoid-s1339" xml:space="preserve">
              <pb o="365" file="0073" n="77" rhead="DE CIRCULI MAGNIT. INVENTA."/>
            benti duplam C G, hoc eſt, C D, & </s>
            <s xml:id="echoid-s1340" xml:space="preserve">altitudinem C A: </s>
            <s xml:id="echoid-s1341" xml:space="preserve">tri-
              <lb/>
            angulum vero A E C æquale triangulo baſin ipſi E F æqua-
              <lb/>
            lem habenti & </s>
            <s xml:id="echoid-s1342" xml:space="preserve">altitudinem dictam A C. </s>
            <s xml:id="echoid-s1343" xml:space="preserve">Itaque apparet duas
              <lb/>
            tertias quadrilateri A E G C ſimul cum triente trianguli A E C
              <lb/>
            æquari triangulo qui baſin habeat compoſitam ex duabus ter-
              <lb/>
            tiis C D & </s>
            <s xml:id="echoid-s1344" xml:space="preserve">triente E F, altitudinem vero radii A C. </s>
            <s xml:id="echoid-s1345" xml:space="preserve">Qua-
              <lb/>
            re ejuſmodi quoque triangulum majus erit ſectore A E C.
              <lb/>
            </s>
            <s xml:id="echoid-s1346" xml:space="preserve">Unde liquet baſin ipſius, hoc eſt, compoſitam ex duabus
              <lb/>
            tertiis ipſius C D & </s>
            <s xml:id="echoid-s1347" xml:space="preserve">triente ipſius E F, majorem eſſe arcu
              <lb/>
            C E. </s>
            <s xml:id="echoid-s1348" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s1349" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div70" type="section" level="1" n="32">
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            <emph style="sc">Theor</emph>
          . IX.
            <emph style="sc">Prop</emph>
          . IX.</head>
          <p style="it">
            <s xml:id="echoid-s1350" xml:space="preserve">OMnis circuli circumferentia minor eſt duabus
              <lb/>
            tertiis perimetri polygoni æqualium laterum ſibi
              <lb/>
            inſcripti & </s>
            <s xml:id="echoid-s1351" xml:space="preserve">triente perimetri polygoni ſimilis circum-
              <lb/>
            ſcripti.</s>
            <s xml:id="echoid-s1352" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1353" xml:space="preserve">Eſto Circulus cujus A centrum; </s>
            <s xml:id="echoid-s1354" xml:space="preserve">& </s>
            <s xml:id="echoid-s1355" xml:space="preserve">inſcribatur ei polygo-
              <lb/>
              <note position="right" xlink:label="note-0073-01" xlink:href="note-0073-01a" xml:space="preserve">TAB. XXXIX.
                <lb/>
              Fig. 1.</note>
            num æquilaterum, cujus latus C D: </s>
            <s xml:id="echoid-s1356" xml:space="preserve">ſimileque aliud cir-
              <lb/>
            cumſcribatur lateribus ad priora parallelis, quorum unum ſit
              <lb/>
            E F. </s>
            <s xml:id="echoid-s1357" xml:space="preserve">Dico circuli totius circumferentiam minorem eſſe dua-
              <lb/>
            bus tertiis ambitus polygoni C D & </s>
            <s xml:id="echoid-s1358" xml:space="preserve">triente ambitus polygo-
              <lb/>
            ni E F. </s>
            <s xml:id="echoid-s1359" xml:space="preserve">Ducatur namque diameter circuli B G, quæ ſimul
              <lb/>
            inſcripti polygoni latus C D medium dividat in H, & </s>
            <s xml:id="echoid-s1360" xml:space="preserve">cir-
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            cumſcripti latus E F in G, (conſtat autem G fore punctum
              <lb/>
            contactus lateris E F,) Et ponatur H L æqualis ipſi H G,
              <lb/>
            & </s>
            <s xml:id="echoid-s1361" xml:space="preserve">jungantur A C, B C & </s>
            <s xml:id="echoid-s1362" xml:space="preserve">producantur, occurrátque B C
              <lb/>
            lateri E F in K, producta autem A C incidet in E angu-
              <lb/>
            lum polygoni circumſcripti. </s>
            <s xml:id="echoid-s1363" xml:space="preserve">Quoniam igitur H L æqualis
              <lb/>
            H G, erit B L dupla ipſius A H: </s>
            <s xml:id="echoid-s1364" xml:space="preserve">Ideoque ut G A ad A H,
              <lb/>
            ita G B ad B L. </s>
            <s xml:id="echoid-s1365" xml:space="preserve">Major autem eſt ratio H B ad B L, quam
              <lb/>
            G B ad B H; </s>
            <s xml:id="echoid-s1366" xml:space="preserve">quoniam hætres ſeſe æqualiter excedunt G B,
              <lb/>
            H B, L B. </s>
            <s xml:id="echoid-s1367" xml:space="preserve">Itaque major erit ratio G B ad B L, hoc eſt,
              <lb/>
            G A ad A H, quam duplicata rationis G B ad B H. </s>
            <s xml:id="echoid-s1368" xml:space="preserve">Sicut
              <lb/>
            autem G A ad A H, ita eſt E G ad C H; </s>
            <s xml:id="echoid-s1369" xml:space="preserve">& </s>
            <s xml:id="echoid-s1370" xml:space="preserve">ſicut G </s>
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