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

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        <div xml:id="echoid-div41" type="section" level="1" n="18">
          <p>
            <s xml:id="echoid-s461" xml:space="preserve">
              <pb o="330" file="0036" n="39" rhead="ΕΞΕΤΑΣΙΣ CYCLOM."/>
            in priori. </s>
            <s xml:id="echoid-s462" xml:space="preserve">Sed veritus ne intricata & </s>
            <s xml:id="echoid-s463" xml:space="preserve">prolixa hinc nobis diſ-
              <lb/>
            putatio oriretur, ad alias inventiones me converti, & </s>
            <s xml:id="echoid-s464" xml:space="preserve">tan-
              <lb/>
            dem ea ſeſe obtulerunt, quæ paucis hic perſcribere conſtitui.
              <lb/>
            </s>
            <s xml:id="echoid-s465" xml:space="preserve">Nulla per hæc propoſitionum Cl. </s>
            <s xml:id="echoid-s466" xml:space="preserve">Viri in controverſiam vo-
              <lb/>
            cabitur; </s>
            <s xml:id="echoid-s467" xml:space="preserve">ſed contrà multis earum probatis, atque in uſum
              <lb/>
            meum converſis, eò rem deducam, ut ſi quidem non impoſ-
              <lb/>
            ſibile dicet quadraturam ſuam ad exitum perducere, & </s>
            <s xml:id="echoid-s468" xml:space="preserve">per
              <lb/>
            eam reapſe invenire rectilineum circulo æquale, oſtendam
              <lb/>
            qui id facillimè impoſterum aſſequatur. </s>
            <s xml:id="echoid-s469" xml:space="preserve">Deinde veſtigia i-
              <lb/>
            pſius inſiſtens demonſtrabo, quibus hactenus nobis præceſſit,
              <lb/>
            iis nequaquam ad optatum finem perveniri poſſe, ſed eſſe
              <lb/>
            ſubſiſtendum ad concluſiones perquam abſurdas. </s>
            <s xml:id="echoid-s470" xml:space="preserve">Atque ut
              <lb/>
            ad rem veniamus.</s>
            <s xml:id="echoid-s471" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s472" xml:space="preserve">Eſto circulus cujus centrum F, diameter C D. </s>
            <s xml:id="echoid-s473" xml:space="preserve">Et diviſo
              <lb/>
              <note position="left" xlink:label="note-0036-01" xlink:href="note-0036-01a" xml:space="preserve">TAB. XXXVII.
                <lb/>
              Fig. 1.</note>
            radio F C bifariam in G, ducantur ipſi ad angulos rectos
              <lb/>
            F E, G H. </s>
            <s xml:id="echoid-s474" xml:space="preserve">Dico, datâ ratione ſegmenti C H G ad G H E F
              <lb/>
            ſegmentum, dari quoque rationem circuli ad inſcriptum ſibi
              <lb/>
            hexagonum regulare. </s>
            <s xml:id="echoid-s475" xml:space="preserve">Jungantur enim F H, H C, & </s>
            <s xml:id="echoid-s476" xml:space="preserve">mani-
              <lb/>
            feſtum eſt triangulum F H C fore æquilaterum; </s>
            <s xml:id="echoid-s477" xml:space="preserve">item qua-
              <lb/>
            drantis arcum C E triplum fore arcus H E. </s>
            <s xml:id="echoid-s478" xml:space="preserve">Si ergo data ſit
              <lb/>
            ratio ſegmenti C H G ad G H E F ſegmentum, componen-
              <lb/>
            do quoque, data erit ratio quadrantis F E C ad ſegmentum
              <lb/>
            G H E F. </s>
            <s xml:id="echoid-s479" xml:space="preserve">Sed data quoque eſt ratio ſectoris F H E ad qua-
              <lb/>
            drantem F E C, ergo datur quoque ratio ſegmenti G H E F
              <lb/>
            ad ſectorem F H E; </s>
            <s xml:id="echoid-s480" xml:space="preserve">ac proinde dabitur quoque ratio ſe-
              <lb/>
            gmenti G H E F ad triangulum F H G; </s>
            <s xml:id="echoid-s481" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s482" xml:space="preserve">ratio ſe-
              <lb/>
            ctoris F H E ad triangulum F H G data erit. </s>
            <s xml:id="echoid-s483" xml:space="preserve">Sed huic ra-
              <lb/>
            tioni eadem eſt ratio ſectoris F H C ad triangulum F C H,
              <lb/>
            (quoniam hæc utriuſque præcedentium dupla ſunt;) </s>
            <s xml:id="echoid-s484" xml:space="preserve">eadem-
              <lb/>
            que eſt circuli ratio ad hexagonum regulare ſibi inſcriptum.
              <lb/>
            </s>
            <s xml:id="echoid-s485" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s486" xml:space="preserve">hanc datam eſſe apparet: </s>
            <s xml:id="echoid-s487" xml:space="preserve">quod erat demonſtran-
              <lb/>
            dum.</s>
            <s xml:id="echoid-s488" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">TAB. XXXVII.
            <lb/>
          Fig. 1. 2.</note>
          <p>
            <s xml:id="echoid-s489" xml:space="preserve">Sunto nunc lineæ A B, C D, E F, ſingulæ æquales dia-
              <lb/>
            metro circuli C D: </s>
            <s xml:id="echoid-s490" xml:space="preserve">& </s>
            <s xml:id="echoid-s491" xml:space="preserve">ſuper unaquaque harum conſtruantur
              <lb/>
            bina quadrata. </s>
            <s xml:id="echoid-s492" xml:space="preserve">Deinde verticibus A & </s>
            <s xml:id="echoid-s493" xml:space="preserve">B deſcribantur ſemi-
              <lb/>
            parabolæ A V G, B T H, quarum baſes ſint </s>
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