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

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              <pb o="389" file="0103" n="110" rhead="CHR.HUGENII ILL.QUOR.PROB.CONSTR."/>
            Et per N punctum ducatur planum K L quod diametro
              <lb/>
            C A ſit ad angulos rectos. </s>
            <s xml:id="echoid-s2017" xml:space="preserve">Dico hoc ſphæram ſic ſecare, ut
              <lb/>
            portio cujus A vertex eſt ad eam cujus vertex C rationem ha-
              <lb/>
            beat quam S ad T.</s>
            <s xml:id="echoid-s2018" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2019" xml:space="preserve">Secetur enim ſphæra per centrum M plano B D ipſi K L
              <lb/>
            parallelo, & </s>
            <s xml:id="echoid-s2020" xml:space="preserve">jungantur K M, M L; </s>
            <s xml:id="echoid-s2021" xml:space="preserve">& </s>
            <s xml:id="echoid-s2022" xml:space="preserve">intelligatur conus
              <lb/>
            baſin habens circulum factum ſectione K L, verticem vero
              <lb/>
            M. </s>
            <s xml:id="echoid-s2023" xml:space="preserve">Et ſicut quadratum C M ad quadratum M N, ita ſit
              <lb/>
            M N ad N O longitudine. </s>
            <s xml:id="echoid-s2024" xml:space="preserve">Erit igitur per converſionem ra-
              <lb/>
            tionis ut quadratum C M ſive quadr. </s>
            <s xml:id="echoid-s2025" xml:space="preserve">K M ad quadratum
              <lb/>
            K N (eſt enim quadr. </s>
            <s xml:id="echoid-s2026" xml:space="preserve">K N exceſſus quadrati K M ſupra
              <lb/>
            quadr. </s>
            <s xml:id="echoid-s2027" xml:space="preserve">M N) ita linea N M ad M O. </s>
            <s xml:id="echoid-s2028" xml:space="preserve">Sicut autem quadr.
              <lb/>
            </s>
            <s xml:id="echoid-s2029" xml:space="preserve">K M, hoc eſt, quadr. </s>
            <s xml:id="echoid-s2030" xml:space="preserve">B M ad quadr. </s>
            <s xml:id="echoid-s2031" xml:space="preserve">K N, ita eſt circu-
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            lus circa diametrum B D ad eum qui circa diametrum K L. </s>
            <s xml:id="echoid-s2032" xml:space="preserve">
              <lb/>
            Ergo quoque ille circulus ad hunc ſeſe habebit ut N M ad
              <lb/>
            M O. </s>
            <s xml:id="echoid-s2033" xml:space="preserve">Ac proinde conus K M L æqualis erit cono cujus
              <lb/>
            baſis circulus circa diametrum B D, altitudo M O . </s>
            <s xml:id="echoid-s2034" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0103-01" xlink:href="note-0103-01a" xml:space="preserve">15. 12. E.
                <lb/>
              lem.</note>
            autem conus ad hemiſphæram B C D, hoc eſt, ad conum
              <lb/>
            qui baſin habeat eundem circulum circa B D diametrum,
              <lb/>
            & </s>
            <s xml:id="echoid-s2035" xml:space="preserve">altitudinem M H , eam habet rationem quam M O
              <note symbol="*" position="right" xlink:label="note-0103-02" xlink:href="note-0103-02a" xml:space="preserve">32. 1. Ar-
                <lb/>
              chim. de
                <lb/>
              Sphær. &
                <lb/>
              Cylin.</note>
            M H. </s>
            <s xml:id="echoid-s2036" xml:space="preserve">Itaque & </s>
            <s xml:id="echoid-s2037" xml:space="preserve">conus K M L erit ad hemiſphæram B C D
              <lb/>
            ſicut M O ad M H. </s>
            <s xml:id="echoid-s2038" xml:space="preserve">Et invertendo.</s>
            <s xml:id="echoid-s2039" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2040" xml:space="preserve">Porro autem quoniam hemiſphæra B C D eſt ad ſectorem
              <lb/>
            ſolidum M K C L ſicut ſuperficies illius ſphærica ad ſphæ-
              <lb/>
            ricam hujus ſuperficiem , hoc eſt, ut M C ad C N .</s>
            <s xml:id="echoid-s2041" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0103-03" xlink:href="note-0103-03a" xml:space="preserve">42. 1. Ar-
                <lb/>
              chim. de
                <lb/>
              Sphær. &
                <lb/>
              Cyl.</note>
            Erit per converſionem rationis hemiſphæra B C D ad par
              <lb/>
            tem ſui quæ remanet dempto ſectore M K C L, ſicut C M
              <lb/>
              <note symbol="†" position="right" xlink:label="note-0103-04" xlink:href="note-0103-04a" xml:space="preserve">3. 2. Ar-
                <lb/>
              chim. de
                <lb/>
              Sphær.
                <lb/>
              & Cyl.</note>
            ad M N: </s>
            <s xml:id="echoid-s2042" xml:space="preserve">vel ſumptis horum duplis ut H M ad O Q. </s>
            <s xml:id="echoid-s2043" xml:space="preserve">Quod
              <lb/>
            enim O Q dupla ſit ipſius M N poſtea oſtendemus. </s>
            <s xml:id="echoid-s2044" xml:space="preserve">Fuit
              <lb/>
            autem oſtenſum, quod hemiſphæra B C D ad conum K M L
              <lb/>
            ſicut H M ad M O. </s>
            <s xml:id="echoid-s2045" xml:space="preserve">Ergo jam hemiſphæra B C D ad to-
              <lb/>
            tam portionem inter plana B D, K L contentam erit ut H M
              <lb/>
            ad utramque ſimul Q O, O M , hoc eſt, ad M Q. </s>
            <s xml:id="echoid-s2046" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0103-05" xlink:href="note-0103-05a" xml:space="preserve">24. 5 Ele@.</note>
            re & </s>
            <s xml:id="echoid-s2047" xml:space="preserve">per converſionem rationis, erit hemiſphæra B C D ad
              <lb/>
            portionem K C L, ut M H ad H Q. </s>
            <s xml:id="echoid-s2048" xml:space="preserve">Et ſumptis antece-
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            dentium duplis, ſphæra tota ad portionem K C L ut E </s>
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