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

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            <s xml:id="echoid-s3991" xml:space="preserve">
              <pb o="464" file="0184" n="194" rhead="HUGENII OBSERVATIONES"/>
            eodem modo analytice componi e terminis a
              <emph style="super">3</emph>
            + aab, abb
              <lb/>
            + b
              <emph style="super">3</emph>
            quo componitur e terminis aab + bba, 2 bba. </s>
            <s xml:id="echoid-s3992" xml:space="preserve">Hæc ni-
              <lb/>
            hilominus invenitur per eandem methodum quam indi-
              <lb/>
            cat in 7. </s>
            <s xml:id="echoid-s3993" xml:space="preserve">Propoſitione. </s>
            <s xml:id="echoid-s3994" xml:space="preserve">Methodus autem hæc eſt. </s>
            <s xml:id="echoid-s3995" xml:space="preserve">Pri-
              <lb/>
            mo quærenda eſt quantitas perquam ſi multiplices a
              <emph style="super">3</emph>
            + aab,
              <lb/>
            & </s>
            <s xml:id="echoid-s3996" xml:space="preserve">producto addas productum abb + b
              <emph style="super">3</emph>
            multiplicati per da-
              <lb/>
            tam quantitatem m, ſumma æqualis ſit ſummæ duorum alio-
              <lb/>
            rum productorum, unius aab + bba multiplicati per eandem
              <lb/>
            quantitatem quæſitam, alterius 2 bba multiplicati per datam
              <lb/>
            quantitatem m. </s>
            <s xml:id="echoid-s3997" xml:space="preserve">Ponamus igitur quantitatem illam æqualem
              <lb/>
            z, erit a
              <emph style="super">3</emph>
            z + aabz + abbm + b
              <emph style="super">3</emph>
            m = aabz + bbaz + 2 bbam;
              <lb/>
            </s>
            <s xml:id="echoid-s3998" xml:space="preserve">& </s>
            <s xml:id="echoid-s3999" xml:space="preserve">z = {bbm/aa + ab}: </s>
            <s xml:id="echoid-s4000" xml:space="preserve">Et certum eſt, ſive multiplicetur {bbm/aa + ab} per a
              <emph style="super">3</emph>
            + aab
              <lb/>
            & </s>
            <s xml:id="echoid-s4001" xml:space="preserve">addatur abb + b
              <emph style="super">3</emph>
            multiplicatum per m, ſive eadem illa
              <lb/>
            quantitas multiplicetur per aab + bba & </s>
            <s xml:id="echoid-s4002" xml:space="preserve">addatur 2 bbam,
              <lb/>
            ſemper prodire eandem quantitatem 2 abbm + b
              <emph style="super">3</emph>
            m, & </s>
            <s xml:id="echoid-s4003" xml:space="preserve">conſe-
              <lb/>
            quenter ultimam hanc quantitatem componi eodem modo e
              <lb/>
            primis & </s>
            <s xml:id="echoid-s4004" xml:space="preserve">ſecundis terminis progreſſionis convergentis pro-
              <lb/>
            poſitæ, quod Autor fieri poſſe negavit.</s>
            <s xml:id="echoid-s4005" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4006" xml:space="preserve">III°. </s>
            <s xml:id="echoid-s4007" xml:space="preserve">Datâ autem hac quantitate 2 abbm + bbbm, ſi hac
              <lb/>
            utamur ad quærendam terminationem progreſſionis propo-
              <lb/>
            ſitæ, juxta methodum ab auctore indicatam in 7 propoſi-
              <lb/>
            tione, & </s>
            <s xml:id="echoid-s4008" xml:space="preserve">in 10, reperietur = {3 aab3 + ab4 + 2 a3 bb/bb + ab + aa}; </s>
            <s xml:id="echoid-s4009" xml:space="preserve">& </s>
            <s xml:id="echoid-s4010" xml:space="preserve">poſito a = 1
              <lb/>
            & </s>
            <s xml:id="echoid-s4011" xml:space="preserve">b = 2, illa terminatio, quæ deſignat in eo caſu ſectorem
              <lb/>
            circuli continentem {1/3} totius circuli, erit = {48/7}; </s>
            <s xml:id="echoid-s4012" xml:space="preserve">& </s>
            <s xml:id="echoid-s4013" xml:space="preserve">primus ter-
              <lb/>
            minus progreſſionis a
              <emph style="super">3</emph>
            + aab, qui deſignat {1/3} trianguli æquila-
              <lb/>
            teri inſcripti in eodem Circulo, erit æqualis 3; </s>
            <s xml:id="echoid-s4014" xml:space="preserve">ita ut propor-
              <lb/>
            tio circuli ad triangulum æquilaterum inſcriptum ſit ut {48/7} ad
              <lb/>
            3@ id eſt 16 ad 7. </s>
            <s xml:id="echoid-s4015" xml:space="preserve">a vero nihilominus omnes has proportiones ab-
              <lb/>
            errare facile patet.</s>
            <s xml:id="echoid-s4016" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4017" xml:space="preserve">IV°. </s>
            <s xml:id="echoid-s4018" xml:space="preserve">Si examinemus, cur terminatio aliquando occurrat ve-
              <lb/>
            ra per methodum Autoris, ut in 7 Propoſitione, interdum
              <lb/>
            verò non; </s>
            <s xml:id="echoid-s4019" xml:space="preserve">reperiemus id ex eo oriri quod problema 10
              <emph style="super">mæ</emph>
            </s>
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