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

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            <s xml:id="echoid-s1007" xml:space="preserve">
              <pb o="348" file="0056" n="60" rhead="CHRIST. HUGENII AD XAVERIUM"/>
            Proportionalitatibus & </s>
            <s xml:id="echoid-s1008" xml:space="preserve">de Ductibus, ne ſert qu’ à l’embaraſſer,
              <lb/>
            & </s>
            <s xml:id="echoid-s1009" xml:space="preserve">ne me ſemble d’ aucun uſage, pour ce que fruſtra fit per plur a
              <lb/>
            quod poteſt fieri per pauciora.</s>
            <s xml:id="echoid-s1010" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1011" xml:space="preserve">Quorum latinè hæc eſt ſententia.</s>
            <s xml:id="echoid-s1012" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1013" xml:space="preserve">Libros tuos retinui diutius, quod remittere eos nolebam quin
              <lb/>
            ſimul opinionem meam tibi exponerem de nova iſta quam vendi-
              <lb/>
            tant circuli Quadratura; </s>
            <s xml:id="echoid-s1014" xml:space="preserve">vix autem à me ipſo impetr are poteram,
              <lb/>
            ut ingentia quibus tractatur volumina evolverem. </s>
            <s xml:id="echoid-s1015" xml:space="preserve">Tandem ta-
              <lb/>
            men nonnulla in iis delibavi, è quibus ſatis tutò mihi pronunciare
              <lb/>
            poſſe videor, nihil ibi boni inveniri, quod non captu facile ſit;
              <lb/>
            </s>
            <s xml:id="echoid-s1016" xml:space="preserve">unâque aut alter â paginâ explicari potuerit. </s>
            <s xml:id="echoid-s1017" xml:space="preserve">Cætera merum pa-
              <lb/>
            ralogiſmum de quadratura circuli continent, multis propoſitio-
              <lb/>
            nibus implicitum, quæque hoc tantum efficiunt, ut omnia eva-
              <lb/>
            dant intricatior a. </s>
            <s xml:id="echoid-s1018" xml:space="preserve">Pler æque vero ſimpliciſſimæ ſunt & </s>
            <s xml:id="echoid-s1019" xml:space="preserve">facili ratio-
              <lb/>
            ne conſtant, licet tractandi methodus obſcuriores reddiderit. </s>
            <s xml:id="echoid-s1020" xml:space="preserve">Pa-
              <lb/>
            ralogiſmum quærere inſtitui, initio facto ad paginam 1134. </s>
            <s xml:id="echoid-s1021" xml:space="preserve">ubi
              <lb/>
            hoc ait: </s>
            <s xml:id="echoid-s1022" xml:space="preserve">Nota autem eſt proportio ſegmenti L M N K ad ſegmen-
              <lb/>
            tum E G H F; </s>
            <s xml:id="echoid-s1023" xml:space="preserve">quod falſum eſt, pendet enim hujus demonſtratio
              <lb/>
            à propoſitione 39, pag. </s>
            <s xml:id="echoid-s1024" xml:space="preserve">1121. </s>
            <s xml:id="echoid-s1025" xml:space="preserve">ejuſdem libri, ubi manifeſtus er-
              <lb/>
            ror occurrit, dum pluribus quantitatibus conjunctim applicatur,
              <lb/>
            quod de ſingulis ſeorſim fuerat oſtenſum. </s>
            <s xml:id="echoid-s1026" xml:space="preserve">Etenim ex. </s>
            <s xml:id="echoid-s1027" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s1028" xml:space="preserve">poſitis
              <lb/>
            quatuor proportionalium ordinibus
              <lb/>
              <note position="right" xlink:label="note-0056-01" xlink:href="note-0056-01a" xml:space="preserve">
                <lb/>
              2, 4, 8, # 2, 8, 32,
                <lb/>
              ## &
                <lb/>
              2, 6, 18, # 2, 10, 50,
                <lb/>
              </note>
            licet verum ſit rationem 8. </s>
            <s xml:id="echoid-s1029" xml:space="preserve">ad 32. </s>
            <s xml:id="echoid-s1030" xml:space="preserve">duplicatam eſſe ejus quæ 4. </s>
            <s xml:id="echoid-s1031" xml:space="preserve">ad
              <lb/>
            8. </s>
            <s xml:id="echoid-s1032" xml:space="preserve">itemque rationem 18. </s>
            <s xml:id="echoid-s1033" xml:space="preserve">ad 50. </s>
            <s xml:id="echoid-s1034" xml:space="preserve">duplicatam eſse ejus quæ 6. </s>
            <s xml:id="echoid-s1035" xml:space="preserve">ad 10.
              <lb/>
            </s>
            <s xml:id="echoid-s1036" xml:space="preserve">non tamen idcirco verum eſt 8 + 18. </s>
            <s xml:id="echoid-s1037" xml:space="preserve">hoc eſt, 26. </s>
            <s xml:id="echoid-s1038" xml:space="preserve">eſſe ad 32 + 50. </s>
            <s xml:id="echoid-s1039" xml:space="preserve">
              <lb/>
            hoc eſt ad 82. </s>
            <s xml:id="echoid-s1040" xml:space="preserve">inratione duplicata ejus quæ 4 + 6. </s>
            <s xml:id="echoid-s1041" xml:space="preserve">hoc eſt, 10. </s>
            <s xml:id="echoid-s1042" xml:space="preserve">ad
              <lb/>
            8 + 10. </s>
            <s xml:id="echoid-s1043" xml:space="preserve">hoc eſt, 18. </s>
            <s xml:id="echoid-s1044" xml:space="preserve">Unicum ei fundamentum hæc vitioſa argu-
              <lb/>
            mentatio; </s>
            <s xml:id="echoid-s1045" xml:space="preserve">quæque de Proportionalitatibus ſcribit & </s>
            <s xml:id="echoid-s1046" xml:space="preserve">de Ducti-
              <lb/>
            bus, tantum majoribus ipſum diſſicultatibus involvunt, neque
              <lb/>
            alicujus uſus videntur, ſiquidem fruſtra fit per plura quod poteſt
              <lb/>
            fieri per pauciora.</s>
            <s xml:id="echoid-s1047" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1048" xml:space="preserve">Vides, Vir Egregie, neque Carteſium, veſtrum illud Hoc
              <lb/>
            eſt juxta mentem autoris, agniturum fuiſſe, ſed potius, quod
              <lb/>
            res eſt, dicturum, deſperatâ causâ hoc vobis effugium quæſi-
              <lb/>
            tum, ut quadratura veſtra ad inſtar Protei cujuſdem aliâ </s>
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