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

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            <s xml:id="echoid-s9188" xml:space="preserve">
              <pb o="683" file="0423" n="442" rhead="COSMOTHEOROS, LIB. I."/>
            Geometricas, velut circulos, triangula, polygona, ſphæ-
              <lb/>
            ras, multis modis natura ipſa oculis objicit, ad variaſque
              <lb/>
            eorum proprietates indagandas quaſi invitat; </s>
            <s xml:id="echoid-s9189" xml:space="preserve">in quarum
              <lb/>
            contemplatione, etiam extra utilitatem omnem, ſumma eſt
              <lb/>
            oblectatio. </s>
            <s xml:id="echoid-s9190" xml:space="preserve">Quis enim non admiratur, cum diſcit ea quæ
              <lb/>
            de circulo in Elementis Euclideis, & </s>
            <s xml:id="echoid-s9191" xml:space="preserve">Apollonii locis Pla-
              <lb/>
            nis docentur? </s>
            <s xml:id="echoid-s9192" xml:space="preserve">aut quæ de ſphæræ ſuperficie & </s>
            <s xml:id="echoid-s9193" xml:space="preserve">quadratu-
              <lb/>
            ra Parabolæ Archimedes prodidit, aut recentiorum ſubti-
              <lb/>
            liſſima inventa? </s>
            <s xml:id="echoid-s9194" xml:space="preserve">Quorum omnium eadem, & </s>
            <s xml:id="echoid-s9195" xml:space="preserve">ad diſcen-
              <lb/>
            dum æque expoſita, eſt veritas in Saturno, ac Jove, atque
              <lb/>
            apud nos, & </s>
            <s xml:id="echoid-s9196" xml:space="preserve">ex iiſdem ſimpliciſſimis principiis pendens,
              <lb/>
            quo facilius credi poteſt pulcherrimi jucundiſſimique ſtudii
              <lb/>
            in illis ac cæteris planetis aliquos participes eſſe: </s>
            <s xml:id="echoid-s9197" xml:space="preserve">Etſi præ-
              <lb/>
            cipue hoc ſuadet utilitas quæ ex eo in omnem vitam ema-
              <lb/>
            nat. </s>
            <s xml:id="echoid-s9198" xml:space="preserve">Quod ſi jam eo uſque rei Geometricæ peritos qui in
              <lb/>
            Planetis ſunt dicerem, ut & </s>
            <s xml:id="echoid-s9199" xml:space="preserve">Tabulas Sinuum, & </s>
            <s xml:id="echoid-s9200" xml:space="preserve">Logari-
              <lb/>
            thmos, & </s>
            <s xml:id="echoid-s9201" xml:space="preserve">calculum Analyticum invenerint; </s>
            <s xml:id="echoid-s9202" xml:space="preserve">abſona ac pe-
              <lb/>
            ne ridicula proferre viderer. </s>
            <s xml:id="echoid-s9203" xml:space="preserve">Nec tamen quidquam obſtat
              <lb/>
            quin horum aliquid reperiſſe potuerint, aut aliquando re-
              <lb/>
            perturi ſint; </s>
            <s xml:id="echoid-s9204" xml:space="preserve">atque etiam his noſtris fortaſſe majora. </s>
            <s xml:id="echoid-s9205" xml:space="preserve">Non
              <lb/>
            debemus enim, ut jam ſæpe diximus, præferre nos ipſos
              <lb/>
            ac res noſtras rebus Planeticolarum.</s>
            <s xml:id="echoid-s9206" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9207" xml:space="preserve">Cæterum illud quod uniuſmodi & </s>
            <s xml:id="echoid-s9208" xml:space="preserve">æternum in Geome-
              <lb/>
            trica ſcientia ineſſe animadvertimus, ſimiliter quoque in
              <lb/>
            Harmonicis inveniri certum eſt; </s>
            <s xml:id="echoid-s9209" xml:space="preserve">cum conſonantiæ omnes
              <lb/>
            conſtanti menſura ac proportione conſtituantur; </s>
            <s xml:id="echoid-s9210" xml:space="preserve">omnis
              <lb/>
            vero phtongorum ordo, omniſque cantus delectatio, etiam
              <lb/>
            vocis ſingulæ, in conſonantiis fundata ſit. </s>
            <s xml:id="echoid-s9211" xml:space="preserve">Quo fit ut
              <lb/>
              <note position="right" xlink:label="note-0423-01" xlink:href="note-0423-01a" xml:space="preserve">Muſicam@</note>
            apud omnes gentes eadem tonorum intervalla canantur,
              <lb/>
            ſive per gradus continuos, ſive ſaltu vox progrediatur.
              <lb/>
            </s>
            <s xml:id="echoid-s9212" xml:space="preserve">Imo animal quoddam in terris Americæ reperiri fide di-
              <lb/>
            gni auctores narrant, quod ſex muſicos tonos deinceps vo-
              <lb/>
            ce exprimat: </s>
            <s xml:id="echoid-s9213" xml:space="preserve">Ut appareat ipſam naturam immutabili ratio-
              <lb/>
            ne eos præſcribere. </s>
            <s xml:id="echoid-s9214" xml:space="preserve">Quandoquidem igitur quæ huc ſpe-
              <lb/>
            ctant, certa quoque & </s>
            <s xml:id="echoid-s9215" xml:space="preserve">unica, & </s>
            <s xml:id="echoid-s9216" xml:space="preserve">neceſſaria ratione ſe-
              <lb/>
            ſe habent, veriſimile eſt, non minus quam </s>
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