Bošković, Ruđer Josip, Theoria philosophiae naturalis redacta ad unicam legem virium in natura existentium

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          <pb o="284" file="0336" n="336" rhead="SUPPLEMENTA §. III."/>
          <p>
            <s xml:space="preserve">y= x
              <emph style="super">m</emph>
            , qui quidem locus eſt Parabola quædam; </s>
            <s xml:space="preserve">ſi m ſit nu-
              <lb/>
            merus poſitivus, nec ſit unitas: </s>
            <s xml:space="preserve">recta; </s>
            <s xml:space="preserve">ſi ſit unitas, vel zero:
              <lb/>
            </s>
            <s xml:space="preserve">quædam Hyperbola; </s>
            <s xml:space="preserve">ſi ſit numerus negativus: </s>
            <s xml:space="preserve">formula autem
              <lb/>
            continens functionem aliam quamvis exprimit ordinatam ad a-
              <lb/>
            liam curvam, quæ erit continua, & </s>
            <s xml:space="preserve">ſimplex, ſi illa formu-
              <lb/>
            la per diviſionem non poſſit diſcerpi in alias plures. </s>
            <s xml:space="preserve">Omnes
              <lb/>
            autem ejuſmodi curvæ ſunt æque ſimplices in ſe, & </s>
            <s xml:space="preserve">aliæ aliis
              <lb/>
            ſunt magis affines, aliæ minus. </s>
            <s xml:space="preserve">Nobis hominibus recta eſt
              <lb/>
            omnium ſimpliciſſima, cum ejus naturam intueamur, & </s>
            <s xml:space="preserve">evi-
              <lb/>
            dentiſſime perſpiciamus, ad quam idcirco reducimus alias cur-
              <lb/>
            vas, & </s>
            <s xml:space="preserve">prout ſunt ipſi magis, vel minus affines, habemus eas
              <lb/>
            pro ſimplicioribus, vel magis compoſitis; </s>
            <s xml:space="preserve">cum tamen in ſe æ-
              <lb/>
            que ſimplices ſint omnes illæ, quæ ductum uniformem habent,
              <lb/>
            & </s>
            <s xml:space="preserve">naturam ubique conſtantem.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">63. </s>
            <s xml:space="preserve">Hinc ipſa ordinata ad quamvis naturæ uniformis curvam
              <lb/>
              <note position="left" xlink:label="note-0336-01" xlink:href="note-0336-01a" xml:space="preserve">Eſſe æque ſim-
                <lb/>
              plicem relatio-
                <lb/>
              nem ordinata-
                <lb/>
              rum ad abſciſ-
                <lb/>
              ſas: terminorum
                <lb/>
              multitudinem
                <lb/>
              pro ea expri-
                <lb/>
              menda oriri a
                <lb/>
              noſtro cogno-
                <lb/>
              fcendi modo.</note>
            eſt quidam terminus ſimpliciſſimæ relationis cujuſdam, quam
              <lb/>
            habet ordinata ad abſciffam, cui termino impoſitum eſt gene-
              <lb/>
            rale nomen functionis continens ſub ſe omnia functionum ge-
              <lb/>
            nera, ut etiam quamcunque ſolam potentiam, & </s>
            <s xml:space="preserve">ſi haberemus
              <lb/>
            nomina ad ejuſmodi functiones denominandas ſingillatim; </s>
            <s xml:space="preserve">ha-
              <lb/>
            beret nomen ſuum quævis ex ipſis, ut habet quadratum, cu-
              <lb/>
            bus, poteſtas quævis. </s>
            <s xml:space="preserve">Si omnia curvarum genera, omnes ejuſ-
              <lb/>
            modi relationes noſtra mens intueretur immediate in ſe ipſis;
              <lb/>
            </s>
            <s xml:space="preserve">nulla indigeremus terminorum farragine, nec multitudine ſi-
              <lb/>
            gnorum ad cognoſcendam, & </s>
            <s xml:space="preserve">enuntiandam ejuſmodi functionem,
              <lb/>
            vel ejus relationem ad abſciſſam.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">64. </s>
            <s xml:space="preserve">Verum nos, quibus uti monui recta linea eſt omnium
              <lb/>
              <note position="left" xlink:label="note-0336-02" xlink:href="note-0336-02a" xml:space="preserve">Origo ejus mo-
                <lb/>
              di ab intuitio-
                <lb/>
              ne, quam ha-
                <lb/>
              bemus nos ho-
                <lb/>
              mines naturæ
                <lb/>
              ſolius rectæ, ad
                <lb/>
              quam omnes
                <lb/>
              curvas referi-
                <lb/>
              mus.</note>
            locorum geometricorum ſimpliciſſima, omnia referimus ad re-
              <lb/>
            ctam, & </s>
            <s xml:space="preserve">idcirco etiam ad ea, quæ oriuntur ex recta, ut eſt
              <lb/>
            quadratum, quod fit ducendo perpendiculariter rectam ſuper
              <lb/>
            aliam rectam æqualem, & </s>
            <s xml:space="preserve">cubus, qui fit ducendo quadratum
              <lb/>
            eodem pacto per aliam rectam primæ radici æqualem, qui-
              <lb/>
            bus & </s>
            <s xml:space="preserve">ſua ſigna dedimus ope exponentium, & </s>
            <s xml:space="preserve">univerſalizan-
              <lb/>
            do exponentes efformavimus nobis ideas jam non geometricas
              <lb/>
            ſuperiorum potentiarum, nec integrarum tantummodo, & </s>
            <s xml:space="preserve">po-
              <lb/>
            ſitivarum, ſed etiam ſractionariarum, & </s>
            <s xml:space="preserve">negativarum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ve-
              <lb/>
            ro etiam, abſtrahendo ſemper magis, irrationalium. </s>
            <s xml:space="preserve">Ad haſce
              <lb/>
            potentias, & </s>
            <s xml:space="preserve">ad producta, quæ ſimili ductu concipiuntur ge-
              <lb/>
            nita, reducimus cæteras functiones omnes per relationem, quam
              <lb/>
            habent ad ejuſmodi potentias, & </s>
            <s xml:space="preserve">producta earum cum rectis
              <lb/>
            datis, ac ad eam reductionem, ſive ad expreſſionem illarum
              <lb/>
            functionum per haſce potentias, & </s>
            <s xml:space="preserve">per hæc producta, indige-
              <lb/>
            mus terminis jam paucioribus, jam pluribus, & </s>
            <s xml:space="preserve">quandoque
              <lb/>
            etiam, ut in functionibus tranſcendentalibus, ſerie terminorum
              <lb/>
            infinita, quæ ad valorem, vel naturam functionis propoſitæ
              <lb/>
            accedat ſemper magis, utut in hiſce caſibus eam nunquam ac-</s>
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