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

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            <s xml:space="preserve">209. </s>
            <s xml:space="preserve">Si pro duobus punctis tantummodo agentibus in ter-
              <lb/>
              <note position="right" xlink:label="note-0147-01" xlink:href="note-0147-01a" xml:space="preserve">Methodus de-
                <lb/>
              terminandivim
                <lb/>
              compoſitam ex
                <lb/>
              viribus reſpi-
                <lb/>
              cientibus pun-
                <lb/>
              cta quotcun-
                <lb/>
              que. Legum
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              multitudo, &
                <lb/>
              varietas.</note>
            tium daretur numerus quicunque punctorum poſitorum in da-
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            tis locis, ac agentium in idem punctum, poſſet utique con-
              <lb/>
            ſtructione ſimili inveniri vis, qua ſingula agunt in ipſum col-
              <lb/>
            locatum in quovis aſſumpto loci puncto, ac vis ex ejuſimodi
              <lb/>
            viribus compoſita deſiniretur tam directione, quam magnitu-
              <lb/>
            dine, per notam virium compoſitionem. </s>
            <s xml:space="preserve">Poſſet etiam ana-
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            lyſis adhiberi ad exprimendas curvas per æquationes duarum in-
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            determinatarum pro rectis quibuſcunque, & </s>
            <s xml:space="preserve"> ſi omnia pun- cta jaceant in eodem plano, ſuperſicies per æquationem trium.
              <lb/>
            </s>
            <s xml:space="preserve">
              <note position="foot" xlink:label="note-0147-02" xlink:href="note-0147-02a" xml:space="preserve">Calculas quidem eſſet immenſus, ſed patet methodus, qua deveniri poſſit
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              ad æquationem quæſitam. Mirum autem, quanta curvarum, & ſuperſicierum,
                <lb/>
              adeoque & legum virium varietas obveniret, mutatatantummodo diſtantia A B
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              binorum punctorum agentium in tertium, qua mutata, mutatur tota lex,
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              & æquatio.</note>
              <note symbol="(o)" position="foot" xlink:label="note-0147-03" xlink:href="note-0147-03a" xml:space="preserve">Hæc conditio punctorum jacentium in eodem plano neceſſaria fuit
                <lb/>
              pro loco ad ſuperſiciem, & pro æquatione, quæ legem virium exhibeat
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              per æquationem indeterminatarum tantummodo trium: at ſi puncta ſint
                <lb/>
              plara, & in eodem plano non jaceant, quod punctis tantummodo tribus
                <lb/>
              accidere omnino non poteſt; tum vero locus ad ſuperſiciem, & æquatio
                <lb/>
              tr
                <unsure/>
              ium indeterminatarum non ſuſſicit, ſed ad eam generaliter exprimendam
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              legem Geometria omnis eſt incapax, & analyſis indiget aquatione indeter-
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              minatarum quatuor. Primum patet ex eo, quod ſi manentibus punctis
                <lb/>
              A, B, exeat punctum C ex dato quodam plano, pro quo conſtructus
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              ſit locus ad ſuperſiciem; liceret convertere circa rectam A B planum illud
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              cum ſuperſicie curva legem virium determinante, donec ad punctum C
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              deveniret planum ipſum: tum enim erecto perpendiculo uſque ad ſuper-
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              ſiciem illam curvam, deſiniretur per ipſum vis agens ſecundum rectam
                <lb/>
              C D, vel ipſi perpendicularis, prout locus ille ad curvam ſuperſiciem con-
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              ſtructus fuerit pro altera ex iis.</note>
              <note position="foot" xlink:label="note-0147-04" xlink:href="note-0147-04a" xml:space="preserve">At ſecundum ſit manifeſlum ex eo, quod ſi puncta agentia ſint etiam
                <lb/>
              omnia in eodem plano, & punctum, cujus vis compoſita quæritur, in qua-
                <lb/>
              vis recta poſita extra ipſum planum, relationes omnes diſtantiarum a reli-
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              quis punctis, ac directionum, a quibus pendent vires ſingulorum, &
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              compoſitio ipſarum virium, longe aliæ eſſent, ac in quavis recta in eo-
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              dem plano poſita, uti facile videre eſt. Hinc pro quovis puncto loci u-
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              bicunque aſſumpto ſua reſponderet vis compoſita, & quarta aliqua plaga,
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              ſeu dimenſio, præter longum, latum, & profundum, requireretur ad ducendas
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              ex omnibus punctis ſpatii rectas iis viribus proportionales, quarum rectarum
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              vertices locum continuum aliquem exhiberent determinantem virium legem.</note>
              <note position="foot" xlink:label="note-0147-05" xlink:href="note-0147-05a" xml:space="preserve">Sed quod Geometria non aſſequitur, aſſequeretur quarta alia dimenſio
                <unsure/>
                <lb/>
              mente concepta, ut ſi co
                <unsure/>
              nciperetur ſpati
                <unsure/>
              um totum plenum materia conti-
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              nua, quod in mea ſententia cogitatione tantummodo eſſingi poteſt, & ea
                <unsure/>
                <lb/>
              eſſet in omnibus ſpatii punctis denſitatis diverſæ, vel diverſi pretii; tum illa
                <unsure/>
                <lb/>
              diverſa denſitas, vel illud pretium, vel quidpiam ejusmodi, exbibere poſſet
                <lb/>
              legem virium ipſi reſpondentium, que nimirum ipſi eſſent proportionales.
                <lb/>
              Sed ibi iterum ad determinandam directionem vis compoſitæ non eſſet ſa-
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              tis reſolutio in duas vires, alteram ſecundum rectam tranſeuntem per
                <lb/>
              datum punctum; alteram ipſi perpendicularem; ſed requirerentur tres, ni-
                <lb/>
              mirum vel omnes ſecundum tres da
                <gap/>
              as directiones, vel tendentes per rectas,
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              quæ per data tria puncta tranſeant, vel quavis alia certa lege deſinitas:
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              adeoque tria loca ejusmodi ad ſpatium, quarta aliqua dimenſione, vel
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              qualitate affectum requirerentur, quæ tribus ejusmo
                <unsure/>
              di plusquam Geometri-</note>
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