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

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              <pb o="94" file="0146" n="146" rhead="THEORIÆ"/>
            alteram OF, & </s>
            <s xml:space="preserve">vertices ejuſmodi normalium determinarent bi-
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            nas ſuperſicies quaſdam continuas, quarum altera exhiberet vi-
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            res in directione C D attractivas ad D, vel repulſivas reſpectu
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            ipſius, prout, cadente O citra, vel ultra C, normalis illa fuiſ-
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            ſet erecta ſupra, vel infra hoc planum; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">altera pariter vires
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            perpendiculares. </s>
            <s xml:space="preserve">Ejuſmodi locus geometricus, ſi algebraice tra-
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            ctari deberet, eſſet ex iis, quos Geometræ tractant tribus in-
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            determinatis per unicam æquationem inter ſe connexis; </s>
            <s xml:space="preserve">ac data
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            æquatione ad illam primam curvam ſiguræ 1, poſſet utique in-
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            veniri tam æquatio ad utramlibet curvam reſpondentem ſingu-
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            lis rectis DC, conſtans binis tantum indeterminatis, quam æ-
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            quatio determinans utramlibet ſuperſiciem ſimul indeſinite per
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            tres indeterminatas. </s>
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          <note position="left" xml:space="preserve">Fig. 22.</note>
          <note symbol="(n)" position="foot" xml:space="preserve">Stantibus in fig. 22 punctis ADBCKFLO, ut in fig. 21, du-
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          cantur perpendicula B P, A Q in C D, quæ dabuntur data inclinatione D C, & punctis B, A, ac pariter dabuntur & D P, D Q. Dicatur præterea D C = x, & dabuntur analytice C Q, C P. Quare ob angu- los rectos P, Q, dabuntur etiam analytice C B, C A. Denominentur C K = u, C L = z, C F = y. Quoniam datur A B, & dantur analy- sice A C, C B; dabitur analytice ex applicatione Algebræ ad Trigonome- triam ſinas anguli A C B per x, & datas quantitates, qui eſt idem, ac ſinus anguli C K F complementi ad duos rectos. Datur autem idem ex datis analytice valoribus C K = u, K F = C L = z, C F = y; quare babetur ibi una æquatio per x, y, z, u, & conſtantes. Si præterea valor C B ponatur pro valore abſciſſæ in æquatione curvæ ſiguræ 1; ac- quiritur altera æquatio per valores C K, C B, ſive per x, u, & con- ſtantes. Eodem pacto invenietur ope æquationis curvæ figuræ 1 tertia æquatio per A C, & C L, adeoque per x, z, & conſtantes. Quare jam babebuntur æquationes tres per x, u, z, y, & conſtantes, quæ, eliminatis u, & z, reducentur ad unicam per x, y, & conſtantes, as ea primam il- lam carvam definiet.</note>
          <note position="foot" xml:space="preserve">Quod ſi quæratur æquatio ad ſecundam curvam, cujus ordinata eſt
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          CO, vel tertiam, cujus ordinata OF, inveniri itidem poterit. Nam da-
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          tur analytice ſinus anguli D C B = {BP/CB}, & in triangule F C K datur
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          analytice ſinus F C K = {FK/CF} x ſin C K F. Quare datur analytice et-
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          iam ſinus differentiæ O C F, adeoque & ejus coſinus, & inde, ac ex C F, datur
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          analytice O F, vel C O. Si igitur altera ex illis dicatur p, acquiritur nova
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          æquatio, cujus ope una cum ſuperioribus eliminari poterit præterea una
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          alia indetermin
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          ata; adeoque eliminata C F = y, babebitur unica æquatio
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          per x, p, & conſtantes, quæ exbibebit utramlibet e reliquis curvis deter-
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          minantibus legem virium CO, vel OF.</note>
          <note position="foot" xml:space="preserve">Pro æquatione cum binis indeterminatis, quæ exbibeat locum ad ſu-
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          perſiciem, ducatur C R perpendicularis ad A B, & dicatur D R = x,
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          R C = q, denominatis, ut prius, C K = u, C L = z, C F = y; &
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          quoniam dantur A D, D B; dabuntur analytis
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          e per x, & conſtantes A R,
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          R B, adeoque per x, q, & conſtantes A C, C B, & factis omnibus reli-
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          quis, ut prius, habebuntur quatuor æquationes per x, q, u, z, y, p, &
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          conſtantes, quæ eliminatis valoribus u, z, y, reducentur ad unicam datam
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          per conſtantes, & tres indeterminatas x, p, q, ſive D R, R C, & C O,
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          vel OF, quæ exhibebit quæſitum locum ad ſuperſiciem.</note>
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