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

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          <pb o="282" file="0334" n="334" rhead="SUPPLEMENTA §. III."/>
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            <s xml:space="preserve">cunque majus quantitate quacunque data: </s>
            <s xml:space="preserve">ac ſi differentia abſciſ-
              <lb/>
              <note position="left" xlink:label="note-0334-01" xlink:href="note-0334-01a" xml:space="preserve">natæ relatio-
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              nem quancun-
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              que.</note>
            ſæ ſit infiniteſima, & </s>
            <s xml:space="preserve">dicatur ordinis primi; </s>
            <s xml:space="preserve">poterit differentia
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            ordinatæ eſſe ordinis cujuſcunque, vel utcunque inferioris, vel
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            intermedii, inter quantitates finitas, & </s>
            <s xml:space="preserve">quantitates ordinis pri-
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            mi.</s>
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          </p>
          <p>
            <s xml:space="preserve">51. </s>
            <s xml:space="preserve">Patet primum ex eo, quod, ubi determinatur valor R,
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              <note position="left" xlink:label="note-0334-02" xlink:href="note-0334-02a" xml:space="preserve">Demonſtratur
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              pro ratione fi-
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              nita.</note>
            poteſt curva tranſire per quotcunque, & </s>
            <s xml:space="preserve">quæcunque puncta,
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            adeoque per puncta, ex quibus ductæ ordinatæ ſint utcunque in-
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            ter ſe proximæ, & </s>
            <s xml:space="preserve">utcunque inæquales.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">52. </s>
            <s xml:space="preserve">Patet ſecundum: </s>
            <s xml:space="preserve">quia in curvis, ad quas accedit arcus
              <lb/>
              <note position="left" xlink:label="note-0334-03" xlink:href="note-0334-03a" xml:space="preserve">Itidem pro quo-
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              vis infiniteſimo-
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              rum ordine.</note>
            curvæ inventæ, vel quas oſculatur quocunque oſculi genere,
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            poteſt differentia abſciſſæ ad differentiam ordinatæ eſſe pro di-
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            verſa curvarum natura in datis earum punctis in quavis ratio-
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            ne, quantitatis infiniteſimæ ordinis cujuſcunque ad infiniteſi-
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            mam cujuſcunque alterius.</s>
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          <p>
            <s xml:space="preserve">53. </s>
            <s xml:space="preserve">Scholium 2. </s>
            <s xml:space="preserve">Illud notandum, ubicunque fuerit tangens
              <lb/>
              <note position="left" xlink:label="note-0334-04" xlink:href="note-0334-04a" xml:space="preserve">Relationem
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              ejuſmodi pen-
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              dere a poſitione
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              tangentis.</note>
            curvæ inventæ inclinata in angulo finito ad axem, fore diffe-
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            rentiam abſciſſæ ejuſdem ordinis, ac eſt differentia ordinatæ:
              <lb/>
            </s>
            <s xml:space="preserve">ubi tangens fuerit parallela axi, fore differentiam ordinatæ or-
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            dinis inferioris, quam ſit differentia abſciſſæ, & </s>
            <s xml:space="preserve">vice verſa,
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            abi tangens fuerit perpendicularis axi.</s>
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          <p>
            <s xml:space="preserve">54. </s>
            <s xml:space="preserve">Præterea notandum: </s>
            <s xml:space="preserve">ſi abſciſſa fuerit ipſa diſtantia limi-
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              <note position="left" xlink:label="note-0334-05" xlink:href="note-0334-05a" xml:space="preserve">Quid, ubi abſciſ.
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              ſa terminetur in
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              limite.</note>
            tis, quæ vel augeatur, vel minuatur utcunque; </s>
            <s xml:space="preserve">differentia or-
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            dinatæ erit ipſa ordinata integra: </s>
            <s xml:space="preserve">cum nimirum in limite or-
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            dinata ſit nihilo æqualis.</s>
            <s xml:space="preserve"/>
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          <p>
            <s xml:space="preserve">55. </s>
            <s xml:space="preserve">Coroll. </s>
            <s xml:space="preserve">5. </s>
            <s xml:space="preserve">Arcus repulſionum, vel attractionum inter-
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              <note position="left" xlink:label="note-0334-06" xlink:href="note-0334-06a" xml:space="preserve">Poſſe arcus ut
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              cunque recedere
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                <gap/>
              b axe.</note>
            cepti binis limitibus quibuſcunque, poſſunt recedere ab axe,
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            quantum libuerit, adeoque fieri poteſt, ut alii propiores aſym-
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            ptoto recedant minus, quam alii remotiores, vel ut quodam
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            ordine eo minus recedant ab axe, quo ſunt remotiores ab aſym-
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            ptoto, vel ut poſt aliquot arcus minus recedentes aliquis arcus
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            longiſſime recedat.</s>
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          <p>
            <s xml:space="preserve">56. </s>
            <s xml:space="preserve">Omnia manifeſto conſequuntur ex eo, quod curva poſſit
              <lb/>
              <note position="left" xlink:label="note-0334-07" xlink:href="note-0334-07a" xml:space="preserve">Demonſtratio.</note>
            tranſire per quævis data puncta.</s>
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          <p>
            <s xml:space="preserve">57. </s>
            <s xml:space="preserve">Coroll. </s>
            <s xml:space="preserve">6. </s>
            <s xml:space="preserve">Poteſt curva ipſum axem C'AC habere pro
              <lb/>
              <note position="left" xlink:label="note-0334-08" xlink:href="note-0334-08a" xml:space="preserve">Poſſe haberi
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              poſtremum crus
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              aſymptoticum,
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              & alia crura a-
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              ſymptotica.</note>
            aſymptoto ad partes C', & </s>
            <s xml:space="preserve">C ita, ut arcus aſymptoticus ſit
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            vel repulſivus, vel attractivus; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">poteſt arcus quivis binis li-
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            mitibus quibuſcunque interceptus abire in infinitum, ac habere
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            pro aſymptoto rectam axi perpendicularem, utcunque proxi-
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            mam utrilibet limiti, vel ab eo remotam.</s>
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          <p>
            <s xml:space="preserve">58. </s>
            <s xml:space="preserve">Nam ſi concipiatur, binos poſtremos limites coire, ab-
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              <note position="left" xlink:label="note-0334-09" xlink:href="note-0334-09a" xml:space="preserve">Ratio præſtan-
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              di primum.</note>
            euntibus binis interſectionibus in contactum, tum concipiatur,
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            ipſam diſtantiam contactus excreſcere in infinitum; </s>
            <s xml:space="preserve">jam axis
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            æquivalet rectæ curvam tangenti in puncto infinite remoto,
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            adeoque evadit aſymptotus: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi arcus evaneſcens inter poſtre-
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            mos duos limites coeuntes fuerit arcus repulſionis; </s>
            <s xml:space="preserve">poſtremus
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            arcus aſymptoticus erit arcus attractionis. </s>
            <s xml:space="preserve">Contra vero, ſi ar-
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            cus evaneſcens fuerit arcus attractionis.</s>
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