Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="039/01/051.jpg" pagenum="23"/>
              virium æſtimatæ, ſunt reciproce ut vires. </s>
              <s>Sie pondera æquipollent
                <lb/>
              ad movenda brachia Libræ, quæ oſcillante Libra ſunt reciproce ut
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              eorum velocitates ſurſum & deorſum: hoc eſt, pondera, ſi recta
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              aſcendunt & deſcendunt, æquipollent, quæ ſunt reciproce ut pun­
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              ctorum a quibus ſuſpenduntur diſtantiæ ab axe Libræ; ſin planis
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              obliquis aliiſve admotis obſtaculis impedita aſcendunt vel deſcen­
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              dunt oblique, æquipollent quæ ſunt reciproce ut aſcenſus & deſcen­
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              ſus, quatenus facti ſecundum perpendiculum: id adeo ob determi­
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              nationem gravitatis deorſum. </s>
              <s>Similiter in Trochlea ſeu Polyſpaſto
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              vis manus funem directe trahentis, quæ ſit ad pondus vel directe
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              vel oblique aſcendens ut velocitas aſcenſus perpendicularis ad ve­
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              locitatem manus funem trahentis, ſuſtinebit pondus. </s>
              <s>In Horolo­
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              giis & ſimilibus inſtrumentis, quæ ex rotulis commiſſis conſtructa
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              ſunt, vires contrariæ ad motum rotularum promovendum & impe­
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              diendum, ſi ſunt reciproce ut velocitates partium rotularum in quas
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              imprimuntur, ſuſtinebunt ſe mutuo. </s>
              <s>Vis Cochleæ ad premendum
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              corpus eſt ad vim manus manubrium circumagentis, ut circularis
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              velocitas manubrii ea in parte ubi a manu urgetur, ad velocitatem
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              progreſſivam cochleæ verſus corpus preſſum. </s>
              <s>Vires quibus Cu­
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              neus urget partes duas ligni fiſſi ſunt ad vim mallei in cuneum, ut
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              progreſſus cunei ſecundum determinationem vis a malleo in ipſum
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              impreſſæ, ad velocitatem qua partes ligni cedunt cuneo, ſecundum
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              lineas faciebus cunei perpendiculares. </s>
              <s>Et par eſt ratio Machina­
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              rum omnium. </s>
            </p>
            <p type="main">
              <s>Harum efficacia & uſus in eo ſolo conſiſtit, ut diminuendo velo­
                <lb/>
              citatem augeamus vim, & contra: Unde ſolvitur in omni aptorum
                <lb/>
              inſtrumentorum genere Problema,
                <emph type="italics"/>
              Datum pondus data vi moven­
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              di,
                <emph.end type="italics"/>
              aliamve datam reſiſtentiam vi data ſuperandi. </s>
              <s>Nam ſi Ma­
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              chinæ ita formentur, ut velocitates Agentis & Reſiſtentis ſine reci­
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              proce ut vires; Agens reſiſtentiam ſuſtinebit: & majori cum veloci­
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              tatum diſparitate eandem vincet. </s>
              <s>Certe ſi tanta ſic velocitatum
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              diſparitas, ut vincatur etiam reſiſtentia omnis, quæ tam ex conti­
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              guorum & inter ſe labentium corporum attritione, quam ex con­
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              tinuorum & ab invicem ſeparandorum cohæſione & elevandorum
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              ponderibus orirj ſolet; ſuperata omni ea reſiſtentia, vis redun­
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              dans accelerationem motus ſibi proportionalem, partim in parti­
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              bus machinæ, partim in corpore reſiſtente producet. </s>
              <s>Ceterum
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              Mechanicam tractare non eſt hujus inſtituti. </s>
              <s>Hiſce volui tan­
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              tum oſtendere, quam late pateat quamque certa ſit Lex tertia
                <lb/>
              Motus. </s>
              <s>Nam ſi æſtimetur Agentis actio ex ejus vi & veloci-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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