Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

< >
[Figure 51]
[Figure 52]
[Figure 53]
[Figure 54]
[Figure 55]
[Figure 56]
[Figure 57]
[Figure 58]
[Figure 59]
[Figure 60]
[Figure 61]
[Figure 62]
[Figure 63]
[Figure 64]
[Figure 65]
[Figure 66]
[Figure 67]
[Figure 68]
[Figure 69]
[Figure 70]
[Figure 71]
[Figure 72]
[Figure 73]
[Figure 74]
[Figure 75]
[Figure 76]
[Figure 77]
[Figure 78]
[Figure 79]
[Figure 80]
< >
page |< < of 524 > >|
    <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
                <lb/>
              eorum velocitates ſurſum & deorſum: hoc eſt, pondera, ſi recta
                <lb/>
              aſcendunt & deſcendunt, æquipollent, quæ ſunt reciproce ut pun­
                <lb/>
              ctorum a quibus ſuſpenduntur diſtantiæ ab axe Libræ; ſin planis
                <lb/>
              obliquis aliiſve admotis obſtaculis impedita aſcendunt vel deſcen­
                <lb/>
              dunt oblique, æquipollent quæ ſunt reciproce ut aſcenſus & deſcen­
                <lb/>
              ſus, quatenus facti ſecundum perpendiculum: id adeo ob determi­
                <lb/>
              nationem gravitatis deorſum. </s>
              <s>Similiter in Trochlea ſeu Polyſpaſto
                <lb/>
              vis manus funem directe trahentis, quæ ſit ad pondus vel directe
                <lb/>
              vel oblique aſcendens ut velocitas aſcenſus perpendicularis ad ve­
                <lb/>
              locitatem manus funem trahentis, ſuſtinebit pondus. </s>
              <s>In Horolo­
                <lb/>
              giis & ſimilibus inſtrumentis, quæ ex rotulis commiſſis conſtructa
                <lb/>
              ſunt, vires contrariæ ad motum rotularum promovendum & impe­
                <lb/>
              diendum, ſi ſunt reciproce ut velocitates partium rotularum in quas
                <lb/>
              imprimuntur, ſuſtinebunt ſe mutuo. </s>
              <s>Vis Cochleæ ad premendum
                <lb/>
              corpus eſt ad vim manus manubrium circumagentis, ut circularis
                <lb/>
              velocitas manubrii ea in parte ubi a manu urgetur, ad velocitatem
                <lb/>
              progreſſivam cochleæ verſus corpus preſſum. </s>
              <s>Vires quibus Cu­
                <lb/>
              neus urget partes duas ligni fiſſi ſunt ad vim mallei in cuneum, ut
                <lb/>
              progreſſus cunei ſecundum determinationem vis a malleo in ipſum
                <lb/>
              impreſſæ, ad velocitatem qua partes ligni cedunt cuneo, ſecundum
                <lb/>
              lineas faciebus cunei perpendiculares. </s>
              <s>Et par eſt ratio Machina­
                <lb/>
              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
                <lb/>
              di,
                <emph.end type="italics"/>
              aliamve datam reſiſtentiam vi data ſuperandi. </s>
              <s>Nam ſi Ma­
                <lb/>
              chinæ ita formentur, ut velocitates Agentis & Reſiſtentis ſine reci­
                <lb/>
              proce ut vires; Agens reſiſtentiam ſuſtinebit: & majori cum veloci­
                <lb/>
              tatum diſparitate eandem vincet. </s>
              <s>Certe ſi tanta ſic velocitatum
                <lb/>
              diſparitas, ut vincatur etiam reſiſtentia omnis, quæ tam ex conti­
                <lb/>
              guorum & inter ſe labentium corporum attritione, quam ex con­
                <lb/>
              tinuorum & ab invicem ſeparandorum cohæſione & elevandorum
                <lb/>
              ponderibus orirj ſolet; ſuperata omni ea reſiſtentia, vis redun­
                <lb/>
              dans accelerationem motus ſibi proportionalem, partim in parti­
                <lb/>
              bus machinæ, partim in corpore reſiſtente producet. </s>
              <s>Ceterum
                <lb/>
              Mechanicam tractare non eſt hujus inſtituti. </s>
              <s>Hiſce volui tan­
                <lb/>
              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>