Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/359.jpg" pagenum="331"/>
                    <arrow.to.target n="note339"/>
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                <p type="margin">
                  <s>
                    <margin.target id="note338"/>
                  DE MOTU
                    <lb/>
                  CORPORUM.</s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note339"/>
                  LIBER
                    <lb/>
                  SECUNDUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XLII. THEOREMA XXXIII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Motus omnis per Fluidum propagatus divergit a recto tramite
                    <lb/>
                  in ſpatia immota.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  1. Propagetur motus a puncto
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  per foramen
                    <emph type="italics"/>
                  BC,
                    <emph.end type="italics"/>
                  per­
                    <lb/>
                  gatque (ſi fieri poteſt) in ſpatio conico
                    <emph type="italics"/>
                  BCQP,
                    <emph.end type="italics"/>
                  ſecundum li­
                    <lb/>
                  neas rectas divergentes a puncto
                    <emph type="italics"/>
                  C.
                    <emph.end type="italics"/>
                  Et ponamus primo quod
                    <lb/>
                  motus iſte ſit undarum in ſuperficie ſtagnantis aquæ. </s>
                  <s>Sintque
                    <lb/>
                    <emph type="italics"/>
                  de, fg, hi, kl,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>undarum ſingularum partes altiſſimæ, valli­
                    <lb/>
                  bus totidem intermediis ab invicem diſtinctæ. </s>
                  <s>Igitur quoniam
                    <lb/>
                  aqua in undarum jugis altior eſt quam in Fluidi partibus immo­
                    <lb/>
                  tis
                    <emph type="italics"/>
                  LK, NO,
                    <emph.end type="italics"/>
                  defluet eadem de jugorum terminis
                    <emph type="italics"/>
                  e, g, i, l,
                    <emph.end type="italics"/>
                  &c.
                    <lb/>
                    <emph type="italics"/>
                  d, f, h, k,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>hinc inde, verſus
                    <emph type="italics"/>
                  KL
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  NO
                    <emph.end type="italics"/>
                  : & quoniam in un­
                    <lb/>
                  darum vallibus depreſſior eſt quam in Fluidi partibus immotis
                    <lb/>
                    <emph type="italics"/>
                  KL, NO
                    <emph.end type="italics"/>
                  ; defluet eadem de partibus illis immotis in undarum
                    <lb/>
                  valles. </s>
                  <s>Defluxu priore undarum juga, poſteriore valles hinc
                    <lb/>
                  inde dilatantur & propagantur verſus
                    <emph type="italics"/>
                  KL
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  NO.
                    <emph.end type="italics"/>
                  Et quo­
                    <lb/>
                  niam motus undarum ab
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  verſus
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  fit per continuum de­
                    <lb/>
                  fluxum jugorum in valles proximos, adeoque celerior non eſt
                    <lb/>
                  quam pro celeritate deſcenſus; & deſcenſus aquæ, hinc inde, ver­
                    <lb/>
                  ſus
                    <emph type="italics"/>
                  KL
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  NO
                    <emph.end type="italics"/>
                  eadem velocitate peragi debet; propagabitur
                    <lb/>
                  dilatatio undarum, hinc inde, verſus
                    <emph type="italics"/>
                  KL
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  NO,
                    <emph.end type="italics"/>
                  eadem velo­
                    <lb/>
                  citate qua undæ ipſæ ab
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  verſus
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  recta progrediuntur. </s>
                  <s>
                    <lb/>
                  Proindeque ſpatium totum hinc inde, verſus
                    <emph type="italics"/>
                  KL
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  NO,
                    <emph.end type="italics"/>
                  ab
                    <lb/>
                  undis dilatatis
                    <emph type="italics"/>
                  rfgr, shis, tklt, vmnv,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>occupabitur.
                    <lb/>
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  Hæc ita ſe habere quilibet in aqua ſtagnante expe­
                    <lb/>
                  riri poteſt. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  2. Ponamus jam quod
                    <emph type="italics"/>
                  de, fg, hi, kl, mn
                    <emph.end type="italics"/>
                  deſignent pul­
                    <lb/>
                  ſus a puncto
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  per Medium Elaſticum, ſucceſſive propagatos. </s>
                  <s>
                    <lb/>
                  Pulſus propagari concipe per ſucceſſivas condenſationes & rare­
                    <lb/>
                  factiones Medii, ſic ut pulſus cujuſque pars denſiſſima ſphæricam
                    <lb/>
                  occupet ſuperficiem circa centrum
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  deſcriptam, & inter pulſus
                    <lb/>
                  ſucceſſivos æqualia intercedant intervalla. </s>
                  <s>Deſignent autem lineæ
                    <lb/>
                    <emph type="italics"/>
                  de, fg, hi, kl,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>denſiſſimas pulſuum partes, per foramen
                    <emph type="italics"/>
                  BC
                    <emph.end type="italics"/>
                    <lb/>
                  propagatas. </s>
                  <s>Et quoniam Medium ibi denſius eſt quam in ſpatiis
                    <lb/>
                  hinc inde verſus
                    <emph type="italics"/>
                  KL
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  NO,
                    <emph.end type="italics"/>
                  dilatabit ſeſe tam verſus ſpatia illa
                    <lb/>
                    <emph type="italics"/>
                  KL, NO
                    <emph.end type="italics"/>
                  utrinque ſita, quam verſus pulſuum rariora intervalla; </s>
                </p>
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