Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/293.jpg" pagenum="265"/>
                  Prop. </s>
                  <s>XIX, quod non mutabunt ſitum partium internarum inter
                    <lb/>
                    <arrow.to.target n="note241"/>
                  ſe: proindeque, ſi Animalia immergantur, & ſenſatio omnis a mo­
                    <lb/>
                  tu partium oriatur; nec lædent corpora immerſa, nec ſenſatio­
                    <lb/>
                  nem ullam excitabunt, niſi quatenus hæc corpora a compreſſione
                    <lb/>
                  condenſari poſſunt. </s>
                  <s>Et par eſt ratio cujuſcunque corporum Sy­
                    <lb/>
                  ſtematis fluido comprimente circundati. </s>
                  <s>Syſtematis partes omnes
                    <lb/>
                  iiſdem agitabuntur motibus, ac ſi in vacuo conſtituerentur, ac ſo­
                    <lb/>
                  lam retinerent gravitatem ſuam comparativam, niſi quatenus flui­
                    <lb/>
                  dum vel motibus earum nonnihil reſiſtat, vel ad eaſdem compreſſi­
                    <lb/>
                  one conglutinandas requiratur. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note241"/>
                  LIBER
                    <lb/>
                  SECUNDUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XXI. THEOREMA XVI.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Sit Fluidi cujuſdam denſitas compreſſioni proportionalis, & partes
                    <lb/>
                  ejus a vi centripeta diſtantiis ſuis a centro reciproce proportio­
                    <lb/>
                  nali deorſum trabantur: dico quod, fi diſtantiæ illæ ſumantur
                    <lb/>
                  continue proportionales, denſitates Fluidi in iiſdem diſtantiis e­
                    <lb/>
                  runt etiam continue proportionales.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Deſignet
                    <emph type="italics"/>
                  ATV
                    <emph.end type="italics"/>
                  fundum Sphæricum cui fluidum incumbit,
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                    <lb/>
                  centrum,
                    <emph type="italics"/>
                  SA, SB, SC, SD, SE,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>diſtantias continue propor­
                    <lb/>
                  tionales. </s>
                  <s>Erigantur perpendicula
                    <emph type="italics"/>
                  AH, BI, CK, DL, EM, &c.
                    <emph.end type="italics"/>
                    <lb/>
                  quæ ſint ut denſitates Medii in locis
                    <emph type="italics"/>
                  A, B, C, D, E
                    <emph.end type="italics"/>
                  ; & ſpecificæ
                    <lb/>
                  gravitates in iiſdem locis erunt ut
                    <emph type="italics"/>
                  (AH/AS), (BI/BS), (CK/CS),
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>vel, quod
                    <lb/>
                  perinde eſt, ut
                    <emph type="italics"/>
                  (AH/AB), (BI/BC), (CK/CD),
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>Finge pri­
                    <lb/>
                    <figure id="id.039.01.293.1.jpg" xlink:href="039/01/293/1.jpg" number="170"/>
                    <lb/>
                  mum has gravitates uniformiter continuari ab
                    <lb/>
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  B,
                    <emph.end type="italics"/>
                  a
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  C,
                    <emph.end type="italics"/>
                  a
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  D,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>factis per
                    <lb/>
                  gradus decrementis in punctis
                    <emph type="italics"/>
                  B, C, D,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>Et
                    <lb/>
                  hæ gravitates ductæ in altitudines
                    <emph type="italics"/>
                  AB, BC,
                    <lb/>
                  CD,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>conficient preſſiones
                    <emph type="italics"/>
                  AH, BI, CK,
                    <emph.end type="italics"/>
                    <lb/>
                  quibus fundum
                    <emph type="italics"/>
                  ATV
                    <emph.end type="italics"/>
                  (juxta Theorema XV.)
                    <lb/>
                  urgetur. </s>
                  <s>Suſtinet ergo particula
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  preſſiones
                    <lb/>
                  omnes
                    <emph type="italics"/>
                  AH, BI, CK, DL,
                    <emph.end type="italics"/>
                  pergendo in
                    <lb/>
                  infinitum; & particula
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  preſſiones omnes
                    <lb/>
                  præter primam
                    <emph type="italics"/>
                  AH
                    <emph.end type="italics"/>
                  ; & particula
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  omnes
                    <lb/>
                  præter duas primas
                    <emph type="italics"/>
                  AH, BI
                    <emph.end type="italics"/>
                  ; & ſic deinceps: adeoque parti­
                    <lb/>
                  culæ primæ
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  denſitas
                    <emph type="italics"/>
                  AH
                    <emph.end type="italics"/>
                  eſt ad particulæ ſecundæ
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  denſi-</s>
                </p>
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