Newton, Isaac, Philosophia naturalis principia mathematica, 1713

List of thumbnails

< >
211
211 		212
212
213
213 		214
214
215
215 		216
216
217
217 		218
218
219
219 		220
220
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/203.jpg" pagenum="175"/>
                  arcus
                    <emph type="italics"/>
                  IH
                    <emph.end type="italics"/>
                  convolutione ſemicirculi
                    <emph type="italics"/>
                  AKB
                    <emph.end type="italics"/>
                  circa diametrum
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                    <lb/>
                    <arrow.to.target n="note151"/>
                  deſcribet, ad ſuperficiem circularem, quam arcus
                    <emph type="italics"/>
                  ih
                    <emph.end type="italics"/>
                  convolutione
                    <lb/>
                  ſemicirculi
                    <emph type="italics"/>
                  akb
                    <emph.end type="italics"/>
                  circa diametrum
                    <emph type="italics"/>
                  ab
                    <emph.end type="italics"/>
                  deſcribet. </s>
                  <s>Et vires, quibus
                    <lb/>
                  hæ ſuperficies ſecundum lineas ad ſe tendentes attrahunt corpuſcu­
                    <lb/>
                  la
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  p,
                    <emph.end type="italics"/>
                  ſunt (per Hypotheſin) ut ipſæ ſuperficies applicatæ
                    <lb/>
                  ad quadrata diſtantiarum ſuarum a corporibus, hoc eſt, ut
                    <emph type="italics"/>
                  pfXps
                    <emph.end type="italics"/>
                    <lb/>
                  ad
                    <emph type="italics"/>
                  PFXPS.
                    <emph.end type="italics"/>
                  Suntque hæ vires ad ipſarum partes obliquas
                    <lb/>
                  quæ (facta per Legum Corol. </s>
                  <s>2. reſolutione virium) ſecundum
                    <lb/>
                  lineas
                    <emph type="italics"/>
                  PS, ps
                    <emph.end type="italics"/>
                  ad centra tendunt, ut
                    <emph type="italics"/>
                  PI
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PQ,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  pi
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                    <expan abbr="pq;">pque</expan>
                    <emph.end type="italics"/>
                  id
                    <lb/>
                  eſt (ob ſimilia triangula
                    <emph type="italics"/>
                  PIQ
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  PSF, piq
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  psf
                    <emph.end type="italics"/>
                  ) ut
                    <emph type="italics"/>
                  PS
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  PF
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  ps
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  pf.
                    <emph.end type="italics"/>
                  Unde, ex æquo, fit attractio corpuſculi hujus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                    <lb/>
                  verſus
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  ad attractionem corpuſculi
                    <emph type="italics"/>
                  p
                    <emph.end type="italics"/>
                  verſus
                    <emph type="italics"/>
                  s,
                    <emph.end type="italics"/>
                  ut (
                    <emph type="italics"/>
                  PFXpfXps/PS
                    <emph.end type="italics"/>
                  ) ad
                    <lb/>
                  (
                    <emph type="italics"/>
                  pfXPFXPS/ps
                    <emph.end type="italics"/>
                  ), hoc eſt, ut
                    <emph type="italics"/>
                  ps quad.
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PS quad.
                    <emph.end type="italics"/>
                  Et ſimili argu­
                    <lb/>
                  mento vires, quibus ſuperficies convolutione arcuum
                    <emph type="italics"/>
                  KL, kl
                    <emph.end type="italics"/>
                  de­
                    <lb/>
                  ſcriptæ trahunt corpuſcula, erunt ut
                    <emph type="italics"/>
                  ps quad.
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PS quad.
                    <emph.end type="italics"/>
                  ; inque
                    <lb/>
                  eadem ratione erunt vires ſuperficierum omnium circularium in quas
                    <lb/>
                  utraque ſuperficies Sphærica, capiendo ſemper
                    <emph type="italics"/>
                  sd
                    <emph.end type="italics"/>
                  æqualem
                    <emph type="italics"/>
                  SD
                    <emph.end type="italics"/>
                  &
                    <lb/>
                    <emph type="italics"/>
                  se
                    <emph.end type="italics"/>
                  æqualem
                    <emph type="italics"/>
                  SE,
                    <emph.end type="italics"/>
                  diſtingui poteſt. </s>
                  <s>Et, per compoſitionem, vires
                    <lb/>
                  totarum ſuperficierum Sphæricarum in corpuſcula exercitæ erunt
                    <lb/>
                  in eadem ratione.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note151"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO LXXII. THEOREMA XXXII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si ad Sphæræ cujuſvis puncta ſingula tendant vires æquales cen­
                    <lb/>
                  tripetæ decreſcentes in duplicata ratione diſtantiarum a punctis,
                    <lb/>
                  ac detur tum Sphæræ denſitas, tum ratio diametri Sphæræ ad
                    <lb/>
                  diſtantiam corpuſculi a centro ejus; dico quod vis qua corpuſ­
                    <lb/>
                  culum attrahitur proportionalis erit ſemidiametro Sphæræ.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Nam concipe corpuſcula duo ſeorſim a Sphæris duabus attrahi,
                    <lb/>
                  unum ab una & alterum ab altera, & diſtantias eorum a Sphæra­
                    <lb/>
                  rum centris proportionales eſſe diametris Sphærarum reſpective,
                    <lb/>
                  Sphæras autem reſolvi in particulas ſimiles & ſimiliter poſitas ad
                    <lb/>
                  corpuſcula. </s>
                  <s>Et attractiones corpuſculi unius, factæ verſus ſingulas
                    <lb/>
                  particulas Sphæræ unius, erunt ad attractiones alterius verſus ana­
                    <lb/>
                  logas totidem particulas Sphæræ alterius, in ratione compoſita ex
                    <lb/>
                  ratione particularum directe & ratione duplicata diſtantiarum in-</s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum