Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <pb xlink:href="039/01/187.jpg" pagenum="159"/>
                <p type="margin">
                  <s>
                    <margin.target id="note134"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>Exponatur corporis
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  attractio acceleratrix verſus
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  per lineam
                    <lb/>
                    <arrow.to.target n="note135"/>
                    <emph type="italics"/>
                  SN;
                    <emph.end type="italics"/>
                  & ſi attractiones acceleratrices
                    <emph type="italics"/>
                  SM, SN
                    <emph.end type="italics"/>
                  æquales eſſent; hæ,
                    <lb/>
                  trahendo corpora
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  æqualiter & ſecundum lineas parallelas,
                    <lb/>
                  nil mutarent ſitum eorum ad invicem. </s>
                  <s>Iidem jam forent corporum
                    <lb/>
                  illorum motus inter ſe (per Legum Corol. </s>
                  <s>6.) ac ſi hæ attractio­
                    <lb/>
                  nes tollerentur. </s>
                  <s>Et pari ratione ſi attractio
                    <emph type="italics"/>
                  SN
                    <emph.end type="italics"/>
                  minor eſſet at­
                    <lb/>
                  tractione
                    <emph type="italics"/>
                  SM,
                    <emph.end type="italics"/>
                  tolleret ipſa attractionis
                    <emph type="italics"/>
                  SM
                    <emph.end type="italics"/>
                  partem
                    <emph type="italics"/>
                  SN,
                    <emph.end type="italics"/>
                  & ma­
                    <lb/>
                  neret pars ſola
                    <emph type="italics"/>
                  MN,
                    <emph.end type="italics"/>
                  qua temporum & arearum proportionalitas
                    <lb/>
                  & Orbitæ forma illa Elliptica perturbaretur. </s>
                  <s>Et ſimiliter ſi attra­
                    <lb/>
                  ctio
                    <emph type="italics"/>
                  SN
                    <emph.end type="italics"/>
                  major eſſet attractione
                    <emph type="italics"/>
                  SM,
                    <emph.end type="italics"/>
                  oriretur ex differentia ſola
                    <lb/>
                    <emph type="italics"/>
                  MN
                    <emph.end type="italics"/>
                  perturbatio proportionalitatis & Orbitæ. </s>
                  <s>Sic per attractio­
                    <lb/>
                  nem
                    <emph type="italics"/>
                  SN
                    <emph.end type="italics"/>
                  reducitur ſemper attractio tertia ſuperior
                    <emph type="italics"/>
                  SM
                    <emph.end type="italics"/>
                  ad attra­
                    <lb/>
                  ctionem
                    <emph type="italics"/>
                  MN,
                    <emph.end type="italics"/>
                  attractione prima & ſecunda manentibus prorſus im­
                    <lb/>
                  mutatis: & propterea areæ ac tempora ad proportionalitatem, &
                    <lb/>
                  Orbita
                    <emph type="italics"/>
                  PAB
                    <emph.end type="italics"/>
                  ad formam præfatam Ellipticam tum maxime acce­
                    <lb/>
                  dunt, ubi attractio
                    <emph type="italics"/>
                  MN
                    <emph.end type="italics"/>
                  vel nulla eſt, vel quam fieri poſſit miNI­
                    <lb/>
                  ma; hoc eſt, ubi corporum
                    <emph type="italics"/>
                  P & T
                    <emph.end type="italics"/>
                  attractiones acceleratrices, fa­
                    <lb/>
                  ctæ verſus corpus
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  accedunt quantum fieri poteſt ad æqualita­
                    <lb/>
                  tem; id eſt, ubi attractio
                    <emph type="italics"/>
                  SN
                    <emph.end type="italics"/>
                  non eſt nulla, neque minor minima
                    <lb/>
                  attractionum omnium
                    <emph type="italics"/>
                  SM,
                    <emph.end type="italics"/>
                  ſed inter attractionum omnium
                    <emph type="italics"/>
                  SM
                    <emph.end type="italics"/>
                    <lb/>
                  maximam & minimam quaſi mediocris, hoc eſt, non multo major
                    <lb/>
                  neque multo minor attractione
                    <emph type="italics"/>
                  SK. Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note135"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  2. Revolvantur jam corpora minora
                    <emph type="italics"/>
                  P, S
                    <emph.end type="italics"/>
                  circa maximum
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                    <lb/>
                  in planis diverſis; & vis
                    <emph type="italics"/>
                  LM,
                    <emph.end type="italics"/>
                  agendo ſecundum lineam
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  in pla­
                    <lb/>
                  no Orbitæ
                    <emph type="italics"/>
                  PAB
                    <emph.end type="italics"/>
                  ſitam, eundem habebit effectum ac prius, neque
                    <lb/>
                  corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  de plano Orbitæ ſuæ deturbabit. </s>
                  <s>At vis altera
                    <emph type="italics"/>
                  NM,
                    <emph.end type="italics"/>
                    <lb/>
                  agendo ſecundum lineam quæ ipſi
                    <emph type="italics"/>
                  ST
                    <emph.end type="italics"/>
                  parallela eſt, (atque adco,
                    <lb/>
                  quando corpus
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  verſatur extra lineam Nodorum, inclinatur ad
                    <lb/>
                  planum Orbitæ
                    <emph type="italics"/>
                  PAB
                    <emph.end type="italics"/>
                  ;) præter perturbationem motus in Longitu­
                    <lb/>
                  dinem jam ante expoſitam, inducet perturbationem motus in Lati­
                    <lb/>
                  tudinem, trahendo corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  de plano ſuæ Orbitæ. </s>
                  <s>Et hæc per­
                    <lb/>
                  turbatio, in dato quovis corporum
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  ad invicem ſitu, erit ut
                    <lb/>
                  vis illa generans
                    <emph type="italics"/>
                  MN,
                    <emph.end type="italics"/>
                  adeoque minima evadet ubi
                    <emph type="italics"/>
                  MN
                    <emph.end type="italics"/>
                  eſt miNI­
                    <lb/>
                  ma, hoc eſt (uti jam expoſui) ubi attractio
                    <emph type="italics"/>
                  SN
                    <emph.end type="italics"/>
                  non eſt multo ma­
                    <lb/>
                  jor, neque multo minor attractione
                    <emph type="italics"/>
                  SK. Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Ex his facile colligitur quod, ſi corpora plura minora
                    <lb/>
                    <emph type="italics"/>
                  P, S, R,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>revolvantur circa maximum
                    <emph type="italics"/>
                  T,
                    <emph.end type="italics"/>
                  motus corporis inti­
                    <lb/>
                  mi
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  minime perturbabitur attractionibus exteriorum, ubi corpus
                    <lb/>
                  maximum
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  pariter a cæteris, pro ratione virium acceleratricum,
                    <lb/>
                  attrahitur & agitatur atque cætera a ſe mutuo. </s>
                </p>
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