Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <pb xlink:href="039/01/433.jpg" pagenum="405"/>
                <p type="margin">
                  <s>
                    <margin.target id="note433"/>
                  DE MUNDI
                    <lb/>
                  SYSTEMATE</s>
                </p>
                <p type="main">
                  <s>Deſignet jam
                    <emph type="italics"/>
                  PM
                    <emph.end type="italics"/>
                  arcum, quem Luna dato tempore quam
                    <lb/>
                    <arrow.to.target n="note434"/>
                  minimo deſcribit, &
                    <emph type="italics"/>
                  ML
                    <emph.end type="italics"/>
                  lineolam quam Luna, impellente vi
                    <lb/>
                  præfata 3
                    <emph type="italics"/>
                  IT,
                    <emph.end type="italics"/>
                  eodem tempore deſcribere poſſet. </s>
                  <s>Jungantur
                    <lb/>
                    <emph type="italics"/>
                  PL, MP,
                    <emph.end type="italics"/>
                  & producantur eæ ad
                    <emph type="italics"/>
                  m
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  l,
                    <emph.end type="italics"/>
                  ubi ſecent planum E­
                    <lb/>
                  clipticæ; inque
                    <emph type="italics"/>
                  Tm
                    <emph.end type="italics"/>
                  demittatur perpendiculum
                    <emph type="italics"/>
                  PH.
                    <emph.end type="italics"/>
                  Et quo­
                    <lb/>
                  niam recta
                    <emph type="italics"/>
                  ML
                    <emph.end type="italics"/>
                  parallela eſt plano Eclipticæ, ideoque cum recta
                    <lb/>
                    <emph type="italics"/>
                  ml
                    <emph.end type="italics"/>
                  quæ in plano illo jacet concurrere non poteſt, & tamen ja­
                    <lb/>
                  cent hæ rectæ in plano communi
                    <emph type="italics"/>
                  LMP ml
                    <emph.end type="italics"/>
                  ; parallelæ erunt hæ­
                    <lb/>
                  rectæ, & propterea ſimilia erunt triangula
                    <emph type="italics"/>
                  LMP, Lmp.
                    <emph.end type="italics"/>
                  Jam
                    <lb/>
                  cum
                    <emph type="italics"/>
                  MPm
                    <emph.end type="italics"/>
                  ſit in plano Orbis, in quo Luna in loco
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  moveba­
                    <lb/>
                  tur, incidet punctum
                    <emph type="italics"/>
                  m
                    <emph.end type="italics"/>
                  in lineam
                    <emph type="italics"/>
                  Nn
                    <emph.end type="italics"/>
                  per Orbis illius Nodos.
                    <lb/>
                    <emph type="italics"/>
                  N, n
                    <emph.end type="italics"/>
                  dictam. </s>
                  <s>Et quoniam vis qua lineola
                    <emph type="italics"/>
                  LM
                    <emph.end type="italics"/>
                  generatur, ſi
                    <lb/>
                  tota ſimul & ſemel in loco
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  impreſſa eſſet, efficeret ut Luna
                    <lb/>
                  moveretur in arcu, cujus chorda eſſet
                    <emph type="italics"/>
                  LP,
                    <emph.end type="italics"/>
                  atque adeo trans­
                    <lb/>
                  ferret Lunam de plano
                    <emph type="italics"/>
                  MPmT
                    <emph.end type="italics"/>
                  in planum
                    <emph type="italics"/>
                  LPIT
                    <emph.end type="italics"/>
                  ; motus an­
                    <lb/>
                  gularis Nodorum a vi illa genitus, æqualis erit angulo
                    <emph type="italics"/>
                  mTl.
                    <emph.end type="italics"/>
                  Eſt
                    <lb/>
                  autem
                    <emph type="italics"/>
                  ml
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  mP
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  ML
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  MP,
                    <emph.end type="italics"/>
                  adeoque cum
                    <emph type="italics"/>
                  MP
                    <emph.end type="italics"/>
                  ob da­
                    <lb/>
                  tum tempus data ſit, eſt
                    <emph type="italics"/>
                  ml
                    <emph.end type="italics"/>
                  ut rectangulum
                    <emph type="italics"/>
                  MLXmP,
                    <emph.end type="italics"/>
                  id eſt,
                    <lb/>
                  ut rectangulum
                    <emph type="italics"/>
                  ITXmP.
                    <emph.end type="italics"/>
                  Et angulus
                    <emph type="italics"/>
                  mTl,
                    <emph.end type="italics"/>
                  ſi modo angulus
                    <lb/>
                    <emph type="italics"/>
                  Tml
                    <emph.end type="italics"/>
                  rectus ſit, eſt ut (
                    <emph type="italics"/>
                  ml/Tm
                    <emph.end type="italics"/>
                  ), & propterea ut (
                    <emph type="italics"/>
                  ITXPm/Tm
                    <emph.end type="italics"/>
                  ), id eſt,
                    <lb/>
                  (ob proportionales
                    <emph type="italics"/>
                  Tm
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  mP, TP
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  PH
                    <emph.end type="italics"/>
                  ) ut (
                    <emph type="italics"/>
                  ITXPH/TP
                    <emph.end type="italics"/>
                  ),
                    <lb/>
                  adeoque ob datam
                    <emph type="italics"/>
                  TP,
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  ITXPH.
                    <emph.end type="italics"/>
                  Quod ſi angulus
                    <emph type="italics"/>
                  Tml,
                    <emph.end type="italics"/>
                    <lb/>
                  ſeu
                    <emph type="italics"/>
                  STN
                    <emph.end type="italics"/>
                  obliquus fit, erit angulus
                    <emph type="italics"/>
                  mTl
                    <emph.end type="italics"/>
                  adhuc minor, in rati­
                    <lb/>
                  one ſinus anguli
                    <emph type="italics"/>
                  STN
                    <emph.end type="italics"/>
                  ad Radium. </s>
                  <s>Eſt igitur velocitas No­
                    <lb/>
                  dorum ut
                    <emph type="italics"/>
                  ITXPHXAZ,
                    <emph.end type="italics"/>
                  ſive ut contentum ſub ſinubus trium
                    <lb/>
                  angulorum
                    <emph type="italics"/>
                  TPI, PTN
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  STN.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note434"/>
                  LIBER
                    <lb/>
                  TERTIUS.</s>
                </p>
                <p type="main">
                  <s>Si anguli illi, Nodis in Quadraturis & Luna in Syzygia exiſten­
                    <lb/>
                  tibus, recti ſint, lineola
                    <emph type="italics"/>
                  ml
                    <emph.end type="italics"/>
                  abibit in infinitum, & angulus
                    <emph type="italics"/>
                  mTl
                    <emph.end type="italics"/>
                    <lb/>
                  evadet angulo
                    <emph type="italics"/>
                  mPl
                    <emph.end type="italics"/>
                  æqualis. </s>
                  <s>Hoc autem in caſu, angulus
                    <emph type="italics"/>
                  mPl
                    <emph.end type="italics"/>
                    <lb/>
                  eſt ad angulum
                    <emph type="italics"/>
                  PTM,
                    <emph.end type="italics"/>
                  quem Luna eodem tempore motu ſuo
                    <lb/>
                  apparente circa Terram deſcribit ut 1 ad 59,575. Nam angulus
                    <lb/>
                    <emph type="italics"/>
                  mPl
                    <emph.end type="italics"/>
                  æqualis eſt angulo
                    <emph type="italics"/>
                  LPM,
                    <emph.end type="italics"/>
                  id eſt, angulo deflexionis Lunæ
                    <lb/>
                  a recto tramite, quem ſola vis præfata Solaris 3
                    <emph type="italics"/>
                  IT
                    <emph.end type="italics"/>
                  ſi tum ceſſa­
                    <lb/>
                  ret Lunæ gravitas dato illo tempore generare poſſet; & angulus
                    <lb/>
                    <emph type="italics"/>
                  PTM
                    <emph.end type="italics"/>
                  æqualis eſt angulo deflexionis Lunæ a recto tramite, quem
                    <lb/>
                  vis illa, qua Luna in Orbe ſuo retinetur, ſi tum ceſſaret vis Sola­
                    <lb/>
                  ris 3
                    <emph type="italics"/>
                  IT
                    <emph.end type="italics"/>
                  eodem tempore generaret. </s>
                  <s>Et hæ vires, ut ſupra dixi-</s>
                </p>
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