Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/193.jpg" pagenum="165"/>
                  dentibus Corollariis: manifeſtum eſt quod effectus illi omnes, ſtan­
                    <lb/>
                    <arrow.to.target n="note141"/>
                  te corporum
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  Syſtemate, & mutatis tantum diſtantia
                    <emph type="italics"/>
                  ST
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  vi abſoluta corporis
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  ſint quamproxime in ratione compoſita ex
                    <lb/>
                  ratione directa vis abſolutæ corporis
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  & ratione triplicata inverſa
                    <lb/>
                  diſtantiæ
                    <emph type="italics"/>
                  ST.
                    <emph.end type="italics"/>
                  Unde ſi Syſtema corporum
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  revolvatur cir­
                    <lb/>
                  ca corpus longinquum
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  vires illæ
                    <emph type="italics"/>
                  NM, ML
                    <emph.end type="italics"/>
                  & earum effectus
                    <lb/>
                  erunt (per Corol. </s>
                  <s>2. & 6. Prop. </s>
                  <s>IV.) reciproce in duplicata ratione
                    <lb/>
                  temporis periodici. </s>
                  <s>Et inde etiam, ſi magnitudo corporis
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  propor­
                    <lb/>
                  tionalis ſit ipſius vi abſolutæ, erunt vires illæ
                    <emph type="italics"/>
                  NM, ML
                    <emph.end type="italics"/>
                  & earum
                    <lb/>
                  effectus directe ut cubus diametri apparentis longinqui corporis
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  e
                    <lb/>
                  corpore
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  ſpectati, & vice verſa. </s>
                  <s>Namque hæ rationes eædem ſunt
                    <lb/>
                  atque ratio ſuperior compoſita. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note141"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  15. Et quoniam ſi, manentibus Orbium
                    <emph type="italics"/>
                  ESE
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  PAB
                    <emph.end type="italics"/>
                    <lb/>
                  forma, proportionibus & inclinatione ad invicem, mutetur eorum
                    <lb/>
                  magnitudo, & ſi corporum
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  vel maneant vel mutentur vires
                    <lb/>
                  in data quavis ratio­
                    <lb/>
                    <figure id="id.039.01.193.1.jpg" xlink:href="039/01/193/1.jpg" number="111"/>
                    <lb/>
                  ne, hæ vires (hoc eſt,
                    <lb/>
                  vis corporis
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  qua cor­
                    <lb/>
                  pus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  de recto trami­
                    <lb/>
                  te in Orbitam
                    <emph type="italics"/>
                  PAB
                    <emph.end type="italics"/>
                    <lb/>
                  deflectere, & vis cor­
                    <lb/>
                  poris
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  qua corpus
                    <lb/>
                  idem
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  de Orbita illa
                    <lb/>
                  deviare cogitur) agunt
                    <lb/>
                  ſemper eodem mo­
                    <lb/>
                  do & eadem proportione: neceſſe eſt ut ſimiles & proportiona­
                    <lb/>
                  les ſint effectus omnes & proportionalia effectuum tempora; hoc
                    <lb/>
                  eſt, ut errores omnes lineares ſint ut Orbium diametri, angulares
                    <lb/>
                  vero iidem qui prius, & errorum linearium ſimilium vel angularium
                    <lb/>
                  æqualium tempora ut Orbium tempora periodica. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  16. Unde, ſi dentur Orbium formæ & inclinatio ad invi­
                    <lb/>
                  cem, & mutentur utcunque corporum magnitudines, vires & di­
                    <lb/>
                  ſtantiæ; ex datis erroribus & errorum temporibus in uno Caſu, col­
                    <lb/>
                  ligi poſſunt errores & errorum tempora in alio quovis, quam pro­
                    <lb/>
                  xime: Sed brevius hac Methodo. </s>
                  <s>Vires
                    <emph type="italics"/>
                  NM, ML,
                    <emph.end type="italics"/>
                  cæteris ſtan­
                    <lb/>
                  tibus, ſunt ut Radius
                    <emph type="italics"/>
                  TP,
                    <emph.end type="italics"/>
                  & harum effectus periodici (per Corol.2,
                    <lb/>
                  Lem. </s>
                  <s>X) ut vires & quadratum temporis periodici corporis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  con­
                    <lb/>
                  junctim. </s>
                  <s>Hi ſunt errores lineares corporis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  ; & hinc errores an­
                    <lb/>
                  gulares e centro
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  ſpectati (id eſt, tam motus Augis & Nodorum,
                    <lb/>
                  quam omnes in Longitudinem & Latitudinem errores apparentes)
                    <lb/>
                  ſunt, in qualibet revolutione corporis
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  ut quadratum temporis </s>
                </p>
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