Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

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                  penduli quam habet reſiſtentia ad gravitatem, erit
                    <emph type="italics"/>
                  DK
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                  exponens </s>
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                <p type="main">
                  <s>
                    <arrow.to.target n="note257"/>
                  reſiſtentiæ. </s>
                  <s>Centro
                    <emph type="italics"/>
                  C
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                  & intervallo
                    <emph type="italics"/>
                  CA
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  CB
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                  conſtruatur Semi­
                    <lb/>
                  circulus
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                  BEeA.
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                  Deſcribat autem corpus tempore quam minimo
                    <lb/>
                  ſpatium
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                  Dd,
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                  & erectis perpendiculis
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                  DE, de
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                  circumferentiæ oc­
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                  currentibus in
                    <emph type="italics"/>
                  E
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  e,
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                  erunt hæc ut velocitates quas corpus in va­
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                  cuo, deſcendendo a puncto
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                  B,
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                  acquireret in locis
                    <emph type="italics"/>
                  D
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                  &
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                  d.
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                  Patet
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                  hoc per Prop. </s>
                  <s>LII. Lib. </s>
                  <s>1. Exponantur itaque hæ velocitates per
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                  perpendicula illa
                    <emph type="italics"/>
                  DE, de
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                  ; ſitque
                    <emph type="italics"/>
                  DF
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                  velocitas quam acquirit
                    <lb/>
                  in
                    <emph type="italics"/>
                  D
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                  cadendo de
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  in Medio reſiſtente. </s>
                  <s>Et ſi centro
                    <emph type="italics"/>
                  C
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                  & inter­
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                  vallo
                    <emph type="italics"/>
                  CF
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                  deſcribatur Circulus
                    <emph type="italics"/>
                  FfM
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                  occurrens rectis
                    <emph type="italics"/>
                  de
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                  &
                    <emph type="italics"/>
                  AB
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                  in
                    <lb/>
                    <emph type="italics"/>
                  f
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  M,
                    <emph.end type="italics"/>
                  erit
                    <emph type="italics"/>
                  M
                    <emph.end type="italics"/>
                  locus ad quem deinceps abſque ulteriore reſiſten­
                    <lb/>
                  tia aſcenderet, &
                    <emph type="italics"/>
                  df
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                  velocitas quam acquireret in
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                  d.
                    <emph.end type="italics"/>
                  Unde etiam
                    <lb/>
                  ſi
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                  Fg
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                  deſignet velocitatis momentum quod corpus
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                  D,
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                  deſcribendo
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                  ſpatium quam minimum
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                  Dd,
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                  ex reſiſtentia Medii amittit; & ſu­
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                  matur
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                  CN
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                  æqualis
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                  Cg:
                    <emph.end type="italics"/>
                  erit
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                  N
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                  locus ad quem corpus deinceps
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                  abſque ulteriore reſiſtentia aſcenderet, &
                    <emph type="italics"/>
                  MN
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                  erit decrementum
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                  aſcenſus ex velocitatis illius amiſſione oriundum. </s>
                  <s>Ad
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                  df
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                  demitta­
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                  tur perpendiculum
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                  Fm,
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                  & velocitatis
                    <emph type="italics"/>
                  DF
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                  decrementum
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                  Fg
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                  a
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                  reſiſtentia
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                  DK
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                  genitum, erit ad velocitatis ejuſdem incrementum
                    <lb/>
                    <emph type="italics"/>
                  fm
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                  a vi
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                  CD
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                  genitum, ut vis generans
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                  DK
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                  ad vim generantem
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                    <emph type="italics"/>
                  CD.
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                  Sed & ob ſimilia
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                    <figure id="id.039.01.309.1.jpg" xlink:href="039/01/309/1.jpg" number="179"/>
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                  triangula
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                  Fmf, Fhg,
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                  FDC,
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                  eſt
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                  fm
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                  ad
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                  Fm
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                    <lb/>
                  ſeu
                    <emph type="italics"/>
                  Dd,
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                  ut
                    <emph type="italics"/>
                  CD
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  DF
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                  ; & ex æquo
                    <emph type="italics"/>
                  Fg
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  Dd
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  DK
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  DF.
                    <emph.end type="italics"/>
                    <lb/>
                  Item
                    <emph type="italics"/>
                  Fh
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                  ad
                    <emph type="italics"/>
                  Fg
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                  ut
                    <emph type="italics"/>
                  DF
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                    <lb/>
                  ad
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                  CF
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                  ; & ex æquo
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                  perturbate,
                    <emph type="italics"/>
                  Fh
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                  ſeu
                    <emph type="italics"/>
                  MN
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                    <lb/>
                  ad
                    <emph type="italics"/>
                  Dd
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                  ut
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                  DK
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                  ad
                    <emph type="italics"/>
                  CF
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                    <lb/>
                  ſeu
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                  CM
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                  ; ideoque ſumma omnium
                    <emph type="italics"/>
                  MNXCM
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                  æqualis erit ſummæ
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                  omnium
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                  DdXDK.
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                  Ad punctum mobile
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                  M
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                  erigi ſemper intelli­
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                  gatur ordinata rectangula æqualis indeterminatæ
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                  CM,
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                  quæ motu
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                  continuo ducatur in totam longitudinem
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                  Aa
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                  ; & trapezium ex illo
                    <lb/>
                  motu deſcriptum ſive huic æquale rectangulum
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                  Aa
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                  X1/2
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                  aB
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                  æquabitur
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                  ſummæ omnium
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                  MNXCM,
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                  adeoque ſummæ omnium
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                  DdXDK,
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                    <lb/>
                  id eſt, areæ
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                  BKkVTa. </s>
                  <s>Q.E.D.
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                  </s>
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                <p type="margin">
                  <s>
                    <margin.target id="note257"/>
                  LIBER
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                  SECUNDUS</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  Hinc ex lege reſiſtentiæ & arcuum
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                  Ca, CB
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                  differentia
                    <emph type="italics"/>
                  Aa,
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                    <lb/>
                  colligi poteſt proportio reſiſtentiæ ad gravitatem quam proxime. </s>
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