Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <pb xlink:href="039/01/243.jpg" pagenum="215"/>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  4. Spatium vero a corpore deſcriptum differentia eſt duo­
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                    <arrow.to.target n="note191"/>
                  rum ſpatiorum, quorum alterum eſt ut tempus ſumptum ab initio
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                  deſcenſus, & alterum ut velocitas, quæ etiam ipſo deſcenſus initio
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                  æquantur inter ſe. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note191"/>
                  LIBER
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                  SECUNDUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO IV. PROBLEMA II.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Poſito quod vis gravitatis in Medio aliquo ſimilari uniformis ſit,
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                  ac tendat perpendiculariter ad planum Horizontis; definire mo­
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                  tum Projectilis in eodem, reſiſtentiam velocitati proportionalem
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                  patientis.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Eloco quovis
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  egrediatur Pro­
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                    <figure id="id.039.01.243.1.jpg" xlink:href="039/01/243/1.jpg" number="145"/>
                    <lb/>
                  jectile ſecundum lineam quam­
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                  vis rectam
                    <emph type="italics"/>
                  DP,
                    <emph.end type="italics"/>
                  & per longitu­
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                  dinem
                    <emph type="italics"/>
                  DP
                    <emph.end type="italics"/>
                  exponatur ejuſdem
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                  velocitas ſub initio motus. </s>
                  <s>A
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                  puncto
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  ad lineam Horizonta­
                    <lb/>
                  lem
                    <emph type="italics"/>
                  DC
                    <emph.end type="italics"/>
                  demittatur perpendi­
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                  culum
                    <emph type="italics"/>
                  PC,
                    <emph.end type="italics"/>
                  & ſecetur
                    <emph type="italics"/>
                  DC
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                    <lb/>
                  ut ſit
                    <emph type="italics"/>
                  DA
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  ut reſiſtentia
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                  Medii, ex motu in altitudinem
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                  ſub initio orta, ad vim gravi­
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                  tatis; vel (quod perinde eſt) ut
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                  ſit rectangulum ſub
                    <emph type="italics"/>
                  DA
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  DP
                    <emph.end type="italics"/>
                    <lb/>
                  ad rectangulum ſub
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  CP
                    <emph.end type="italics"/>
                    <lb/>
                  ut reſiſtentia tota ſub initio mo­
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                  tus ad vim gravitatis. </s>
                  <s>Aſymptotis
                    <lb/>
                    <emph type="italics"/>
                  DC, CP,
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                  deſcribatur Hyperbo­
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                  la quævis
                    <emph type="italics"/>
                  GTBS
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                  ſecans perpen­
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                  dicula
                    <emph type="italics"/>
                  DG, AB
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  ; &
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                  compleatur parallelogrammum
                    <lb/>
                    <emph type="italics"/>
                  DGKC,
                    <emph.end type="italics"/>
                  cujus latus
                    <emph type="italics"/>
                  GK
                    <emph.end type="italics"/>
                  ſecet
                    <lb/>
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                    <emph.end type="italics"/>
                  Capiatur linea N in
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                  ratione ad
                    <emph type="italics"/>
                  QB
                    <emph.end type="italics"/>
                  qua
                    <emph type="italics"/>
                  DC
                    <emph.end type="italics"/>
                  ſit ad
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                    <emph type="italics"/>
                  CP
                    <emph.end type="italics"/>
                  ; & ad rectæ
                    <emph type="italics"/>
                  DC
                    <emph.end type="italics"/>
                  pun­
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                  ctum quodvis
                    <emph type="italics"/>
                  R
                    <emph.end type="italics"/>
                  erecto perpen­
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                  diculo
                    <emph type="italics"/>
                  RT,
                    <emph.end type="italics"/>
                  quod Hyperbolæ
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                  in
                    <emph type="italics"/>
                  T,
                    <emph.end type="italics"/>
                  & rectis
                    <emph type="italics"/>
                  EH, GK, DP
                    <emph.end type="italics"/>
                    <lb/>
                  in
                    <emph type="italics"/>
                  I, t
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  V
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                  occurrat; in eo cape
                    <emph type="italics"/>
                  Vr
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                  æqualem (
                    <emph type="italics"/>
                  tGT
                    <emph.end type="italics"/>
                  /N), vel quod per-</s>
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