Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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Corol.
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2. Si corpus in ſuperficiem quamvis
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CD,
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ſecundum lineam
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rectam
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AD
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lege quavis ductam incidens, emergat ſecundum aliam
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quamvis rectam
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DK,
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& a puncto
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C
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duci in
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telligantur Lineæ curvæ
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<
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CP, CQ
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ipſis
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AD, DK
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ſemper perpendiculares:
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erunt incrementa linea
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rum
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PD, QD,
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<
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atq;
">atque</
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ad
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eo lineæ ipſæ
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PD, QD,
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incrementis iſtis genitæ,
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ut ſinus incidentiæ & e
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mergentiæ ad invicem:
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& contra. </
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LIBER
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PRIMUS.</
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PROPOSITIO XCVIII. PROBLEMA XLVIII.
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Iiſdem poſitis, & circa axem
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AB
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deſcripta ſuperficie quacunque
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attractiva
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CD,
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regulari vel irregulari, per quam corpora de
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loco dato
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A
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exeuntia tranſire debent: invenire ſuperficiem ſe
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cundam attractivam
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EF,
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quæ corpora illa ad locum datum
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B
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<
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convergere faciat.
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<
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>Juncta
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AB
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ſecet ſuperficiem primam in
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C
<
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& ſecundam in
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E,
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<
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puncto
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D
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utcunque aſſumpto. </
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<
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>Et poſito ſinu incidentiæ in ſuper
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ficiem primam ad ſinum emergentiæ ex eadem, & ſinu emergentiæ
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e ſuperficie ſecunda ad ſinum incidentiæ in eandem, ut quantitas
<
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aliqua data M ad aliam datam N; produc tum
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AB
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ad
<
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G
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ut ſit
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type
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BG
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type
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<
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ad
<
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type
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CE
<
emph.end
type
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ut M-N ad N, tum
<
emph
type
="
italics
"/>
AD
<
emph.end
type
="
italics
"/>
ad
<
emph
type
="
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H
<
emph.end
type
="
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ut ſit
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type
="
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AH
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type
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æqualis
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type
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AG,
<
emph.end
type
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tum
<
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etiam
<
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type
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DF
<
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ad
<
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type
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K
<
emph.end
type
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ut ſit
<
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type
="
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DK
<
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type
="
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ad
<
emph
type
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italics
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DH
<
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type
="
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ut N ad M. </
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<
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>Junge
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KB,
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&
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centro
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type
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D
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intervallo
<
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type
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DH
<
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type
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deſcribe circulum occurrentem
<
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type
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KB
<
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pro
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ductæ in
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type
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L,
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ipſique
<
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type
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DL
<
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type
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parallelam age
<
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type
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BF:
<
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type
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& punctum
<
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type
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F
<
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type
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tan
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get Lineam
<
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type
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EF,
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type
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quæ circa axem
<
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type
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AB
<
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revoluta deſcribet ſuperfi
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ciem quæſitam.
<
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<
expan
abbr
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q.
">que</
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>
E. F.
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<
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<
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>Nam concipe Lineas
<
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CP, CQ
<
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type
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ipſis
<
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type
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AD, DF
<
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type
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reſpective, & Li
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neas
<
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type
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ER, ES
<
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ipſis
<
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type
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FB, FD
<
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ubique perpendiculares eſſe, adeoque
<
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<
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QS
<
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ipſi
<
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CE
<
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ſemper æqualem; & erit (per Corol. </
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<
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>2. Prop. </
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>
<
s
>XCVII)
<
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<
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PD
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ad
<
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QD
<
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ut M ad N, adeoque ut
<
emph
type
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DL
<
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ad
<
emph
type
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italics
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DK
<
emph.end
type
="
italics
"/>
vel
<
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type
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italics
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FB
<
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ad
<
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type
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FK
<
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type
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; </
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</
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</
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</
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