Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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Corol.
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4. Spatium vero a corpore deſcriptum differentia eſt duo
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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. </
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LIBER
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SECUNDUS.</
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PROPOSITIO IV. PROBLEMA II.
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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.
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<
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>Eloco quovis
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D
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egrediatur Pro
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jectile ſecundum lineam quam
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vis rectam
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DP,
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& per longitu
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dinem
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DP
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exponatur ejuſdem
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velocitas ſub initio motus. </
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puncto
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P
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ad lineam Horizonta
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lem
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DC
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demittatur perpendi
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culum
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PC,
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& ſecetur
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DC
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in
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A
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ut ſit
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DA
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ad
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AC
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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
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DA
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&
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DP
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ad rectangulum ſub
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AC
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&
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CP
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ut reſiſtentia tota ſub initio mo
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tus ad vim gravitatis. </
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DC, CP,
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deſcribatur Hyperbo
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la quævis
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GTBS
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ſecans perpen
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dicula
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DG, AB
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in
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G
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&
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B
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; &
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compleatur parallelogrammum
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DGKC,
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cujus latus
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GK
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ſecet
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AB
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in
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Capiatur linea N in
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ratione ad
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QB
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qua
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DC
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ſit ad
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CP
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; & ad rectæ
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DC
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pun
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ctum quodvis
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R
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erecto perpen
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diculo
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RT,
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quod Hyperbolæ
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in
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T,
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& rectis
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EH, GK, DP
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in
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I, t
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&
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V
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occurrat; in eo cape
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Vr
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æqualem (
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tGT
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/N), vel quod per-</
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