Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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Medio reſiſtente aſcendendo poſſit amittere, ad tempus quo velo
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citatem eandem in ſpatio non reſiſtente aſcendendo poſſet amit
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tere, ut arcus
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At
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ad ejus tangentem
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Ap.
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DE MOTU
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CORPORUM</
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Corol.
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6. Hinc ex dato tempore datur ſpatium aſcenſu vel de
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ſcenſu deſcriptum. </
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velocitas maxima, per Corol. </
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>2, & 3, Theor. </
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>VI, Lib. </
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>11; indeque
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datur tempus quo corpus velocitatem illam in ſpatio non reſiſtente
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cadendo poſſet acquirere. </
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<
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>Et ſumendo Sectorem
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ADT
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vel
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ADt
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ad triangulum
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ADC
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in ratione temporis dati ad tempus modo
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inventum; dabitur tum velocitas
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AP
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vel
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Ap,
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tum area
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ABNK
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vel
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ABnk,
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quæ eſt ad ſectorem
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ADT
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vel
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ADt
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ut ſpatium quæ
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ſitum ad ſpatium quod tempore dato, cum velocitate illa maxima
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jam ante inventa, uniformiter deſcribi poteſt. </
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Corol.
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7. Et regrediendo, ex dato aſcenſus vel deſcenſus ſpatio
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ABnk
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vel
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ABNK,
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dabitur tempus
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ADt
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vel
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ADT.
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PROPOSITIO X. PROBLEMA III.
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Tendat uniformis vis gravitatis directe ad planum Horizontis,
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ſitque reſiſtentia ut Medii denſitas & quadratum velocitatis
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conjunctim: requiritur tum Medii denſitas in locis ſingulis,
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quæ faciat ut corpus in data quavis linea curva moveatur,
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tum corporis velocitas & Medii reſiſtentia in locis ſingulis.
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<
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PQ
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planum illud pla
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no Schematis perpendicu
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lare;
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PFHQ
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linea curva
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plano huic occurrens in
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punctis
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P
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&
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G, H, I, K
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loca quatuor corporis in hac
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curva ab
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F
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ad
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Q
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pergentis;
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&
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GB, HC, ID, KE
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or
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dinatæ quatuor parallelæ ab
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his punctis ad horizontem
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demiſſæ & lineæ horizontali
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PQ
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ad puncta
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B, C, D, E
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inſiſten
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tes; & ſint
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BC, CD, DE
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diſtantiæ Ordinatarum inter ſe æqua
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les. </
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<
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G
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&
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H
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ducantur rectæ
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GL, HN
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curvam tan
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gentes in
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G
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&
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H,
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& Ordinatis
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CH, DI
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ſurſum productis occur
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rentes in
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L
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&
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N,
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& compleatur parallelogrammum
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HCDM.
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